On three-dimensional Gerstner-like equatorial water waves

Abstract

This paper reviews some recent mathematical research activity in the field of nonlinear geophysical water waves. In particular, we survey a number of exact Gerstner-like solutions which have been derived to model various geophysical oceanic waves, and wave–current interactions, in the equatorial region. These solutions are nonlinear, three-dimensional and explicit in terms of Lagrangian variables.