Uniformly stratified flows approaching long and dynamically tall ridges develop two distinct flow components over disparate time scales. The fluid upstream and below a "blocking level" is stagnant in the limit of an infinite ridge and flows around the sides when the ridge extent is finite. The streamwise half-width of the obstacle at the blocking level arises as a natural inner length scale for the flow, while the excursion time over this half-width is an associated short time scale for the streamwise flow evolution. Over a longer time scale, low-level horizontal flow splitting leads to the establishment of an upstream layerwise potential flow beneath the blocking level. We demonstrate through numerical experiments that for sufficiently long ridges, crest control and streamwise asymmetry are seen on both the short and long time scales. On the short time scale, upstream blocking is established quickly and the flow is well described as a purely infinite-ridge overflow. Over the long time scale associated with flow splitting, low-level flow escapes around the sides, but the overflow continues to be hydraulically controlled and streamwise asymmetric in the neighborhood of the crest. We quantify this late-time overflow by estimating its volumetric transport and then briefly demonstrate how this approach can be extended to predict the overflow across nonuniform ridge shapes.

}, keywords = {blocking, downslope winds, fluid, Meteorology \& Atmospheric Sciences, model, mountain flows, Mountain meteorology, nonlinear dynamics, valley}, isbn = {0022-4928}, doi = {10.1175/jas-d-18-0145.1}, url = {We investigate the excitation and radiation of near-inertial internal gravity waves continuously excited by a latitudinally confined temporally fluctuating wind in a numerical model of a stratified ocean on a beta-plane at mid-latitude. The surface wind forcing contains both high- and low-frequency components which excite propagating waves and a baroclinically unstable zonal jet respectively. Wentzel-Kramers-Brillouin (WKB) ray theory implies that near-inertial waves propagate strictly towards the equator. We seek to refine this view here by (i) adding the non-traditional Coriolis force (accounting for the horizontal component of the Earth{\textquoteright}s rotation) into the equations of motion, in order to allow poleward sub-inertial propagation to occur, and (ii) relaxing the conceptual constraint of no zonal variability, to allow the zonal jet to undergo instability, to meander and to sustain an active field of mesoscale eddies, potentially impacting the excitation of near-inertial waves. The key results are that, while (i) permits weakly stratified waveguides with sub-inertial poleward wave propagation to develop in accord with theory, the sub-inertial energy flux observed is very small compared with the equatorward flux. Thus, in terms of energy radiated from the storm track, non-traditional effects are small for wind-driven near-inertial waves. The consequences of (ii) are much more pronounced. Refinement (ii) produces a radiating wave field that is bidirectional, i.e. with both poleward and equatorward components. We show that the presence of regions of significant background vorticity with horizontal scales significantly smaller than the width of the storm track provides the scale selection mechanism to excite waves with sufficiently super-inertial frequencies to propagate poleward distances of the order of 1000 km.

}, keywords = {approximation, deep-ocean, energy, geostrophic turbulence, instability, internal waves, mixed-layer, motions, nontraditional beta-plane, shelf, stratified flows, waves in rotating fluids}, isbn = {0022-1120}, doi = {10.1017/jfm.2017.698}, url = {We investigate the dynamic stability of stratified flow configurations characteristic of hydraulically controlled downslope flow over topography. Extraction of the correct {\textquoteright}base state{\textquoteright} for stability analysis from spatially and temporally evolving flows that exhibit instability is not easy since the observed flow in most cases has already been modified by nonlinear interactions between the instability modes and the mean flow. Analytical studies, however, can yield steady solutions under idealized conditions which can then be analysed for stability. Following the latter approach, we study flow profiles whose essential character is determined by recently obtained solutions of Winters \& Armi (J. Fluid Mech., vol. 753, 2014, pp. 80-103) for topographically controlled stratified flows. Their condition of optimal control necessitates a streamline bifurcation which then naturally produces a stagnant isolating layer overlying an accelerating stratified jet in the lee of the topography. We show that the inclusion of the isolating layer is an essential component of the stability analysis and further clarify the nature and mechanism of the instability in light of the wave-interaction theory. The spatial stability problem is also briefly examined in order to estimate the downstream location where finite-amplitude features might be manifested in streamwise slowly varying flows over topography.

}, keywords = {instability, mechanism, stratified flows, topographic effects, turbulence, waves, windstorm}, isbn = {0022-1120}, doi = {10.1017/jfm.2016.683}, url = {The effects of internal waves (IWs), externally forced by high-frequency wind, on energy pathways are studied in submesoscale-resolving numerical simulations of an idealized wind-driven channel flow. Two processes are examined: the direct extraction of mesoscale energy by externally forced IWs followed by an IW forward energy cascade to dissipation and stimulated imbalance, a mechanism through which externally forced IWs trigger a forward mesoscale to submesoscale energy cascade to dissipation. This study finds that the frequency and wavenumber spectral slopes are shallower in solutions with high-frequency forcing compared to solutions without and that the volume-averaged interior kinetic energy dissipation rate increases tenfold. The ratio between the enhanced dissipation rate and the added high-frequency wind work is 1.3, demonstrating the significance of the IW-mediated forward cascades. Temporal-scale analysis of energy exchanges among low-(mesoscale), intermediate-(submesoscale), and high-frequency (IW) bands shows a corresponding increase in kinetic energy E-k and available potential energy APE transfers from mesoscales to submesoscales (stimulated imbalance) and mesoscales to IWs (direct extraction). Two direct extraction routes are identified: a mesoscale to IW Ek transfer and a mesoscale to IW APE transfer followed by an IW APE to IW Ek conversion. Spatial-scale analysis of eddy-IW interaction in solutions with high-frequency forcing shows an equivalent increase in forward Ek and APE transfers inside both anticyclones and cyclones.

}, keywords = {antarctic circumpolar current, balance, energetics, generation, geostrophic flow, instability, mesoscale, model, ocean inertial motions, wind}, isbn = {0022-3670}, doi = {10.1175/jpo-d-16-0117.1}, url = {Blocked, continuously stratified, crest-controlled flows have hydraulically supercritical downslope flow in the lee of a ridge-like obstacle. The downslope flow separates from the obstacle and, depending on conditions further downstream, transitions to a subcritical state. A controlled, stratified overflow and its transition to a subcritical state are investigated here in a set of three-dimensional numerical experiments in which the height of a second, downstream ridge is varied. The downslope flow is associated with an isopycnal and streamline bifurcation, which acts to form a nearly uniform-density isolating layer and a sharp pycnocline that separates deeper blocked and stratified fluid between the ridges from the flow above. The height of the downstream obstacle is communicated upstream via gravity waves that propagate along the density interface and set the separation depth of the downslope flow. The penetration depth of the downslope flow, its susceptibility to shear instabilities, and the amount of energy dissipated in the turbulent outflow all increase as the height of a downstream ridge, which effectively sets the downstream boundary conditions, is reduced.

}, doi = {http://dx.doi.org/10.1017/jfm.2016.113}, author = {Winters, Kraig B.} } @article {36297, title = {Degeneration of internal Kelvin waves in a continuous two-layer stratification}, journal = {Journal of Fluid Mechanics}, volume = {777}, year = {2015}, note = {n/a}, month = {2015/08}, pages = {68-96}, abstract = {We explore the evolution of the gravest internal Kelvin wave in a two-layer rotating cylindrical basin, using direct numerical simulations (DNS) with a hyper-viscosity/diffusion approach to illustrate different dynamic and energetic regimes. The initial condition is derived from Csanady{\textquoteright}s (J. Geophys. Res., vol. 72, 1967, pp. 4151{\textendash}4162) conceptual model, which is adapted by allowing molecular diffusion to smooth the discontinuous idealized solution over a transition scale, δi, taken to be small compared to both layer thicknesses hl,l=1,2. The different regimes are obtained by varying the initial wave amplitude, η0, for the same stratification and rotation. Increasing η0 increases both the tendency for wave steepening and the shear in the vicinity of the density interface. We present results across several regimes: from the damped, linear{\textendash}laminar regime (DLR), for which η0\~{}δi and the Kelvin wave retains its linear character, to the nonlinear{\textendash}turbulent transition regime (TR), for which the amplitude η0 approaches the thickness of the (thinner) upper layer h1, and nonlinearity and dispersion become significant, leading to hydrodynamic instabilities at the interface. In the TR, localized turbulent patches are produced by Kelvin wave breaking, i.e. shear and convective instabilities that occur at the front and tail of energetic waves within an internal Rossby radius of deformation from the boundary. The mixing and dissipation associated with the patches are characterized in terms of dimensionless turbulence intensity parameters that quantify the locally elevated dissipation rates of kinetic energy and buoyancy variance.

