A quasi-linear theory for rotating flow over topography. Part 2. Beta-plane annulus

Steady rotating flow over topography in a periodic channel is examined, with emphasis on the interaction of waves, topography and mean flow. A simple quasi-linear theory is presented that features an implicit equation relating the net zonal flow to the forcing and topography. A good description of the dynamics is obtained, even when resonant Rossby waves appear. Multiple solutions for given external parameters are predicted in some cases, and confirmed by comparison with a fully nonlinear numerical model.The nonlinear results also indicate that the zonally averaged shear can be important when topographic effects or Rossby numbers are large. With this factor taken into account the theory gives good agreement with the fully nonlinear model, as long as eddy–eddy interactions are minor.The theory is relevant to the dynamics of planetary waves in the atmosphere, and may also be applied to some oceanic problems.

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Getting Rid of Fast Waves: Slow Dynamics

10.1093/oso/9780198804338.003.0005 ◽

2018 ◽

Author(s):

Vladimir Zeitlin

Keyword(s):

Rossby Waves ◽

Baroclinic Instability ◽

Nonlinear Effects ◽

Kelvin Wave ◽

Beta Plane ◽

Equatorial Wave ◽

Flow Over Topography ◽

Wave Guides ◽

Rotating Shallow Water ◽

Fast Waves

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.

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Finite depth stratified flow over topography on a beta-plane

Geophysical & Astrophysical Fluid Dynamics ◽

10.1080/03091927908242675 ◽

1979 ◽

Vol 12 (1) ◽

pp. 35-43 ◽

Cited By ~ 9

Author(s):

E. R. Johnson

Keyword(s):

Stratified Flow ◽

Finite Depth ◽

Beta Plane ◽

Flow Over Topography

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Near-critical free-surface rotating flow over topography

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2004.1317 ◽

2004 ◽

Vol 460 (2050) ◽

pp. 2865-2881 ◽

Cited By ~ 7

Author(s):

G. G Vilenski ◽

E. R. Johnson

Keyword(s):

Free Surface ◽

Rotating Flow ◽

Flow Over Topography

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Supercritical rotating flow over topography

Physics of Fluids ◽

10.1063/1.3139306 ◽

2009 ◽

Vol 21 (6) ◽

pp. 066601 ◽

Cited By ~ 4

Author(s):

J. G. Esler ◽

O. J. Rump ◽

E. R. Johnson

Keyword(s):

Rotating Flow ◽

Flow Over Topography

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Near-inertial dissipation due to stratified flow over abyssal topography

10.5194/egusphere-egu21-16333 ◽

2021 ◽

Author(s):

Varvara Zemskova ◽

Nicolas Grisouard

Keyword(s):

Energy Dissipation ◽

Kinetic Energy ◽

Numerical Simulations ◽

Linear Theory ◽

Internal Waves ◽

Wave Breaking ◽

Large Scale ◽

Stratified Flow ◽

Dissipation Rates ◽

Flow Over 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.&#160;</p>

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