Spin-down of a barotropic vortex by irregular small-scale topography

Radko, Timour

doi:10.1017/jfm.2022.488

Cited by 10 publications

(51 citation statements)

References 51 publications

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“…The present model extends the multiscale theory of Radko (2022) to baroclinic flows, layered and continuously stratified. We develop an explicit closure for the topographically induced eddy stresses and validate it by comparing topography-resolving simulations with their parametric counterparts.…”

Section: Introductionsupporting

confidence: 56%

“…We now proceed to develop a baroclinic version of the sandpaper theory. Our approach is analogous to the barotropic model of Radko (2022) and only an abbreviated description is offered here. To capture the interaction of large-scale patterns with small-scale topography, the solution for is sought in terms of power series in : …”

Section: Multiscale Modelmentioning

confidence: 99%

“…The leading-order balance in all layers except for the bottom one is trivially solved by whereas for the lowest layer we use the steady small-scale pattern that satisfies where . This balance represents the tendency for expulsion of small-scale potential vorticity (PV) in the lowest layer (Radko 2022).…”

Section: Multiscale Modelmentioning

confidence: 99%

“…We are interested in the tendency of rough topography to interact with large-scale currents by generating small-scale eddies associated with considerable Reynolds stresses that, in turn, influence the evolution of primary flows (Radko 2020; Gulliver & Radko 2022). The present investigation builds on the previously reported barotropic model of topographic control (Radko 2022), which contains further background information. The latter study examined the interaction of broad currents with irregular seafloor utilizing techniques of multiscale mechanics (Gama, Vergassola & Frisch 1994; Novikov & Papanicolau 2001; Mei & Vernescu 2010) and has been dubbed the sandpaper model.…”

Section: Introductionmentioning

confidence: 99%

“…The chosen moniker underscores the cumulative impact of a multitude of small-scale topographic features by invoking the association with fine abrasive particles of sandpaper. The model of Radko (2022) was couched in terms of a quasi-geostrophic framework, which made it possible to exclude wave-induced drag and focus the analysis exclusively on eddy stresses. Unlike earlier multiscale theories of topographic control (Benilov 2000, 2001; Vanneste 2000, 2003; Goldsmith & Esler 2021), the sandpaper model determines the topographic forcing from the prescribed statistical spectrum of small-scale bathymetry.…”

Section: Introductionmentioning

confidence: 99%

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Spin-down of a baroclinic vortex by irregular small-scale topography

Radko

2022

J. Fluid Mech.

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This study explores the impact of small-scale variability in the bottom relief on the dynamics and evolution of broad baroclinic flows in the ocean. The analytical model presented here generalizes the previously reported barotropic ‘sandpaper’ theory of flow–topography interaction to density-stratified systems. The multiscale asymptotic analysis leads to an explicit representation of the large-scale effects of irregular bottom roughness. The utility of the multiscale model is demonstrated by applying it to the problem of topography-induced spin-down of an axisymmetric vortex. We find that bathymetry affects vortices by suppressing circulation in their deep regions. As a result, vortices located above rough topography tend to be more stable than their flat-bottom counterparts. The multiscale theory is validated by comparing corresponding topography-resolving and parametric simulations.

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Section: Introductionsupporting

confidence: 56%

Section: Multiscale Modelmentioning

confidence: 99%

Section: Multiscale Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spin-down of a baroclinic vortex by irregular small-scale topography

Radko

2022

J. Fluid Mech.

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Wave propagation through a stationary field of clouds: A homogenisation approach

Goldsmith,

Esler

2023

Quart J Royal Meteoro Soc

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The effect of a sub‐grid scale cloud field on the propagation of long atmospheric waves is investigated using a new scale‐consistent formulation based upon the asymptotic theory of homogenisation. A key aim is to quantify potential model errors in wave propagation speeds, introduced by using averaged fields in place of the fully resolved circulation, in the setting of a simple stratified Boussinesq mid‐latitude β‐channel model. The effect of the cloud field, represented here by a random array of strongly nonlinear axisymmetric circulations, is found to appear in the large‐scale governing equations through new terms which redistribute the large‐scale buoyancy and horizontal momentum fields in the vertical. These new terms, which have the form of non‐local integral operators, are linear in the cloud number density, and are fully determined by the solution of a linear elliptic equation known as a cell problem. The cell problem in turn depends upon the details of the nonlinear cloud circulations. The integral operators are calculated explicitly for example cloud fields and then dispersion relations are compared for different waves in the presence of clouds at realistic densities. The main finding is that baroclinic Rossby waves are significantly slowed and damped by the clouds, whilst inertia‐gravity waves are affected almost exclusively by damping, most strongly at the lowest frequencies. In contrast, all waves with a barotropic structure are found to be almost unaffected by the presence of clouds, even at the highest realistic cloud densities.An important consequence of this study is a new approach to the closure of sub‐grid scale cloud fields in the parameterisation of convection in large‐scale atmospheric models.This article is protected by copyright. All rights reserved.

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A generalized theory of flow forcing by rough topography

Radko

2023

J. Fluid Mech.

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An analytical model is developed which explores the impact of irregular sea-floor roughness on large-scale oceanic flows. The previously reported asymptotic ‘sandpaper’ theory of flow-topography interaction represents relatively swift currents and exhibits singular behaviour in the weak flow limit. The present investigation systematically spans a wider parameter space and identifies the principal dissimilarities in the topographic regulation of slow and fast currents. The fast flows are controlled by the Reynolds stresses produced by topographically generated eddies. In contrast, relatively weak flows are more affected by the eddy-induced bottom form drag. The asymptotic models for fast and slow currents are then combined to arrive at a concise description of flow forcing by small-scale topography in homogeneous and multilayer models. The proposed closure is validated by comparing corresponding topography-resolving and parametric simulations.

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Spin-down of a barotropic vortex by irregular small-scale topography

Cited by 10 publications

References 51 publications

Spin-down of a baroclinic vortex by irregular small-scale topography

Spin-down of a baroclinic vortex by irregular small-scale topography

Wave propagation through a stationary field of clouds: A homogenisation approach

A generalized theory of flow forcing by rough topography

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