}, keywords = {stratified flows,transition to turbulence,waves in rotating fluids}, isbn = {1469-7645}, doi = {10.1017/jfm.2015.311}, author = {Ulloa,Hugo N. and Winters, Kraig B. and de la Fuente, Alberto and Ni{\~n}o,Yarko} } @article {35689, title = {Energy cascades and loss of balance in a reentrant channel forced by wind stress and buoyancy fluxes}, journal = {Journal of Physical Oceanography}, volume = {45}, number = {1}, year = {2015}, note = {n/a}, month = {2015/01}, pages = {272-293}, type = {Article}, abstract = {A large fraction of the kinetic energy in the ocean is stored in the "quasigeostrophic" eddy field. This "balanced" eddy field is expected, according to geostrophic turbulence theory, to transfer energy to larger scales. In order for the general circulation to remain approximately steady, instability mechanisms leading to loss of balance (LOB) have been hypothesized to take place so that the eddy kinetic energy (EKE) may be transferred to small scales where it can be dissipated. This study examines the kinetic energy pathways in fully resolved direct numerical simulations of flow in a flat-bottomed reentrant channel, externally forced by surface buoyancy fluxes and wind stress in a configuration that resembles the Antarctic Circumpolar Current. The flow is allowed to reach a statistical steady state at which point it exhibits both a forward and an inverse energy cascade. Flow interactions with irregular bathymetry are excluded so that bottom drag is the sole mechanism available to dissipate the upscale EKE transfer. The authors show that EKE is dissipated preferentially at small scales near the surface via frontal instabilities associated with LOB and a forward energy cascade rather than by bottom drag after an inverse energy cascade. This is true both with and without forcing by the wind. These results suggest that LOB caused by frontal instabilities near the ocean surface could provide an efficient mechanism, independent of boundary effects, by which EKE is dissipated. Ageostrophic anticyclonic instability is the dominant frontal instability mechanism in these simulations. Symmetric instability is also important in a "deep convection" region, where it can be sustained by buoyancy loss.

}, keywords = {baroclinic, california current system, convection, instability, ocean fronts, overturning circulation, part i, southern-ocean, submesoscale transition, symmetric, vertical motion}, isbn = {0022-3670}, doi = {10.1175/jpo-d-14-0068.1}, url = {A tidally driven, stratified boundary layer over supercritical topography is simulated numerically. The near-boundary flow is characterized by quasiperiodic, bore-like motions and episodic expulsion events where fluid is ejected into the stratified interior. The character of the bores is compared to 14 the high-resolution ocean mooring data of van Haren (2006). The diffusivity of the flow near the boundary is estimated by means of a synthetic dye tracer experiment. The average dissipation rate within the dye cloud is computed and combined with the diffusivity estimate to yield an overall mixing efficiency of 0.15. Both the estimated diffusivity and dissipation rates are in reasonable agreement with the microstructure observations of Kunze et al. (2012) when scaled to the environmental conditions at the Monterey and Soquel Canyons and to the values estimated by van Haren and Gostiaux (2012) above the sloping bottom of 20 the Great Meteor Seamount in the Canary Basin.

}, doi = {doi:10.1002/2015GL064676}, author = {Winters, K. B.} } @article {35935, title = {Tidally-forced flow in a rotating, stratified, shoaling basin}, journal = {Ocean Modelling}, volume = {90}, year = {2015}, pages = {72{\textendash}81}, abstract = {Baroclinic flow of a rotating, stratified fluid in a parabolic basin is computed in response to barotropic tidal forcing using the nonlinear, non-hydrostatic, Boussinesq equations of motion. The tidal forcing is derived from an imposed, boundary-enhanced free-surface deflection that advances cyclonically around a central amphidrome. The tidal forcing perturbs a shallow pycnocline, sloshing it up and down over the shoaling bottom. Nonlinearities in the near-shore internal tide produce an azimuthally independent {\textquoteleft}set-up{\textquoteright} of the isopycnals that in turn drives an approximately geostrophically balanced, cyclonic, near-shore, sub-surface jet. The sub-surface cyclonic jet is an example of a slowly evolving, nearly balanced flow that is excited and maintained solely by forcing in the fast, super-inertial frequency band. Baroclinic instability of the nearly balanced jet and subsequent interactions between eddies produce a weak transfer of energy back into the inertia-gravity band as swirling motions with super-inertial vorticity stir the stratified fluid and spontaneously emit waves. The sub-surface cyclonic jet is similar in many ways to the poleward flows observed along eastern ocean boundaries, particularly the California Undercurrent. It is conjectured that such currents may be driven by the surface tide rather than by winds and/or along-shore pressure gradients.

}, doi = {10.1016/j.ocemod.2015.04.004}, url = {http://www.sciencedirect.com/science/article/pii/S146350031500058X}, author = {Winters, K. B.} } @article {35349, title = {Observations on the lateral structure of wind-driven flows in a stratified, semiarid bay of the Gulf of California}, journal = {Estuaries and Coasts}, volume = {37}, number = {6}, year = {2014}, note = {n/a}, month = {2014/11}, pages = {1319-1328}, type = {Article}, abstract = {Time series of current velocity profiles and thermistor chains were obtained throughout a cross-bay transect for similar to 90 days for the purpose of comparing observed wind-driven stratified flows to theory. This study concentrates on the synoptic scale wind and its influence on the bay{\textquoteright}s circulation. The maximum water column stratification was 3-4 A degrees C/m throughout the deployment and influenced wind-driven flows. Low-pass filtered flows showed more complicated structures than those expected from theory: a depth-dependent recirculating structure with the along-bay flow over one half of the transect moving in opposite direction to the other half. Analysis of complex empirical orthogonal functions indicated that the first six modes explained 80 \% of the flow variability. Therefore, there was no predominantly energetic mode of variability. All modes exhibited a rich spatial structure with vertical and lateral variations. For all modes there was vertically sheared bidirectional flow, as expected from theory, with the largest eigenvector (mode value) asymmetrically influenced by Earth{\textquoteright}s rotation and advection of momentum.

}, keywords = {circulation, concepcion bay, estuaries, semiarid, stratification, Wind-driven flow}, isbn = {1559-2723}, doi = {10.1007/s12237-013-9641-0}, url = {Optimal solutions to the nonlinear, hydrostatic, Boussinesq equations are developed for steady, density-stratified, topographically controlled flows characterized by blocking and upstream influence. These flows are jet-like upstream of an isolated obstacle and are contained within an asymmetric, thinning stream tube that is accelerated as it passes over the crest. A stagnant, nearly uniform-density isolating layer, surrounded by a bifurcated uppermost streamline, separates the accelerated flow from an uncoupled flow above. The flows are optimal in the sense that, for a given stratification, the solutions maximize the topographic rise above the blocking level required for hydraulic control while minimizing the total energy of the flow. Hydraulic control is defined mathematically by the asymmetry of the accelerated flow as it passes the crest. A subsequent analysis of the Taylor-Goldstein equation shows that these sheared, non-uniformly stratified flows are indeed subcritical upstream, critical at the crest, and supercritical downstream with respect to gravest-mode, long internal waves. The flows obtained are relevant to arrested wedge flows, selective withdrawal, stratified towing experiments, tidal flow over topography and atmospheric flows over mountains.

}, keywords = {fluid, hydraulic control, obstacle, stratified flows, topographic effects}, isbn = {0022-1120}, doi = {10.1017/jfm.2014.363}, url = {{\textquoteright}Horizontal convection{\textquoteright} (HC) is the generic name for the flow resulting from a buoyancy variation imposed along a horizontal boundary of a fluid. We study the effects of rotation on three-dimensional HC numerically in two stages: first, when baroclinic instability is suppressed and, second, when it ensues and baroclinic eddies are formed. We concentrate on changes to the thickness of the near-surface boundary layer, the stratification at depth, the overturning circulation and the flow energetics during each of these stages. Our results show that, for moderate flux Rayleigh numbers (O(10(11))), rapid rotation greatly alters the steady-state solution of HC. When the flow is constrained to be uniform in the transverse direction, rapidly rotating solutions do not support a boundary layer, exhibit weaker overturning circulation and greater stratification at all depths. In this case, diffusion is the dominant mechanism for lateral buoyancy flux and the consequent buildup of available potential energy leads to baroclinically unstable solutions. When these rapidly rotating flows are perturbed, baroclinic instability develops and baroclinic eddies dominate both the lateral and vertical buoyancy fluxes. The resulting statistically steady solution supports a boundary layer, larger values of deep stratification and multiple overturning cells compared with non-rotating HC. A transformed Eulerian-mean approach shows that the residual circulation is dominated by the quasi-geostrophic eddy streamfunction and that the eddy buoyancy flux has a non-negligible interior diabatic component. The kinetic and available potential energies are greater than in the non-rotating case and the mixing efficiency drops from similar to 0.7 to similar to 0.17. The eddies play an important role in the formation of the thermal boundary layer and, together with the negatively buoyant plume, help establish deep stratification. These baroclinically active solutions have characteristics of geostrophic turbulence.

