Near-inertial dissipation due to stratified flow over abyssal topography

<p>Linear theory for steady stratified flow over topography sets the range for topographic wavenumbers over which freely propagating internal waves are generated, whose radiation and breaking contribute to energy dissipation in the interior. Previous work demonstrated that dissipation rates can be enhanced over large-scale topographies with wavenumbers outside of such radiative range. We conduct idealized rotating 3D numerical simulations of steady stratified flow over 1D topography and quantify kinetic energy dissipation. We vary topographic width, which determines whether the obstacle is within the radiative range, and height, which measures the degree of flow non-linearity. Simulations with certain width and height combinations develop periodicity in wave breaking and energy dissipation, which is enhanced in the domain interior. Dissipation rates for tall and wide non-radiative topography are comparable to those of radiative topography, even away from the bottom, which is important for the ocean where wider hills also tend to be taller. </p>

Getting Rid of Fast Waves: Slow Dynamics

After analysis of general properties of horizontal motion in primitive equations and introduction of principal parameters, the key notion of geostrophic equilibrium is introduced. Quasi-geostrophic reductions of one- and two-layer rotating shallow-water models are obtained by a direct filtering of fast inertia–gravity waves through a choice of the time scale of motions of interest, and by asymptotic expansions in Rossby number. Properties of quasi-geostrophic models are established. It is shown that in the beta-plane approximations the models describe Rossby waves. The first idea of the classical baroclinic instability is given, and its relation to Rossby waves is explained. Modifications of quasi-geostrophic dynamics in the presence of coastal, topographic, and equatorial wave-guides are analysed. Emission of mountain Rossby waves by a flow over topography is demonstrated. The phenomena of Kelvin wave breaking, and of soliton formation by long equatorial and topographic Rossby waves due to nonlinear effects are explained.

A Barotropic Model of Eddy Saturation

Eddy saturation refers to a regime in which the total volume transport of an oceanic current is insensitive to the wind stress strength. Baroclinicity is currently believed to be the key to the development of an eddy-saturated state. In this paper, it is shown that eddy saturation can also occur in a purely barotropic flow over topography, without baroclinicity. Thus, eddy saturation is a fundamental property of barotropic dynamics above topography. It is demonstrated that the main factor controlling the appearance or not of eddy-saturated states in the barotropic setting is the structure of geostrophic contours, that is, the contours of f/H (the ratio of the Coriolis parameter to the ocean’s depth). Eddy-saturated states occur when the geostrophic contours are open, that is, when the geostrophic contours span the whole zonal extent of the domain. This minimal requirement for eddy-saturated states is demonstrated using numerical integrations of a single-layer quasigeostrophic flow over two different topographies characterized by either open or closed geostrophic contours with parameter values loosely inspired by the Southern Ocean. In this setting, transient eddies are produced through a barotropic–topographic instability that occurs because of the interaction of the large-scale zonal flow with the topography. By studying this barotropic–topographic instability insight is gained on how eddy-saturated states are established.

Analytic solutions for Long's equation and its generalization

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Analytic Solutions for Long's Equation and its Generalization

Two dimensional, steady state, stratified, isothermal, atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic type solutions in addition to regular gravity waves. These new analytical solutions provide insights about the propagation and amplitude of gravity waves over topography.