A thermal Green-Naghdi model with time dependent bathymetry and complete Coriolis force

TL;DR

This paper develops a generalized Green-Naghdi model incorporating time-dependent bathymetry, complete Coriolis force, and thermal buoyancy in the Euler-Poincaré framework, aiming to improve ocean wave dynamics modeling.

Contribution

It introduces a novel Green-Naghdi equation with advanced features derived via a symmetry-broken variational principle, expanding the modeling capabilities for ocean dynamics.

Findings

Derivation of a generalized Green-Naghdi equation with new physical effects

Framework accommodating time-dependent bathymetry and thermal buoyancy

Potential applications in wave dynamics due to bathymetric changes

Abstract

This paper extends the theoretical Euler-Poincar\'e framework for modelling ocean mixed layer dynamics. Through a symmetry-broken Lie group invariant variational principle, we derive a generalised Green-Naghdi equation with time dependent bathymetry, a complete Coriolis force, and inhomogeneity of the thermal buoyancy. The nature of the model derived here lends it a potential future application to wave dynamics generated by changes to the bathymetry.