}, keywords = {available potential-energy, circulation, convection, density, driven, eddies, fluid, generalized eliassen-palm, geostrophic turbulence, models, ocean processes, overturning, thermocline, turbulent}, isbn = {0022-1120}, doi = {10.1017/jfm.2013.136}, url = {An exact expression E-a for available potential energy density in Boussinesq fluid flows (Roullet \& Klein, J. Fluid Mech., vol. 624, 2009, pp. 45-55; Holliday \& McIntyre, J. Fluid Mech., vol. 107, 1981, pp. 221-225) is shown explicitly to integrate to the available potential energy E-a of Winters et al. (J. Fluid Mech., vol. 289, 1995, pp. 115-128). E-a is a positive definite function of position and time consisting of two terms. The first, which is simply the indefinitely signed integrand in the Winters et al. definition of E-a, quantifies the expenditure or release of potential energy in the relocation of individual fluid parcels to their equilibrium height. When integrated over all parcels, this term yields the total available potential energy E-a. The second term describes the energetic consequences of the compensatory displacements necessary under the Boussinesq approximation to conserve vertical volume flux with each parcel relocation. On a pointwise basis, this term adds to the first in such a way that a positive definite contribution to E-a is guaranteed. Globally, however, the second term vanishes when integrated over all fluid parcels and therefore contributes nothing to E-a. In effect, it filters the components of the first term that cancel upon integration, isolating the positive definite residuals. E-a can be used to construct spatial maps of local contributions to E-a for direct numerical simulations of density stratified flows. Because E-a integrates to E-a, these maps are explicitly connected to known, exact, temporal evolution equations for kinetic, available and background potential energies.

}, keywords = {baroclinic flows, circulation, computational methods, HORIZONTAL CONVECTION, stratified flows}, isbn = {0022-1120}, doi = {10.1017/jfm.2012.493}, author = {Winters, K. B. and Barkan, R.} } @article {32817, title = {The response of a continuously stratified fluid to an oscillating flow past an obstacle}, journal = {Journal of Fluid Mechanics}, volume = {727}, year = {2013}, note = {n/a}, month = {7/2013}, pages = {83-118}, type = {Article}, abstract = {An oscillating continuously stratified flow past an isolated obstacle is investigated using scaling arguments and two-dimensional non-hydrostatic numerical experiments. A new dynamic scaling is introduced that incorporates the blocking of fluid with insufficient energy to overcome the background stratification and crest the obstacle. This clarifies the distinction between linear and nonlinear flow regimes near the crest of the obstacle. The flow is decomposed into propagating and non-propagating components. In the linear limit, the non-propagating component is related to the unstratified potential flow past the obstacle and the radiating component exhibits narrow wave beams that are tangent to the obstacle at critical points. When the flow is nonlinear, the near crest flow oscillates between states that include asymmetric, crest-controlled flows. Thin, fast, supercritical layers plunge in the lee, separate from the obstacle and undergo shear instability in the fluid interior. These flow features are localized to the neighbourhood of the crest where the flow transitions from subcriticality to supercriticality and are non-propagating. The nonlinear excitation of energetic non-propagating components reduces the efficiency of topographic radiation in comparison with linear dynamics.

}, keywords = {conversion, diffusion, hydraulic control, internal waves, internal-tide generation, model, ocean, ridge, supercritical topography, topographic effects, waves}, isbn = {0022-1120}, doi = {10.1017/jfm.2013.247}, url = {Dynamical processes leading to deep-cycle turbulence in the Equatorial Undercurrent (EUC) are investigated using a high-resolution large-eddy simulation (LES) model. Components of the model include a background flow similar to the observed EUC, a steady westward wind stress, and a diurnal surface buoyancy flux. An LES of a 3-night period shows the presence of narrowband isopycnal oscillations near the local buoyancy frequency N as well as nightly bursts of deep-cycle turbulence at depths well below the surface mixed layer, the two phenomena that have been widely noted in observations. The deep cycle of turbulence is initiated when the surface heating in the evening relaxes, allowing a region with enhanced shear and a gradient Richardson number Ri(g) less than 0.2 to form below the surface mixed layer. The region with enhanced shear moves downward into the EUC and is accompanied by shear instabilities and bursts of turbulence. The dissipation rate during the turbulence bursts is elevated by up to three orders of magnitude. Each burst is preceded by westward-propagating oscillations having a frequency of 0.004-0.005 Hz and a wavelength of 314-960 m. The Ri(g) that was marginally stable in this region decreases to less than 0.2 prior to the bursts. A downward turbulent flux of momentum increases the shear at depth and reduces Ri(g). Evolution of the deep-cycle turbulence includes Kelvin-Helmholtz-like billows as well as vortices that penetrate downward and are stretched by the EUC shear.

}, keywords = {and modeling, circulation, currents, diurnal cycle, dynamics, evolution, internal waves, Kelvin-Helmholtz instabilities, Large eddy simulations, models, pacific-ocean, shear}, isbn = {0022-3670}, doi = {10.1175/jpo-d-13-016.1}, url = {Motivated by the laboratory experiments of Browand \& Winant (Geophys. Fluid Dyn., vol. 4, 1972, pp. 29-53), a series of two-dimensional numerical simulations of flow past a cylinder of diameter d are run for different values of the approach Froude number Fr-0 = U/Nd between 0.02 and 0.2 at Re = O(100). The observed flow is characterized by blocking and upstream influence in front of the cylinder and by relatively thin, fast jets over the top and bottom of the cylinder. This continuously stratified flow can be understood in terms of an inviscid non-diffusive integral inertia-buoyancy balance reminiscent of reduced-gravity single-layer hydraulics, but one where the reduced gravity is coupled to the thickness of the jets. The proposed theoretical framework describes the flow upstream of the obstacle and at its crest. The most important elements of the theory are the inclusion of upstream influence in the form of blocked flow within an energetically constrained depth range and the recognition that the flow well above and well below the active, accelerated layers is dynamically uncoupled. These constraints determine, through continuity, the transport in the accelerated layers. Combining these results with the observation that the flow is asymmetric around the cylinder, i.e. hydraulically controlled, allows us to determine the active layer thicknesses, the effective reduced gravity and thus all of the integral flow properties of the fast layers in good agreement with the numerically computed flows.

}, keywords = {downslope winds, fluids, hydraulic control, stratified flows, topographic effects}, isbn = {0022-1120}, doi = {10.1017/jfm.2012.157}, url = {We describe the use of spectrally-based numerical methods in process studies of rotating stratified fluid dynamics relevant to oceans, lakes and the atmosphere. The objective is to take advantage of the well-known numerical properties of methods based on expansions in terms of trigonometric functions in applications for which inhomogeneous boundary conditions and/or irregular domains are desired. The underlying mathematical idea is the exchange of inhomogeneity from boundary conditions to forcing terms. The fundamental techniques for handling inhomogeneity in boundary conditions, symmetry mismatches between body forces and dependent variables at boundaries and the imposition of boundary conditions on internal or immersed boundaries are described and illustrated using simple idealized examples. These techniques are then combined to illustrate how these methods can be applied to several examples of flows from laboratory experiments. (C) 2012 Elsevier Ltd. All rights reserved.

}, keywords = {beta-plane, dynamics, evolution, fluid, gravity-waves, internal waves, lakes, Parallel algorithm, Reservoirs, Rotating stratified flow, Spectral methods, surface shear-stress, turbulence}, isbn = {1463-5003}, doi = {10.1016/j.ocemod.2012.04.001}, url = {Moored current and pressure observations were obtained at Bahia Concepcion, a semienclosed bay located on the eastern side of the Baja California peninsula in Mexico, to describe the wind-driven subinertial circulation. In winter and early spring, the bay is well mixed and forced by persistent winds toward the southeast, aligned with the central axis. The authors{\textquoteright} observations show that the sea surface rises downwind in response to wind stress and that there exists a crosswind drift at the surface that is consistent with Ekman dynamics. This feature is typical of a bay that is deeper than one Ekman depth and hence affected by the rotation of the earth. There is a persistent along-bay circulation toward the end of the bay along its western side with return flow on the opposite side. Drifters released near the surface across a transect move westward and downwind toward the closed end, where they recirculate cyclonically. Wind-driven linear theoretical models successfully predict the observed cross-bay circulation but fail to predict the along-bay flow pattern. The role of spatial inhomogeneities of wind stress (suggested by synoptic observations of the wind) and nonlinearities related to advection of momentum is investigated with theoretical and numerical modeling. Both mechanisms can contribute to the observed pattern of along-bay circulation. Even though the observations discussed were taken during the relatively well-mixed season, density fluctuations are shown to play, at times, an active role dynamically.

}, keywords = {cyclonic circulation, Estuarine, inner, lakes, mean circulation, momentum flux, oregon continental-shelf, shelf, tidal exchange, topographic wave, upwelling circulation}, isbn = {0022-3670}, doi = {10.1175/jpo-d-11-0103.1}, url = {Direct numerical simulation (DNS) is used to investigate the role of shear instabilities in turbulent mixing in a model of the upper Equatorial Undercurrent (EUC). The background flow consists of a westward-moving surface mixed layer above a stably stratified EUC flowing to the east. An important characteristic of the eastward current is that the gradient Richardson number Ri(g) is larger than 1/4. Nevertheless, the overall flow is unstable and DNS is used to investigate the generation of intermittent bursts of turbulent motions within the EUC region where Ri(g) \> 1/4. In this model, an asymmetric Holmboe instability emerges at the base of the mixed layer, moves at the speed of the local velocity, and ejects wisps of fluid from the EUC upward. At the crests of the Holmboe waves, secondary Kelvin-Helmholtz instabilities develop, leading to three-dimensional turbulent motions. Vortices formed by the Kelvin-Helmholtz instability are occasionally ejected downward and stretched by the EUC into a horseshoe configuration creating intermittent bursts of turbulence at depth. Vertically coherent oscillations, with wavelength and frequency matching those of the Holmboe waves, propagate horizontally in the EUC where the turbulent mixing by the horseshoe vortices occurs. The oscillations are able to transport momentum and energy from the mixed layer downward into the EUC. They do not overturn the isopycnals, however, and, though correlated in space and time with the turbulent bursts, are not directly responsible for their generation. These wavelike features and intermittent turbulent bursts are qualitatively similar to the near-N oscillations and the deep-cycle turbulence observed at the upper flank of the Pacific Equatorial Undercurrent.

