Global diffeomorphism of the Lagrangian flow-map defining Equatorially trapped water waves

TL;DR

This paper proves that the Lagrangian flow map for equatorially trapped water waves is a global diffeomorphism, ensuring the flow's mathematical well-posedness and physical plausibility.

Contribution

It demonstrates the global diffeomorphism property of the nonlinear exact solution for equatorially trapped water waves using analytical and topological methods.

Findings

The flow map is a global diffeomorphism.

The solution is mathematically well-posed.

The results support the physical realism of the model.

Abstract

The aim of this paper is to prove that a three dimensional Lagrangian flow which defines equatorially trapped water waves is dynamically possible. This is achieved by applying a mixture of analytical and topological methods to prove that the nonlinear exact solution to the geophysical governing equations, derived by Constantin in J. Geophys. Res., 117 (2012), is a global diffeomorphism from the Lagrangian labelling variables to the fluid domain beneath the free surface.