Ekman boundary layers in a domain with topography

TL;DR

This paper studies the asymptotic behavior of rapidly rotating, nearly inviscid incompressible fluids in three-dimensional topographically complex domains, proving convergence of velocity fields to a 2D solution under well-prepared initial data.

Contribution

It establishes a convergence theorem for the velocity fields of the Navier-Stokes-Coriolis system in topographical domains, extending previous results to include land topography.

Findings

Velocity fields converge to a 2D solution

Weak convergence implies strong convergence over time

Results hold for well-prepared initial data

Abstract

We investigate the asymptotic behaviour of fast rotating incompressible fluids with vanishing viscosity, in a {three dimensional} domain with topography including the case of land area. Assuming the initial data is well-prepared, we prove a convergence theorem of the velocity fields to a two-dimensional vector field solving a linear, damped ordinary differential equation.The proof is based on a weak-strong uniqueness argument, combinedwith an abstract result implying that the weak convergence of a familyof weak solutions to the Navier-Stokes-Coriolis system can be translated into a form of uniform-in-time convergence.This argument yields strong convergence of the velocity fields, without a precise rate though.