}, keywords = {dynamics, holmboe, instability, internal gravity-waves, jet, pacific-ocean, simulation, stratified shear-layer, waves}, isbn = {0022-3670}, doi = {10.1175/jpo-d-11-0233.1}, url = {Direct numerical simulation (DNS) is used to investigate the evolution of intermittent patches of turbulence in a background flow with the gradient Richardson number, Ri(g), larger than the critical value of 0.25. The base flow consists of an unstable stratified shear layer (Ri(g) \< 0.25) located on top of a stable shear layer (Ri(g) \> 0.25), whose shear and stratification are varied. The unstable shear layer undergoes a Kelvin-Helmholtz shear instability that develops into billows. Vortices associated with the billows are pulled into the bottom shear layer and stretched by the local shear into a horseshoe configuration. The breakdown of the horseshoe vortices generates localized patches of turbulence. Three cases with different levels of shear and stratification, but with the same Ri(g), in the bottom shear layer are simulated to examine the popular hypothesis that mixing is determined by local Ri(g). In the case with largest shear and stratification, the vortices are less likely to penetrate the bottom layer and are quickly dissipated due to the strong stratification. In the case with moderate shear and stratification, vortices penetrate across the bottom layer and generate turbulence patches with intense dissipation rate. The case with the mildest level of shear and stratification shows the largest net turbulent mixing integrated over the bottom layer. Analysis of the turbulent kinetic energy budget indicates that the mean kinetic energy in the bottom layer contributes a large amount of energy to the turbulent mixing. In all cases, the mixing efficiency is elevated during the penetration of the vortices and has a value of approximately 0.35 when the turbulence in the patches decays.

}, keywords = {dynamics, flows, instability, internal waves, mixing layers, stratified shear layer, turbulence, vortices}, isbn = {1468-5248}, doi = {10.1080/14685248.2012.686666}, url = {The dynamics of a forced, low-mode oceanic internal tide propagating poleward on a beta plane are investigated numerically. The focus is on the transfer of energy from the tide to near-inertial oscillations (NIOs) initiated by a weakly nonlinear interaction known as parametric subharmonic instability (PSI). It is shown that PSI is a mechanism for generating NIOs in the upper ocean, which subsequently radiate to depth. The exponentially growing NIOs eventually reach finite amplitude, and further interaction with the tide leads to a quasi-steady state in which dissipation is balanced by a reduction in the poleward tidal flux. The results are sensitive to the prescribed value of the vertical eddy viscosity v(e) that serves to parameterize the background turbulence. This sensitivity suggests that independent processes leading to turbulence in the upper ocean are able to control the rate of energy transfer from the tide to NIOs. For v(e) = O(10(-5) m(2) s(-1)), the poleward tidal flux decreases approximately 15\%. This value is much smaller than was found in previous numerical studies, but it is in reasonable agreement with recent estimates from observations taken near the M(2)/2 inertial latitude in the Pacific.

}, keywords = {energy, instability}, isbn = {0022-3670}, doi = {10.1175/2011jpo4605.1}, url = {We consider near-inertial waves continuously excited by a localized source and their subsequent radiation and evolution on a two-dimensional beta-plane. Numerical simulations are used to quantify the wave propagation and the energy flux in a realistically stratified ocean basin. We focus on the dynamics near and poleward of the inertial latitude where the local value of the Coriolis parameter f matches the forcing frequency sigma, contrasting the behaviour of waves under the traditional approximation (TA), where only the component of the Earth{\textquoteright}s rotation aligned with gravity is retained in the dynamics, with that obtained under the non-traditional approach (non-TA) in which the horizontal component of rotation is retained. Under the TA, assuming inviscid linear wave propagation in the WKB limit, all energy radiated from the source eventually propagates toward the equator, with the initially poleward propagation being internally reflected at the inertial latitude. Under the non-TA however, these waves propagate sub-inertially beyond their inertial latitude, exhibiting multiple reflections between internal turning points that lie poleward of the inertial latitude and the bottom. The numerical experiments complement and extend existing theory by relaxing the linearity and WKB approximations, and by illustrating the time development of the steadily forced flow and the spatial patterns of energy flux and flux divergence. The flux divergence of the flow at both the forcing frequency and its first harmonic reveal the spatial patterns of nonlinear energy transfer and highlight the importance of nonlinearity in the vicinity of near-critical bottom reflection at the inertial latitude of the forced waves.

}, keywords = {approximation, breaking, density, earths angular velocity, horizontal component, internal waves, nonhydrostatic linear-models, ocean, ocean processes, roles, stratified flows, stratified fluid, waves in rotating fluids}, isbn = {0022-1120}, doi = {10.1017/jfm.2011.280}, url = {The role of wind-driven upwelling in stratifying a semiarid bay in the Gulf of California is demonstrated with observations in Bahia Concepcion, Baja California Sur, Mexico. The stratification in Bahia Concepcion is related to the seasonal heat transfer from the atmosphere as well as to cold water intrusions forced by wind-driven upwelling. During winter, the water column is relatively well-mixed by atmospheric cooling and by northwesterly, downwelling-favorable, winds that typically exceed 10 m/s. During summer, the water column is gradually heated and becomes stratified because of the heat flux from the atmosphere. The wind field shifts from downwelling-favorable to upwelling-favorable at the beginning of summer, i.e., the winds become predominantly southeasterly. The reversal of wind direction triggers a major cold water intrusion at the beginning of the summer season that drops the temperature of the entire water column by 3-5 degrees C. The persistent upwelling-favorable winds during the summer provide a continuous cold water supply that helps maintain the stratification of the bay. Published by Elsevier Ltd.

}, keywords = {california, chesapeake-bay, circulation, Concepcion, currents, dynamics, estuarine stratification, microzooplankton, remote, stratification, wind, Wind straining, Wind-driven upwelling}, isbn = {0278-4343}, doi = {10.1016/j.csr.2010.03.015}, url = {We analyse the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two-dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to supercritical topography. For small tidal excursions, of the order of 1 \% of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15 \% of the topographic width, we find that the scaled mode I conversion rate decreases by less than 15 \%, in spite of nonlinear phenomena that break down the familiar wave-beam structure and generate harmonics and inter-harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration, most of the linear baroclinic energy flux is associated with the mode I tide, so our experiments reveal that nonlinear behaviour does not significantly affect the barotropic to baroclinic energy conversion in this regime, which is relevant to large-scale ocean ridges. This may not be the case, however, for smaller scale ridges that generate a response dominated by higher modes.

}, keywords = {conversion, deep-ocean, energy, ridge, waves}, isbn = {0022-1120}, doi = {10.1017/s0022112009007654}, url = {We consider the mechanical energy budget for horizontal Boussinesq convection and show that there are two distinct energy pathways connecting the mechanical energy (i.e. kinetic, available potential and background potential energies) to the internal energy reservoir and the external energy source. To obtain bounds on the magnitudes of the energy transfer rates around each cycle, we first show that the volume-averaged dissipation rate of buoyancy variance chi equivalent to kappa , where b is the buoyancy, is bounded from above by 4.57h(-1) kappa(2/3) nu(-1/3) b(max)(7/3). Here h is the depth of the container, kappa the molecular diffusion, nu the kinematic viscosity and b(max) the maximum buoyancy difference that exists on the surface. The bound on chi is used to estimate the generation rate of available potential energy E-a and the rate at which E-a is irreversibly converted to background potential energy via diapycnal fluxes, both of which are shown to vanish at least as fast as kappa(1/3) in the limit kappa -\> 0 at fixed Prandtl number Pr = nu/kappa As a thought experiment, consider a hypothetical ocean insulated at all boundaries except at the upper surface, where the buoyancy is prescribed. The bounds on the energy transfer rates in the mechanical energy budget imply that buoyancy forcing alone is insufficient by at least three orders of magnitude to maintain observed oceanic dissipation rates and that additional energy sources such as winds, tides and perhaps bioturbation are necessary to sustain observed levels of turbulent dissipation in the world{\textquoteright}s oceans.

}, keywords = {ocean}, isbn = {0022-1120}, doi = {10.1017/s0022112009006685}, url = {Many nearshore fish and invertebrate populations are overexploited even when apparently coherent management structures are in place. One potential cause of mismanagement may be a poor understanding and accounting of stochasticity, particularly for stock recruitment. Many of the fishes and invertebrates that comprise nearshore fisheries are relatively sedentary as adults but have an obligate larval pelagic stage that is dispersed by ocean currents. Here, we demonstrate that larval connectivity is inherently an intermittent and heterogeneous process on annual time scales. This stochasticity arises from the advection of pelagic larvae by chaotic coastal circulations. This result departs from typical assumptions where larvae simply diffuse from one site to another or where complex connectivity patterns are created by transport within spatially complicated environments. We derive a statistical model for the expected variability in larval settlement patterns and demonstrate how larval connectivity varies as a function of different biological and physical processes. The stochastic nature of larval connectivity creates an unavoidable uncertainty in the assessment of fish recruitment and the resulting forecasts of sustainable yields.

