Exact solution and instability for geophysical edge waves

Fahe Miao; Michal Fečkan; Jinrong Wang

doi:10.3934/cpaa.2022067

Article Contents

2022, Volume 21, Issue 7: 2447-2461. Doi: 10.3934/cpaa.2022067

This issue Previous Article Stability analysis of the boundary value problem modelling a two-layer ocean Next Article The surface current of Ekman flows with time-dependent eddy viscosity

Exact solution and instability for geophysical edge waves

1.
Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China
2.
Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina 842 48, Bratislava, Slovakia
3.
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49,814 73 Bratislava, Slovakia

^* Corresponding author
^* Corresponding author

Received: October 2021

Revised: February 2022

Early access: March 2022

Published: July 2022

This work is partially supported by the National Natural Science Foundation of China (12161015), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA (grant Nos. 1/0358/20 and 2/0127/20).

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Abstract

We present an exact solution to the nonlinear governing equations in the $ \beta $-plane approximation for geophysical edge waves at an arbitrary latitude. Such an exact solution is derived in the Lagrange framework, which describes trapped waves propagating eastward or westward along a sloping beach with a shoreline parallel to the latitude line. Using the short-wavelength instability method, we establish a criterion for the instability of such waves.

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Mathematics Subject Classification: 35Q31 and 76B15 and 83C15.

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Figure 1. The rotation frame of reference

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Figure 2. The coordinate system for the sloping beach

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