An existence result for the steady rotating Prandtl equation

TL;DR

This paper proves the well-posedness of a variant of the Prandtl equation modeling steady geophysical boundary layers, under specific assumptions about interior flow variations and coastline profile.

Contribution

It introduces a new existence result for the steady rotating Prandtl equation using the von Mises change of variables, under particular boundary and interior conditions.

Findings

The equation is well-posed with large interior flow variations.

Moderate variations in coastline profile are sufficient for well-posedness.

The von Mises transformation is effective for analyzing this boundary layer problem.

Abstract

We consider a steady, geophysical 2D fluid in a domain, and focus on its western boundary layer, which is formally governed by a variant of the Prandtl equation. By using the von Mises change of variables, we show that this equation is well-posed under the assumption that the trace of the interior stream function has large variations, and that the variations in the coastline profile are moderate.