}, keywords = {california current system, Coastal oceanography, dispersal, fisheries, invertebrates, life-history, marine ecology, recruitment, statistical-analysis, surface circulation, sustainability, transport}, isbn = {0027-8424}, doi = {10.1073/pnas.0802544105}, url = {Key to the predictive understanding of many nearshore marine ecosystems is the transport of larvae by ocean circulation processes. Many species release thousands to billions of larvae to develop in pelagic waters, but only a few lucky ones successfully settle to suitable habitat and recruit to adult life stages. Methodologies for predicting the larval dispersal are still primitive, and simple diffusive analyses are still used for many important applications. hi this study, we investigate mechanisms of larval dispersal using idealized simulations of time-evolving coastal circulations in the California Current system with Lagrangian particles as models for planktonic larvae. Connectivity matrices, which describe the source-to-destination relationships for larval dispersal for a given larval development time course, are used to diagnose the time-space dynamics of larval settlement. The resulting connectivity matrices are shown to be a function of several important time scales, such as the planktonic larval duration, the frequency and duration of larval release events and inherent time scales for the coastal circulations. Many important fishery management applications require knowledge of fish stocks on a year-to-year or generation-to-generation basis. For these short time scales (typically less than I year), larval dispersal is generally far from a simple diffusive process and the consideration of the stochastic and episodic nature of larval dispersal is required. This work. provides new insights into the spatial-temporal dynamics of nearshore fish stocks. (c) 2007 Elsevier B.V. All rights reserved.

}, keywords = {california, Coastal oceanography, current, dispersal, dispersal kernel, fish, larval dispersal, marine, marine resource management, model, populations, recruitment, reef, retention, seasonal variability, statistical-analysis, surface circulation}, isbn = {0924-7963}, doi = {10.1016/j.jmarsys.2006.02.017}, url = {The dispersion of fluid particles in statistically stationary stably stratified turbulence is studied by means of direct numerical simulations. Due to anisotropy of the flow, horizontal and vertical dispersion show different behavior. Single-particle dispersion in horizorital direction is similar to that in isotropic turbulence for short times, but shows a long-time growth rate proportional to t(2.1 +/- 0.1) , larger than the classical linear diffusion limit. In vertical direction, three successive regimes can be identified: a classical t(2)-regime, a plateau that scales as N(-2) , and a diffusion limit where dispersion is proportional to t. By forcing the flow and performing long-time simulations, we are able to observe this last regime, which was predicted but not observed before in stratified turbulence. This diffusive regime is caused by molecular diffusion of the active scalar (density). The mean squared separation of particle pairs (relative dispersion) in vertical direction shows two plateaus that are not present in isotropic turbulence. They can be associated with the characteristic layered structure of the flow. In the long-time limit again a linear regime is found as for single-particle dispersion. Pair dispersion in horizontal direction behaves similar to that in isotropic turbulence except for long times. Finally, the study of multiparticle statistics in stably stratified turbulent flows is reported. The evolution of tetrads gives an impression of the shape of particle clouds. It is found that with increasing stratification, the volume of the tetrads decreases, and they become flatter and more elongated. (c) 2008 American Institute of Physics.

}, keywords = {direct numerical simulations, dynamics, flows, isotropic, lagrangian statistics, model, motions, relative dispersion, turbulence, vertical diffusion}, isbn = {1070-6631}, doi = {10.1063/1.2838593}, url = {The linear stability of inviscid non-diffusive density-stratified shear flow in a rotating frame is considered. A temporally periodic base flow, characterized by vertical shear S, buoyancy frequency N and rotation frequency f, is perturbed by infinitesimal inertia-gravity waves. The temporal evolution and stability characteristics of the disturbances are analysed using Floquet theory and the growth rates of unstable solutions are computed numerically. The global structure of solutions is addressed in the dimensionless parameter space (N/f, S/f, phi) where phi is the wavenumber inclination angle from the horizontal for the wave-like perturbations. Both weakly stratified rapidly rotating flows (N \< f) and strongly stratified slowly rotating flows (N \> f) are examined. Distinct families of unstable modes are found, each of which can be associated with nearby stable solutions of periodicity T or 2T where T is the inertial frequency 2 pi/f. Rotation is found to be a destabilizing factor in the sense that stable non-rotating shear flows with N N(1)/S(2) \> 1/4 can be unstable in a rotating frame. Morever, instabilities by parametric resonance are found associated with free oscillations at half and integer multiples of the inertial frequency.

}, keywords = {breaking, instability, stability, stratified flows}, isbn = {0022-1120}, doi = {10.1017/s0022112008000621}, url = {We examine observations of turbulence in the geophysical environment, primarily from oceans but also from lakes, in light of theory and experimental studies undertaken in the laboratory and with numerical simulation. Our focus is on turbulence in density-stratified environments and on the irreversible fluxes of tracers that actively contribute to the density field. Our understanding to date has come from focusing on physical problems characterized by high Reynolds number flows with no spatial or temporal variability, and we examine the applicability of these results to the natural or geophysical-scale problems. We conclude that our sampling and interpretation of the results remain a first-order issue, and despite decades of ship-based observations we do not begin to approach a reliable sampling of the overall turbulent structure of the ocean interior.

}, keywords = {dissipation, efficiency, energetics, energy, estuaries, fluid, internal waves, lakes, microstructure, ocean, ocean dynamics, simulations, temperature}, isbn = {0066-4189978-0-8243-0740-0}, doi = {10.1146/annurev.fluid.39.050905.110314}, url = {An idealized numerical study of a northward propagating internal tide reveals a dramatic loss of energy to small-scale subharmonic instabilities near 28.9 degrees N. Inspired by observations of the internal tide radiating northward from the Hawaiian Ridge, a three-dimensional numerical model is initialized with a northward baroclinic tidal flux of approximately 1.7 kW/m. After an initial spinup period, energy is quickly transferred from the baroclinic tide to subharmonic motions, with half the horizontal tidal wavenumber and small vertical scales, through nonlinear advection of horizontal tidal velocity gradients. Potential oceanic implications are twofold. First, once a steady-state has been reached, the instability acts as a partial filter of northward tidal flux between 27.5 and 29.5 degrees N, in rough agreement with some altimetric tidal observations. Second, elevated shear of the subharmonic motions suggests the potential for elevated near-surface dissipation rates near the critical latitude that may be important for upper ocean mixing.

}, keywords = {baroclinic tides, central north pacific, diffusivity, energetics, hawaiian ridge, internal wave spectrum, ocean circulation}, isbn = {0094-8276}, doi = {10.1029/2005gl023376}, url = {[ 1] Turbulent oscillatory flow over sand ripples is examined using three-dimensional numerical simulations. The model solves the time-dependent Navier-Stokes equations on a curvilinear grid in a horizontally periodic domain. The flow transitions to turbulence and the presence of sand ripples increases the rate of dissipation of shoaling wave energy compared to flow over a smooth boundary. The influence of the ripple shape is shown to alter the mean flow field and affect the induced drag and dissipation rates. Shear instabilities near the boundary during phases of flow reversal resulting in vortex shedding from the ripple crest produce a continuously turbulent boundary layer, differing from results obtained in simulations over smooth boundaries.

}, keywords = {apparent roughness, bed, bottom, channels, currents, dissipation rate, drag coefficient, dynamics, turbulent boundary layer, wave}, isbn = {0148-0227}, doi = {10.1029/2002jc001709}, url = {The Lagrangian properties of a high-resolution, three-dimensional, direct numerical simulation of Kelvin-Helmholtz (K-H) instability are examined with the goal of assessing the ability of Lagrangian measurements to determine rates and properties of ocean mixing events. The size and rotation rates of the two-dimensional K-H vortices are easily determined even by individual trajectories. Changes in density along individual trajectories unambiguously show diapycnal mixing. These changes are highly structured during the early phases of the instability but become more random once the flow becomes turbulent. Only 36 particles were tracked, which is not enough to usefully estimate volume-averaged fluxes from the average rates of temperature change. Similarly, time- and volume-averaged vertical advective flux can be estimated to only 20\% accuracy. Despite the relatively low Reynolds number of the flow, R-lambda approximate to 100, the dissipation rates of energy epsilon and density variance chi are correlated with the spectral levels of transverse velocity and density in an inertial subrange, as expected for high-Reynolds-number turbulence. The Kolmogorov constants are consistent with previous studies. This suggests that these inertial dissipation methods are the most promising techniques for making useful measurements of diapycnal mixing rates from practical Lagrangian floats because they converge rapidly and have a clear theoretical basis.

}, keywords = {deep convection, energy, floats, labrador sea, layers, scales, spectra, turbulence, velocity, waves}, isbn = {0739-0572}, doi = {10.1175/1520-0426(2004)021<0799:leodmi>2.0.co;2}, url = {A numerical model designed for three-dimensional process studies of rotating, stratified flows is described. The model is freely available, parallel, and portable across a range of computer architectures. The underlying numerics are high quality, based on spectral expansions, and third-order time stepping. Optional submodels include accurate calculation of Lagrangian trajectories. Special consideration has been taken to ensure ease of use by geophysical, as distinguished from computational, scientists. The mathematical and computational methods underlying the model are presented here as are several illustrative applications highlighting the model capabilities and the types of flows amenable to simulation using the model. Sample applications include forced inertial gravity waves, parametric subharmonic instability, shear-driven mixing layers, instability of a low Froude number vortex street, and geostrophic adjustment of intermittent, isolated mixing patches.

