# American Institute of Mathematical Sciences

August  2019, 39(8): 4443-4453. doi: 10.3934/dcds.2019181

## Wind generated equatorial Gerstner-type waves

 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  July 2018 Revised  December 2018 Published  May 2019

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.

Citation: Anatoly Abrashkin. Wind generated equatorial Gerstner-type waves. Discrete & Continuous Dynamical Systems, 2019, 39 (8) : 4443-4453. doi: 10.3934/dcds.2019181
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