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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.

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, 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.

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.

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.

Ivey, GN, Winters KB, Koseff JR.  2008.  Density stratification, turbulence, but how much mixing? Annual Review of Fluid Mechanics. 40:169-184., Palo Alto: Annual Reviews   10.1146/annurev.fluid.39.050905.110314   Abstract

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.

Barry, ME, Ivey GN, Winters KB, Imberger J.  2001.  Measurements of diapycnal diffusivities in stratified fluids. Journal of Fluid Mechanics. 442:267-291.   10.1017/S0022112001005080   AbstractWebsite

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.