}, isbn = {0739-0572}, doi = {10.1175/1520-0426(2004)021<0069:asmfps>2.0.co;2}, url = {Motivated by the tendency of high-Prandtl-number fluids to form sharp density interfaces, the authors investigate the evolution of Holmboe waves in a stratified shear flow through direct numerical simulation. Like their better-known cousins, Kelvin-Helmholtz waves, Holmboe waves lead the flow to a turbulent state in which rapid irreversible mixing takes place. In both cases, significant mixing also takes place prior to the transition to turbulence. Although Holmboe waves grow more slowly than Kelvin-Helmholtz waves, the net amount of mixing is comparable. It is concluded that Holmboe instability represents a potentially important mechanism for mixing in the ocean.

}, keywords = {entrainment, finite-amplitude, flow, free shear layers, instability, kelvin-helmholtz billows, numerical-simulation, stability, stratified fluids, transition}, isbn = {0022-3670}, doi = {10.1175/1520-0485(2003)33<694:tamihw>2.0.co;2}, url = {[1] We characterize and quantify the transport of heat (Boussinesq density) in a highly idealized entraining convective mixed layer based on simulations of Lagrangian measurements in a two-dimensional model. The primary objectives are to assess and explore the merits and difficulties in estimating the heat budget from perfect and imperfect Lagrangian floats. A significant advantage of Lagrangian measurements is that the time derivative of temperature along these trajectories gives a direct measure of the diffusive heat flux. Using simulated perfect Lagrangian floats, estimates of the surface buoyancy flux, the depth of the mixed layer, vertical profiles of advective and diffusive heat flux, and the overall rate of cooling are shown to agree accurately with the known results extracted from the Eulerian simulations. The Lagrangian nature of the data is exploited to reveal the structure of the flow within the convective layer and to quantify the heat fluxes associated with the different types of eddies. Phase plots of Lagrangian trajectories in density-depth space reveal three distinct classes of motions: (1) plumes, which develop in the cold, heavy near-surface thermal boundary layer and plunge into the mixed layer interior carrying heavy water downward; (2) interior turbulence, comprising random motions between the base of the thermal boundary layer and the base of the surface mixed layer; and (3) entrainment of interior water into plumes below the thermal boundary layer, i.e., a transition from class 2 to class 1. Plumes dominate the heat transport. Simulations were also made using slightly buoyant floats; these are not perfectly Lagrangian. Buoyancy concentrates the floats near the surface resulting in an oversampling of the stronger plumes. Making the same heat budget calculations as with the perfect floats results in a nonzero estimated Lagrangian heating rate in the interior and a curved profile of vertical heat flux that is up to 3 times too large. The local time rate change of density is not significantly affected. A correction of the heat transport for oversampling of the plumes removes most of the error. This technique allows the correct heat budget to be measured for this flow using weakly buoyant floats.

}, keywords = {flux, ocean, turbulence}, isbn = {0148-0227}, doi = {10.1029/2000jc000247}, url = {Linearly stratified salt solutions of different Prandtl number were subjected to turbulent stirring by a horizontally oscillating vertical grid in a closed laboratory system. The experimental set-up allowed the independent direct measurement of a root mean square turbulent lengthscale L-t, turbulent diffusivity for mass K-rho, rate of dissipation of turbulent kinetic energy epsilon, buoyancy frequency N and viscosity nu, as time and volume averaged quantities. The behaviour of both L-t and K-rho, was characterized over a wide range of the turbulence intensity measure, epsilon/nuN(2), and two regimes were identified. In the more energetic of these regimes (Regime E, where 300 \< epsilon /vN(2) \< 10(5)) was found to be a function of nu, kappa and N, whilst K-rho was a function of v, kappa and (epsilon/nuN(2))(1/3). From these expressions for L-t and K-rho a scaling relation for the root mean square turbulent velocity scale U-t was derived, and this relationship showed good agreement with direct measurements from other data sets. In the weaker turbulence regime (Regime W, where 10 \< epsilon/nuN(2) \< 300) K-rho was a function of nu, kappa and epsilon/nuN(2). For 10 \< epsilon/nuN(2) \< 1000, our directly measured diffusivities, K-rho are approximately a factor of 2 different to the diffusivity predicted by the model of Osborn (1980). For epsilon/nuN(2) \> 1000, our measured diffusivities diverge from the model prediction. For example, at epsilon/nuN(2) there is at least an order of magnitude difference between the measured and predicted diffusivities.

}, keywords = {abyssal ocean, decay, dissipation, energetics, fluxes, gradient, internal waves, layers, microstructure, turbulence}, isbn = {0022-1120}, doi = {10.1017/S0022112001005080}, url = {The authors consider the flow in a semienclosed sea, or basin, subjected to a destabilizing surface buoyancy flux and separated from a large adjoining reservoir by a sill. A series of numerical experiments were conducted to quantify the energetics of the flow within the basin, that is, the amount of kinetic and potential energy stored within the basin and the rate at which these quantities are transported to and from the reservoir via the exchange flow over the sill. The numerical experiments were formulated at laboratory scales and conducted using a boundary-fitting, clustered grid to resolve the entrainment and mixing processes within the flow and to facilitate quantitative comparison with previous laboratory experiments. Volume and boundary integrated energetics were computed for both steady and time-varying flows. In the steady-state limit, the rate of energy flux through the surface is balanced by dissipation within the basin and advection of potential energy over the sill and into the reservoir. The analyses focus primarily on this latter quantity because it is closely related to the outflow density and volume transport in two-layered exchange flows. Scaling laws relating the energetics of the flow to the surface buoyancy flux and the geometrical scales of the basin-sill system are derived and validated using the numerical results. A second set of experiments was conducted to quantify the transient energetics in response to a sudden change in the surface forcing. These results, combined with a linear impulse-response analysis, were used to derive a general expression describing the advection of potential energy across the sill for periodically forced systems, The analytical predictions are shown to compare favorably with directly simulated flows and to be reasonably consistent with limited field observations of the seasonal variability through the Strait of Bab al Mandab.

}, keywords = {basin, channel, Exchange flow, mandab, mean flow, strait}, isbn = {0022-3670}, doi = {10.1175/1520-0485(2001)031<2721:rcoabd>2.0.co;2}, url = {Internal hydraulic theory is often used to describe idealized bi-directional exchange flow through a constricted channel. This approach is formally applicable to layered flows in which velocity and density are represented by discontinuous functions that are constant within discrete layers. The theory relies on the determination of flow conditions at points of hydraulic control, where long interfacial waves have zero phase speed. In this paper, we consider hydraulic control in continuously stratified exchange flows. Such flows occur, for example, in channels connecting stratified reservoirs and between homogeneous basins when interfacial mixing is significant. Our focus here is on the propagation characteristics of the gravest vertical-mode internal waves within a laterally contracting channel. Two approaches are used to determine the behaviour of waves propagating through a steady, continuously sheared and stratified exchange flow. In the first, waves are mechanically excited at discrete locations within a numerically simulated bi-directional exchange flow and allowed to evolve under linear dynamics. These waves are then tracked in space and time to determine propagation speeds. A second approach, based on the stability theory of parallel shear flows and examination of solutions to a sixth-order eigenvalue problem, is used to interpret the direct excitation experiments. Two types of gravest mode eigensolutions are identified: vorticity modes, with eigenfunction maxima centred above and below the region of maximum density gradient, and density modes with maxima centred on the strongly stratified layer. Density modes have phase speeds that change sign within the channel and are analogous to the interfacial waves in hydraulic theory. Vorticity modes have finite propagation speed throughout the channel but undergo a transition in form: upwind of the transition point the vorticity mode is trapped in one layer. It is argued that modes trapped in one layer are not capable of communicating interfacial information, and therefore that the transition points are analogous to control points. The location of transition points are identified and used to generalize the notion of hydraulic control in continuously stratified flows.

}, keywords = {bab-al-mandab, contraction, hydraulics}, isbn = {0022-1120}, doi = {10.1017/S0022112001006048}, url = {Numerical simulations of bidirectional density-driven exchange flows are used to study the effects of turbulent mixing in these flows. The numerical experiments are designed so that it is possible to specify the intensity of mixing, which allows the investigation of a wide range of hows that are difficult to model in the laboratory The simulated flows are compared to two analytical solutions, first, the two-layer hydraulic solution which has no mixing, and second, a solution in which turbulent mixing dominates the flow. We are able to model exchange flows similar to either of these limits by modifying the turbulent mixing, as well as simulating behavior between these two extremes. The simulations demonstrate that the two analytical solutions form the limits of a wide class of problems and that the flow regime in between the limiting solutions can be described by a single nondimensional parameter Gr(T)A(2).

