Variational formulations of steady rotational equatorial waves-Reference-Cited by-同舟云学术

Variational formulations of steady rotational equatorial waves

Published:2020-08-22 Issue:1 Volume:10 Page:534-547
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Chu Jifeng¹,Escher Joachim²

Affiliation:

1. Department of Mathematics , Shanghai Normal University , Shanghai , 200234 , China

2. Institute for Applied Mathematics , Leibniz Universität Hannover , Hannover , Germany

Abstract

Abstract When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2020-0146/pdf

Reference46 articles.

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3. J. Chu, Q. Ding, Y. Yang, Steady periodic waves and formal stability for fixed-depth rotational equatorial flows, J. Differential Equations, 269 (2020), 4192-4214.

4. J. Chu, J. Escher, Steady periodic equatorial water waves with vorticity, Discrete Cont. Dyn. Syst. 39 (2019), 4713-4729.

5. J. Chu, D. Ionescu-Kruse, Y. Yang, Exact solution and instability for geophysical waves with centripetal forces and at arbitrary latitude, J. Math. Fluid Mech. 21 (2019), no. 2, 21:19.

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