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Jagannathan, A, Winters K, Armi L.  2019.  Stratified flows over and around long dynamically tall mountain ridges. Journal of the Atmospheric Sciences. 76:1265-1287.   10.1175/jas-d-18-0145.1   AbstractWebsite

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.

Tort, M, Winters KB.  2018.  Poleward propagation of near-inertial waves induced by fluctuating winds over a baroclinically unstable zonal jet. Journal of Fluid Mechanics. 834:510-530.   10.1017/jfm.2017.698   AbstractWebsite

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'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.

Jagannathan, A, Winters KB, Armi L.  2017.  Stability of stratified downslope flows with an overlying stagnant isolating layer. Journal of Fluid Mechanics. 810:392-411.   10.1017/jfm.2016.683   AbstractWebsite

We investigate the dynamic stability of stratified flow configurations characteristic of hydraulically controlled downslope flow over topography. Extraction of the correct 'base state' 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.

Barkan, R, Winters KB, McWilliams JC.  2017.  Stimulated imbalance and the enhancement of eddy kinetic energy dissipation by internal waves. Journal of Physical Oceanography. 47:181-198.   10.1175/jpo-d-16-0117.1   AbstractWebsite

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.

Winters, KB.  2016.  The turbulent transition of a supercritical downslope flow: sensitivity to downstream conditions. Journal of Fluid Mechanics. 792:997-1012.   Abstract

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.

Ulloa, HN, Winters KB, de la Fuente A, Niño Y.  2015.  Degeneration of internal Kelvin waves in a continuous two-layer stratification. Journal of Fluid Mechanics. 777:68-96.   10.1017/jfm.2015.311   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’s (J. Geophys. Res., vol. 72, 1967, pp. 4151–4162) 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–laminar regime (DLR), for which η0∼δi and the Kelvin wave retains its linear character, to the nonlinear–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.

Barkan, R, Winters KB, Smith SGL.  2015.  Energy cascades and loss of balance in a reentrant channel forced by wind stress and buoyancy fluxes. Journal of Physical Oceanography. 45:272-293.   10.1175/jpo-d-14-0068.1   AbstractWebsite

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.

Winters, KB.  2015.  Tidally driven mixing and dissipation in the stratified boundary layer above steep submarine topography. Geophysical Research Letters. 42   doi:10.1002/2015GL064676   Abstract

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.

Winters, KB.  2015.  Tidally-forced flow in a rotating, stratified, shoaling basin. Ocean Modelling. 90:72–81.   10.1016/j.ocemod.2015.04.004   AbstractWebsite

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 ‘set-up’ 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.

Winant, C, Valle-Levinson A, Ponte A, Winant C, Gutierrez-de-Velasco G, Winters K.  2014.  Observations on the lateral structure of wind-driven flows in a stratified, semiarid bay of the Gulf of California. Estuaries and Coasts. 37:1319-1328.   10.1007/s12237-013-9641-0   AbstractWebsite

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'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's rotation and advection of momentum.

Winters, KB, Armi L.  2014.  Topographic control of stratified flows: upstream jets, blocking and isolating layers. Journal of Fluid Mechanics. 753:80-103.   10.1017/jfm.2014.363   AbstractWebsite

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.

Barkan, R, Winters KB, Smith SGL.  2013.  Rotating horizontal convection. Journal of Fluid Mechanics. 723:556-586.   10.1017/jfm.2013.136   AbstractWebsite

'Horizontal convection' (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.

Winters, KB, Barkan R.  2013.  Available potential energy density for Boussinesq fluid flow. Journal of Fluid Mechanics. 714:476-488.   10.1017/jfm.2012.493   Abstract

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.

Winters, KB, Armi L.  2013.  The response of a continuously stratified fluid to an oscillating flow past an obstacle. Journal of Fluid Mechanics. 727:83-118.   10.1017/jfm.2013.247   AbstractWebsite

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.

Pham, HT, Sarkar S, Winters KB.  2013.  Large-eddy simulation of deep-cycle turbulence in an equatorial undercurrent model. Journal of Physical Oceanography. 43:2490-2502.   10.1175/jpo-d-13-016.1   AbstractWebsite

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.

Winters, KB, Armi L.  2012.  Hydraulic control of continuously stratified flow over an obstacle. Journal of Fluid Mechanics. 700:502-513.   10.1017/jfm.2012.157   AbstractWebsite

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.

Winters, KB, de la Fuente A.  2012.  Modelling rotating stratified flows at laboratory-scale using spectrally-based DNS. Ocean Modelling. 49-50:47-59.   10.1016/j.ocemod.2012.04.001   AbstractWebsite

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.

Ponte, AL, de Velasco GG, Valle-Levinson A, Winters KB, Winant CD.  2012.  Wind-driven subinertial circulation inside a semienclosed bay in the Gulf of California. Journal of Physical Oceanography. 42:940-955.   10.1175/jpo-d-11-0103.1   AbstractWebsite

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' 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.

Pham, HT, Sarkar S, Winters KB.  2012.  Near-N oscillations and deep-cycle turbulence in an upper-equatorial undercurrent model. Journal of Physical Oceanography. 42:2169-2184.   10.1175/jpo-d-11-0233.1   AbstractWebsite

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.

Pham, HT, Sarkar S, Winters KB.  2012.  Intermittent patches of turbulence in a stratified medium with stable shear. Journal of Turbulence. 13:1-17.   10.1080/14685248.2012.686666   AbstractWebsite

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.

Hazewinkel, J, Winters KB.  2011.  PSI of the internal tide on a β plane: flux divergence and near-inertial wave propagation. Journal of Physical Oceanography. 41:1673-1682.   10.1175/2011jpo4605.1   AbstractWebsite

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.

Winters, KB, Bouruet-Aubertot P, Gerkema T.  2011.  Critical reflection and abyssal trapping of near-inertial waves on a β-plane. Journal of Fluid Mechanics. 684:111-136.   10.1017/jfm.2011.280   AbstractWebsite

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'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.

Cheng, P, Valle-Levinson A, Winant CD, Ponte ALS, de Velasco GG, Winters KB.  2010.  Upwelling-enhanced seasonal stratification in a semiarid bay. Continental Shelf Research. 30:1241-1249.   10.1016/j.csr.2010.03.015   AbstractWebsite

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.

Echeverri, P, Flynn MR, Winters KB, Peacock T.  2009.  Low-mode internal tide generation by topography: an experimental and numerical investigation. Journal of Fluid Mechanics. 636:91-108.   10.1017/s0022112009007654   AbstractWebsite

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.

Winters, KB, Young WR.  2009.  Available potential energy and buoyancy variance in horizontal convection. Journal of Fluid Mechanics. 629:221-230.   10.1017/s0022112009006685   AbstractWebsite

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's oceans.