Variational formulations of steady rotational equatorial waves

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 -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. © 2021 Jifeng Chu and Joachim Escher, published by De Gruyter 2021.