}, keywords = {bosporus, cavity, contraction, gibraltar, heated end walls, maximal 2-layer exchange, natural-convection, shallow, sill, strait}, isbn = {0148-0227}, doi = {10.1029/2000jc000266}, url = {The purpose of this paper is to analyze diapycnal mixing induced by the breaking of an internal gravity wave - the primary wave - either standing or propagating. To achieve this aim we apply two different methods. The first method consists of a direct estimate of vertical eddy diffusion from particle dispersion while the second method relies upon potential energy budgets [Winters, K.B., Lombard, P.N., Riley, J.J., D{\textquoteright}Asaro, E.A., 1995. J. Fluid Mech. 289, 115-128; Winters, K.B., D{\textquoteright}Asaro, E.A., 1996. J. Fluid Mech. 317, 179-193]. The primary wave we consider is of small amplitude and is statically stable, a case for which the breaking process involves two-dimensional instabilities. The dynamics of the waves have been previously analyzed by means of two-dimensional direct numerical simulations [Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1995. J. Fluid Mech. 285, 265-301; Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1996. Dyn. Atmos. Oceans 29, 41-63; Koudella, C., Staquet, C., 1998. In: Davis, P. (Ed.), Proceedings of the IMA Conference on Mixing and Dispersion on Stably-stratified Flows, Dundee, September 1996. IMA Publication]. High resolution three-dimensional calculations of the same wave are also reported here [Koudella, C., 1999]. A local estimate of mixing is first inferred from the time evolution of sets of particles released in the flow during the breaking regime. We show that, after an early evolution dominated by shear effects, a diffusion law is reached and the dispersion coefficient is fairly independent of the initial seeding location of the particles in the flow. The eddy diffusion coefficient, K,is then estimated from the diapycnal diffusive flux. A good agreement with the value inferred from particle dispersion is obtained. This finding is of particular interest regarding the interpretation of in situ estimates of K inferred either from tracer dispersion or from microstructure measurements. Computation of the Cox number equal to the ratio of eddy diffusivity to molecular diffusivity, shows that the Cox number varies within the interval [9, 262], which corresponds to the range of vertical eddy diffusivity measured in the interior of the ocean. The Cox number is found to depend on the turbulent Froude number squared. We show eventually that mixing results in a weak distortion of the initial density profile and we relate this result to observations made at small scale in the ocean. Comparisons between the analysis of the two-dimensional and high resolution (256(3)) three-dimensional direct numerical simulations of the primary wave were also conducted. We show that the energetics and the amount of mixing are very close when the primary wave is of small amplitude. This results from the fact that, for a statically stable wave, the dynamics of the initially two-dimensional primary wave remains mostly two-dimensional even after the onset of wavebreaking. (C) 2001 Elsevier Science B.V. All rights reserved.

}, keywords = {fine-structure, Gravity waves, internal, mixing, models, numerical experiments, ocean, parameterization, parametric-instabilities, particle dispersion, potential-energy, stratified fluid, turbulence, vertical diffusion, wave breaking}, isbn = {0377-0265}, doi = {10.1016/s0377-0265(00)00056-7}, url = {A laboratory study was carried out to directly measure the turbulence properties in a benthic boundary layer (BBL) above a uniformly sloping bottom where the BBL is energized by internal waves. The ambient fluid was continuously stratified and the steadily forced incoming wave field consisted of a confined beam, restricting the turbulent activity to a finite region along the bottom slope. Measurements of dissipation showed some variation over the wave phase, but cycle-averaged values indicated that the dissipation was nearly constant with height within the BBL. Dissipation levels were up to three orders of magnitude larger than background laminar values and the thickness of the BBL could be defined in terms of the observed dissipation variation with height. Assuming that most of the incoming wave energy was dissipated within the BBL, predicted levels of dissipation were in good agreement with the observations. Measurements were also made of density and two orthogonal components of the velocity fluctuations at discrete heights above the bottom. Cospectral estimates of density and velocity fluctuations showed that the major contributions to both the vertical density flux and the momentum flux resulted from frequencies near the wave forcing frequency, rather than super-buoyancy frequencies, suggesting a strong nonlinear interaction between the incident and reflected waves close to the bottom. Within the turbulent BBL, time-averaged density fluxes were significant and negative near the wave frequencies but negligible at frequencies greater than the buoyancy frequency N. While dissipation rates were high compared to background laminar values, they were low compared to the value of epsilon(tr) approximate to 15 nu N-2, the transition value often used to assess the capacity of a stratified flow to produce mixing. Existing models relating mixing to dissipation rate rely on the existence of a positive-definite density flux at frequencies greater than N as a signature of fluid mixing and therefore cannot apply to these experiments. We therefore introduce a simple model, based on the concept of diascalar fluxes, to interpret the mixing in the stratified fluid in the BBL and suggest that this may have wider application than to the particular configuration studied here.

}, keywords = {bottom, breaking, lakes, ocean, reflection, stratified fluid}, isbn = {0022-1120}, doi = {10.1017/s0022112000008788}, url = {Basin-scale internal waves provide the driving forces for vertical and horizontal fluxes in a stratified lake below the wind-mixed layer. Thus, correct modeling of lake mixing and transport requires accurate modeling of basin-scale internal waves: examining this capability with a hydrostatic, z-coordinate three-dimensional (3D) numerical model at coarse grid resolutions is the focus of this paper. It is demonstrated that capturing the correct thermocline forcing with a 3D mixed-layer model for surface dynamics results in a good representation of low-frequency internal wave dynamics. The 3D estuary and lake computer model ELCOM is applied to modeling Lake Kinneret, Israel, and is compared with field data under summer stratification conditions to identify and illustrate the spatial structure of the lowest-mode basin-scale Kelvin and Poincare waves that provide the largest two peaks in the internal wave energy spectra. The model solves the unsteady Reynolds-averaged Navier-Stokes equations using a semi-implicit method similar to the momentum solution in the TRIM code with the addition of quadratic Euler-Lagrange discretization, scalar (e.g., temperature) transport using a conservative flux-limited approach, and elimination of vertical diffusion terms in the governing equations. A detailed description is provided of turbulence closure for the vertical Reynolds stress terms and vertical turbulent transport using a 3D mixed-layer model parameterized on wind and shear energy fluxes instead of the convential eddy viscosity/diffusivity assumption. This approach gives a good representation of the depth of the mixed-layer at coarse vertical grid resolutions that allows the internal waves to be energized correctly at the basin scale.

}, keywords = {fluid, free, general-circulation model, kelvin wave, kinneret, mixed-layer model, numerical-simulation, semiimplicit method, shallow-water flow, temperature, turbulence}, isbn = {0024-3590}, url = {We investigate the transport of mass and momentum between layers in idealized exchange flow through a contracting channel. Lock-exchange initial value problems are run to approximately steady state using a three-dimensional, non-hydrostatic numerical model. The numerical model resolves the large-scale exchange flow and shear instabilities that form at the interface, parameterizing the effects of subgrid-scale turbulence. The closure scheme is based on an assumed steady, local balance of turbulent production and dissipation in a density-stratified fluid. The simulated flows are analysed using a two-layer decomposition and compared with predictions from two-layer hydraulic theory. Inter-layer transport leads to a systematic deviation of the simulated maximal exchange flows from predictions. Relative to predictions, the observed flows exhibit lower Froude numbers, larger transports and wider regions of subcritical flow in the contraction. To describe entrainment and mixing between layers, the computed solutions are decomposed into a three-layer structure, with two bounding layers separated by an interfacial layer of finite thickness and variable properties. Both bounding layers lose fluid to the interfacial layer which carries a significant fraction of the horizontal transport. Entrainment is greatest from the faster moving layer, occurring preferentially downstream of the contraction. Bottom friction exerts a drag on the lower layer, fundamentally altering the overall dynamics of the exchange. An example where bed friction leads to a submaximal exchange is discussed. The external forcing required to sustain a net transport is significantly less than predicted in the absence of bottom stresses.

}, keywords = {large-eddy simulation, strait, turbulence}, isbn = {0022-1120}, doi = {10.1017/s0022112099007727}, url = {A numerical model has been developed for simulating density-stratified flow in domains with irregular but simple topography. The model was designed for simulating strong interactions between internal gravity waves and topography, e.g, exchange flows in contracting channels, tidally or convectively driven flow over two-dimensional sills or waves propagating onto a shoaling bed. The model is based on the non-hydrostatic, Boussinesq equations of motion for a continuously stratified fluid in a rotating frame, subject to user-confrgurable boundary conditions. An orthogonal boundary fitting co-ordinate system is used for the numerical computations, which rely on a fourth-order compact differentiation scheme, a third-order explicit time stepping and a multi-grid based pressure projection algorithm. The numerical techniques are described and a suite of validation studies are presented. The validation studies include a pointwise comparison of numerical simulations with both analytical solutions and laboratory measurements of non-linear solitary wave propagation. Simulation results for flows lacking analytical or laboratory data are analysed a posteriori to demonstrate satisfaction of the potential energy balance. Computational results are compared with two-layer hydraulic predictions in the case of exchange flow through a contracting channel. Finally, a simulation of circulation driven by spatially non-uniform surface buoyancy flux in an irregular basin is discussed. Copyright (C) 2000 John Wiley \& Sons, Ltd.

