Barotropic instability of a time-dependent parallel flow

Radko, Timour

doi:10.1017/jfm.2021.544

Cited by 5 publications

(4 citation statements)

References 41 publications

(47 reference statements)

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“…The following simulations are performed using the de-aliased pseudo-spectral model employed in our previous works (e.g. Sutyrin & Radko 2019; Radko 2021). To limit the effects of doubly periodic boundary conditions on vortex evolution, we use a relatively wide computational domain of size The topography-resolving simulations employ a fine mesh with grid points.…”

Section: Spin-down Of a Large-scale Vortexmentioning

confidence: 99%

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

Radko

2022

J. Fluid Mech.

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This study examines the impact of small-scale irregular topographic features on the dynamics and evolution of large-scale barotropic flows in the ocean. A multiscale theory is developed, which makes it possible to represent large-scale effects of the bottom roughness without explicitly resolving small-scale variability. The analytical model reveals that the key mechanism of topographic control involves the generation of a small-scale eddy field associated with considerable Reynolds stresses. These eddy stresses are inversely proportional to the large-scale velocity and adversely affect mean circulation patterns. The multiscale model is applied to the problem of topography-induced spin-down of a large circularly symmetric vortex and is validated by corresponding topography-resolving simulations. The small-scale bathymetry chosen for this configuration conforms to the Goff–Jordan statistical spectrum. While the multiscale model formally assumes a substantial separation between the scales of interacting flow components, it is remarkably accurate even when scale separation is virtually non-existent.

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Section: Spin-down Of a Large-scale Vortexmentioning

confidence: 99%

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

Radko

2022

J. Fluid Mech.

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“…The non-dimensional root-mean-square depth variation corresponding to this spectrum is . Simulations are performed using the de-aliased pseudo-spectral model employed in our previous studies (Radko 2021, 2022 a ) on the computational domain of size . All topography-resolving experiments employ a mesh with grid points.…”

Section: Validationmentioning

confidence: 99%

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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“…A certain limitation of the theory is that, in fact, not the entire Kolmogorov flow, but only a part of it, can undergo periodic oscillations. Consideration of this circumstance reduces to a change ε cos t cos y ⇒ ε 0 cos y + ε 1 cos t cos y in equation ( 6), but generally leads to a significant complication of the theory (see also Radko 2021). Now, additional terms 1 2 iAqε 0 a j−1/2 n+1/2 + a j+3/2 n+1/2 appear in equation ( 6), and it must be replaced ε ⇒ ε 1 in the existing terms of the equations.…”

Section: Instability Analysis In the Traditional Approximationmentioning

confidence: 99%

“…As applied to the classical barotropic (inflection-point) Kolmogorov flow instability, such problems were studied in Frenkel (1991) and Zhang and Frenkel (1998). Radko (2021) considered in a recent paper the barotropic (long-wavelength) instability of the time-dependent Kolmogorov flow on the beta plane. In studying the inertial stability of time-periodic Kolmogorov flow the current work uses the Floquet theory and the analogy of the problem with the parametric instability of pendulum oscillations (Jeffreys and Jeffreys 1972).…”

Section: Introductionmentioning

confidence: 99%

Inertial instability of the time-periodic Kolmogorov flow in a rotating fluid with the full account of the Coriolis force

Kurgansky¹

2022

Fluid Dyn. Res.

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The inertial parametric instability of a time-dependent spatially periodic flow (Kolmogorov flow) of a rotating stratified Boussinesq fluid is studied, taking fully into account the Coriolis force in the problem and with the possibility that the flow has an arbitrary orientation in the horizontal plane. The existence of instability is shown for velocity shears less than those indicated by the criterion of inertial stability of a steady flow with the same spatial period and velocity amplitude. In particular, the instability estimates are obtained for weakly stratified geophysical media, for example for the deep layers of the ocean, and it is suggested that the possible applications of the theory can also be directly related to a laboratory experiment. Two different theoretical scenarios of inclusion of the full Coriolis force account in the problem are considered, and in both cases this leads to a reduction in the degree of inertial instability of the basic flow.

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Barotropic instability of a time-dependent parallel flow

Abstract: Abstract

Cited by 5 publications

References 41 publications

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

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

A generalized theory of flow forcing by rough topography

Inertial instability of the time-periodic Kolmogorov flow in a rotating fluid with the full account of the Coriolis force

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