Wind generated equatorial Gerstner-type waves

Anatoly Abrashkin

doi:10.3934/dcds.2019181

Article Contents

2019, Volume 39, Issue 8: 4443-4453. Doi: 10.3934/dcds.2019181

This issue Previous Article Existence of solutions for nonlinear operator equations Next Article Weak periodic solutions and numerical case studies of the Fornberg-Whitham equation

Wind generated equatorial Gerstner-type waves

Anatoly Abrashkin

National Research University Higher School of Economics, 25/12 Bol'shaya Pecherskaya str., Nizhny Novgorod, 603155, Russia

The paper is for the special theme: Mathematical Aspects of Physical Oceanography, organized by Adrian Constantin

Received: June 30, 2018

Revised: November 30, 2018

Published: May 2019

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Abstract

A class of non-stationary surface gravity waves propagating in the zonal direction in the equatorial region is described in the f-plane approximation. These waves are described by exact solutions of the equations of hydrodynamics in Lagrangian formulation and are generalizations of Gerstner waves. The wave shape and non-uniform pressure distribution on a free surface depend on two arbitrary functions. The trajectories of fluid particles are circumferences. The solutions admit a variable meridional current. The dynamics of a single breather on the background of a Gerstner wave is studied as an example.

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Mathematics Subject Classification: Primary: 76B15; Secondary: 86A05, 74G05, 70H03.

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