Variational problem for vortices attached to seamounts

Jonas Nycander; Behrouz Emamizadeh

doi:10.1016/S0362-546X(03)00207-4

Variational problem for vortices attached to seamounts

Jonas Nycander, Behrouz Emamizadeh

Research output: Journal Publication › Article › peer-review

16 Citations (Scopus)

Abstract

The existence of an energy maximizer relative to a class of rearrangements of a given function is proved. The maximizers are stationary and stable solutions of the two-dimensional barotropic vorticity equation, governing the evolution of geophysical flow over a surface of variable height. The theorem proved implies the existence of a family of stable vortices with anticyclonic potential vorticity over a seamount, and a similar family of vortices with cyclonic potential vorticity over a localized depression.

Original language	English
Pages (from-to)	15-24
Number of pages	10
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	55
Issue number	1-2
DOIs	https://doi.org/10.1016/S0362-546X(03)00207-4
Publication status	Published - Oct 2003
Externally published	Yes

Keywords

Barotropic vorticity equation
Rearrangements
Semilinear elliptic equation
Variational problems
Vortices

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/S0362-546X(03)00207-4

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title = "Variational problem for vortices attached to seamounts",

abstract = "The existence of an energy maximizer relative to a class of rearrangements of a given function is proved. The maximizers are stationary and stable solutions of the two-dimensional barotropic vorticity equation, governing the evolution of geophysical flow over a surface of variable height. The theorem proved implies the existence of a family of stable vortices with anticyclonic potential vorticity over a seamount, and a similar family of vortices with cyclonic potential vorticity over a localized depression.",

keywords = "Barotropic vorticity equation, Rearrangements, Semilinear elliptic equation, Variational problems, Vortices",

author = "Jonas Nycander and Behrouz Emamizadeh",

note = "Funding Information: We are grateful to Geoffrey Burton for valuable comments on the manuscript. The second author was in part supported by a grant from the Institute for Studies in Theoretical Physics and Mathematics (No. 81760115). ",

year = "2003",

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doi = "10.1016/S0362-546X(03)00207-4",

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T1 - Variational problem for vortices attached to seamounts

AU - Nycander, Jonas

AU - Emamizadeh, Behrouz

N1 - Funding Information: We are grateful to Geoffrey Burton for valuable comments on the manuscript. The second author was in part supported by a grant from the Institute for Studies in Theoretical Physics and Mathematics (No. 81760115).

PY - 2003/10

Y1 - 2003/10

N2 - The existence of an energy maximizer relative to a class of rearrangements of a given function is proved. The maximizers are stationary and stable solutions of the two-dimensional barotropic vorticity equation, governing the evolution of geophysical flow over a surface of variable height. The theorem proved implies the existence of a family of stable vortices with anticyclonic potential vorticity over a seamount, and a similar family of vortices with cyclonic potential vorticity over a localized depression.

AB - The existence of an energy maximizer relative to a class of rearrangements of a given function is proved. The maximizers are stationary and stable solutions of the two-dimensional barotropic vorticity equation, governing the evolution of geophysical flow over a surface of variable height. The theorem proved implies the existence of a family of stable vortices with anticyclonic potential vorticity over a seamount, and a similar family of vortices with cyclonic potential vorticity over a localized depression.

KW - Barotropic vorticity equation

KW - Rearrangements

KW - Semilinear elliptic equation

KW - Variational problems

KW - Vortices

UR - http://www.scopus.com/inward/record.url?scp=0042013125&partnerID=8YFLogxK

U2 - 10.1016/S0362-546X(03)00207-4

DO - 10.1016/S0362-546X(03)00207-4

M3 - Article

AN - SCOPUS:0042013125

SN - 0362-546X

VL - 55

SP - 15

EP - 24

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 1-2

ER -

Variational problem for vortices attached to seamounts

Abstract

Keywords

ASJC Scopus subject areas

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