}, keywords = {compact differencing, curvilinear, density-stratified flow, exchange, mudpack, orthogonal grid generation, partial-differential equations, projection, software, topography}, isbn = {0271-2091}, doi = {10.1002/(sici)1097-0363(20000215)32:3<263::aid-fld937>3.0.co;2-q}, url = {A three-dimensional nonhydrostatic numerical model is used to calculate nonlinear energy transfers within decaying Garrett-Munk internal wavefields. Inviscid wave interactions are calculated over horizontal scales from about 1 to 80 km and for vertical mode numbers less than about 40 in an exponentially stratified model ocean 2000 m deep. The rate of energy transfer from these scales to smaller, numerically damped scales is used to make predictions of the dissipation rate epsilon in the open ocean midlatitude thermocline. In agreement with the theoretical analyses based on resonant interaction and eikonal theories, the simulation results predict epsilon proportional to \<(E)over tilde (2)\> N-2, where (E) over tilde and N are the internal wave energy density and the ambient buoyancy frequency respectively. The magnitudes of the simulated dissipation rates are shown to be in good agreement with the dissipation measurements taken from six diverse sites in the midlatitude thermocline. The results suggest that the rates of dissipation and mixing in the ocean thermocline are controlled by the nonlinear dynamics of the large-scale energy-containing internal waves.

}, keywords = {dissipation, float, flux, ocean, scales, thermocline}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1997)027<1937:dsoiwe>2.0.co;2}, url = {We define the rate at which a scalar theta mixes in a fluid flow in terms of the flux of theta across isoscalar surfaces. This flux phi(d) is purely diffusive and is, in principle, exactly known at all times given the scalar field and the coefficient of molecular diffusivity. In general, the complex geometry of isoscalar surfaces would appear to make the calculation of this flux very difficult. In this paper, we derive an exact expression relating the instantaneous diascalar flux to the average squared scalar gradient on an isoscalar surface which does not require knowledge of the spatial structure of the surface itself. To obtain this result, a time-dependent reference state theta(t,z*) is defined. When the scalar is taken to be density, this reference state is that of minimum potential energy. The rate of change of the reference state due to diffusion is shown to equal the divergence of the diffusive flux, i.e. (partial derivative/partial derivative z*)phi(d). This result provides a mathematical framework that exactly separates diffusive and advective scalar transport in incompressible fluid flows. The relationship between diffusive and advective transport is discussed in relation to the scalar variance equation and the Osborn-Cox model. Estimation of water mass transformation from oceanic microstructure profiles and determination of the time-dependent mixing rate in numerically simulated flows are discussed.

}, keywords = {thermocline, turbulence}, isbn = {0022-1120}, doi = {10.1017/s0022112096000717}, url = {A conceptual framework for analysing the energetics of density-stratified Boussinesq fluid flows is discussed. The concept of gravitational available potential energy is used to formulate an energy budget in which the evolution of the background potential energy, i.e. the minimum potential energy attainable through adiabatic motions, can be explicitly examined. For closed systems, the background potential energy can change only due to diabatic processes. The rate of change of background potential energy is proportional to the molecular diffusivity. Changes in the background potential energy provide a direct measure of the potential energy changes due to irreversible diapycnal mixing. For open systems, background potential energy can also change due to boundary fluxes, which can be explicitly measured. The analysis is particularly appropriate for evaluation of diabatic mixing rates in numerical simulations of turbulent flows. The energetics of a shear driven mixing layer is used to illustrate the analysis.

}, keywords = {thermocline, turbulence}, isbn = {0022-1120}, doi = {10.1017/s002211209500125x}, url = {The reconstruction of a two-dimensional moving fluid from acoustic transmission measurements is considered. The fluid is described by both a scalar index of refraction and a vector velocity. If the measured data are assumed to be straight-ray geometric projections of the flow, it is known that inversion for the vector velocity is an underdetermined problem. In the present work, it is shown that if the measured data are assumed to satisfy a linearized time-harmonic wave equation, then a unique inversion for the vector velocity is possible. This result is a distinctly finite wavelength effect indicating why ray-based methods fail to produce a complete reconstruction. A filtered backpropagation algorithm for the tomographic reconstruction of the vector flow field is derived.

}, keywords = {reconstruction, stratified fluid-flow}, isbn = {0266-5611}, doi = {10.1088/0266-5611/10/3/012}, url = {The behaviour of internal gravity wave packets approaching a critical level is investigated through numerical simulation. Initial-value problems are formulated for both small- and large-amplitude wave packets. Wave propagation and the early stages of interaction with the mean shear are two-dimensional and result in the trapping of wave energy near a critical level. The subsequent dynamics of wave instability, however, are fundamentally different for two- and three-dimensional calculations. Three-dimensionality develops by transverse convective instability of the two-dimensional wave. The initially two-dimensional flow eventually collapses into quasi-horizontal vortical structures. A detailed energy balance is presented. Of the initial wave energy, roughly one third reflects, one third results in mean flow acceleration and the remainder cascades to small scales where it is dissipated. The detailed budget depends on the wave amplitude, the amount of wave reflection being particularly sensitive.

}, keywords = {internal gravity-waves, stratified fluids}, isbn = {0022-1120}, doi = {10.1017/s0022112094004465}, url = {A new method for imaging a moving fluid is proposed and evaluated by numerical simulation. A cross-section of a three-dimensional (3-D) fluid is probed by high frequency acoustic waves from several different directions. Assuming straight-ray geometric acoustics, the time-of-flight depends on both the scaler sound speed and the vector fluid velocity. By appropriately combining travel times, projections of both the sound speed and the velocity are isolated. The sound speed is reconstructed using the standard filtered backprojection algorithm. Though complete inversion of velocity is not possible, sufficient information is available to recover the component of fluid vorticity transverse to the plane of insonification. A new filtered backprojection algorithm for vorticity is developed and implemented. To demonstrate the inversion procedure, a 3-D stratified fluid is simulated and travel time data are calculated by path integration. These data are then inverted to recover both the scaler sound speed and the vorticity of the evolving flow.

}, keywords = {Vorticity}, isbn = {0885-3010}, doi = {10.1109/58.184995}, url = {The three-dimensional stability problem is investigated for a family of velocity and density profiles similar in form to those expected for large-amplitude internal gravity waves near a critical level. These profiles exhibit regions of high shear and stable stratification alternating with regions of weak shear and unstable stratification. Analytical solutions are given for inviscid, neutral modes that are similar to those found under neutral conditions with stable stratification. Neutral modes form closed streamline patterns centered at locations of maximal shear. and are not strongly influenced by nearby regions of unstable stratification. Unstable modes are computed numerically. It is shown that the instability mechanism for these wave-like flows is fundamentally three-dimensional in character and exhibits both shear and convective dynamics. For flows with parameter values below the neutral curves, unstable modes oriented in the streamwise direction undergo shear instability, while modes oriented orthogonally are convectively unstable. In addition to their intrinsic physical relevance, the results of this study have important implications for the physics and the numerical modeling of breaking internal gravity waves. Two-dimensional models will bias the breaking dynamics by eliminating the possibility for convection oriented in the transverse plane.

}, keywords = {flow, gravity-waves, kelvin-helmholtz billows, layer, motion}, isbn = {0377-0265}, doi = {10.1016/0377-0265(92)90009-i}, url = {We consider the feasibility of using small-scale acoustic tomography to reconstruct oceanic microstructure. In contrast to altemate measurement techniques, acoustic tomography can produce quantitative, fully three-dimensional images. Tomography uses acoustic data measured by probing the medium from several different directions. To test the proposed approach, numerical realizations typical of anisotropic microstructure are first simulated and then reconstructed by tomography. Two specific forms are evaluated: conventional computed tomography that uses only travel time delay data, and diffraction tomography that requires coherent field measurements. Conventional tomography is shown to produce high-quality cross-sectional images. The effects of reducing the number of views are studied, and error maps are generated. Issues in experimental implementation are considered. This study can serve as a guide to the design of an experimental device.

}, keywords = {diffraction tomography, image projections, internal, north-atlantic, pacific, propagation, waves}, isbn = {0148-0227}, doi = {10.1029/90jc02489}, url = {The authors consider the data obtained from a hypothetical transmission experiment in which a moving fluid with variable index of refraction is probed using acoustic transmitters and receivers. A projection-slice theorem is derived relating the Fourier transform of the data to the transform of fluid vorticity. A modified filter is then derived for data inversion by means of filtered backprojection.

}, isbn = {0266-5611}, doi = {10.1088/0266-5611/6/4/002}, url = {A high-resolution two-dimensional numerical model is used to simulate the propagation of finite amplitude internal wave packets into a mean shear flow that varies slowly in space. For moderate packet amplitudes the interaction is well described by weakly nonlinear asymptotic theory. At higher amplitude, however, a region develops near the critical level in which nonlinearity dominates, the wave packet becomes unstable, and the wavelike motion breaks down into smaller scales. The form of the observed internal wave breakdown is unexpected in that convectively unstable density gradients persist for many buoyancy periods. The eventual rapid transition, from large-amplitude wavelike motion to a more complicated flow, is triggered by an instability driven by the intensified wave shear and not by a convective breakdown of the unstable stratification. This illustrates that unstable stratification does not necessarily lead to convective instability in two dimensions.

}, doi = {10.1029/JC094iC09p12709}, url = {