Linear stability of steady zonal jet flows induced by a small-scale forcing on a β plane

Kiori Obuse; Shin Ichi Takehiro; Michio Yamada

doi:10.1016/j.physd.2011.08.009

Linear stability of steady zonal jet flows induced by a small-scale forcing on a β plane

Kiori Obuse, Shin Ichi Takehiro, Michio Yamada

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We analytically obtain steady isolated zonal jet solutions of the evolution equation of zonal flows on a β plane with a homogeneous zonal flow and a small-scale sinusoidal transversal flow in the background, derived by Manfroi and Young (1999) [9]. It is shown that these steady zonal jet solutions are all linearly unstable. Numerical time integrations of the evolution equation also confirm that the perturbed unstable steady solution becomes a uniform flow in the long run. These results suggest that mergers/disappearances of zonal jets superposed upon background forced two-dimensional turbulence on a β plane or a rotating sphere might be due to the intrinsic instability of the zonal jets.

Original language	English
Pages (from-to)	1825-1834
Number of pages	10
Journal	Physica D: Nonlinear Phenomena
Volume	240
Issue number	22
DOIs	https://doi.org/10.1016/j.physd.2011.08.009
Publication status	Published - 2011 Nov 1

Keywords

Barotropic flow
Beta effect
CahnHilliard equation
Rotating fluid
Turbulence
Zonal jet

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/j.physd.2011.08.009

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title = "Linear stability of steady zonal jet flows induced by a small-scale forcing on a β plane",

abstract = "We analytically obtain steady isolated zonal jet solutions of the evolution equation of zonal flows on a β plane with a homogeneous zonal flow and a small-scale sinusoidal transversal flow in the background, derived by Manfroi and Young (1999) [9]. It is shown that these steady zonal jet solutions are all linearly unstable. Numerical time integrations of the evolution equation also confirm that the perturbed unstable steady solution becomes a uniform flow in the long run. These results suggest that mergers/disappearances of zonal jets superposed upon background forced two-dimensional turbulence on a β plane or a rotating sphere might be due to the intrinsic instability of the zonal jets.",

keywords = "Barotropic flow, Beta effect, CahnHilliard equation, Rotating fluid, Turbulence, Zonal jet",

author = "Kiori Obuse and Takehiro, {Shin Ichi} and Michio Yamada",

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T1 - Linear stability of steady zonal jet flows induced by a small-scale forcing on a β plane

AU - Obuse, Kiori

AU - Takehiro, Shin Ichi

AU - Yamada, Michio

PY - 2011/11/1

Y1 - 2011/11/1

N2 - We analytically obtain steady isolated zonal jet solutions of the evolution equation of zonal flows on a β plane with a homogeneous zonal flow and a small-scale sinusoidal transversal flow in the background, derived by Manfroi and Young (1999) [9]. It is shown that these steady zonal jet solutions are all linearly unstable. Numerical time integrations of the evolution equation also confirm that the perturbed unstable steady solution becomes a uniform flow in the long run. These results suggest that mergers/disappearances of zonal jets superposed upon background forced two-dimensional turbulence on a β plane or a rotating sphere might be due to the intrinsic instability of the zonal jets.

AB - We analytically obtain steady isolated zonal jet solutions of the evolution equation of zonal flows on a β plane with a homogeneous zonal flow and a small-scale sinusoidal transversal flow in the background, derived by Manfroi and Young (1999) [9]. It is shown that these steady zonal jet solutions are all linearly unstable. Numerical time integrations of the evolution equation also confirm that the perturbed unstable steady solution becomes a uniform flow in the long run. These results suggest that mergers/disappearances of zonal jets superposed upon background forced two-dimensional turbulence on a β plane or a rotating sphere might be due to the intrinsic instability of the zonal jets.

KW - Barotropic flow

KW - Beta effect

KW - CahnHilliard equation

KW - Rotating fluid

KW - Turbulence

KW - Zonal jet

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Linear stability of steady zonal jet flows induced by a small-scale forcing on a β plane

Abstract

Keywords

ASJC Scopus subject areas

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