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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.

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.

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.

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.

D'Asaro, EA, Winters KB, Lien RC.  2004.  Lagrangian estimates of diapycnal mixing in a simulated K-H instability. Journal of Atmospheric and Oceanic Technology. 21:799-809.   10.1175/1520-0426(2004)021<0799:leodmi>;2   AbstractWebsite

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.