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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.

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.

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.  2008.  Growth of inertia-gravity waves in sheared inertial currents. Journal of Fluid Mechanics. 601:85-100.   10.1017/s0022112008000621   AbstractWebsite

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.

Smyth, WD, Winters KB.  2003.  Turbulence and mixing in Holmboe waves. Journal of Physical Oceanography. 33:694-711.   10.1175/1520-0485(2003)33<694:tamihw>;2   AbstractWebsite

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.