Boundary Layer Analysis for the Fast Horizontal Rotating Fluids

TL;DR

This paper investigates the boundary layer behavior of fast rotating fluids with rotation axes parallel to the boundary, deriving a nonlinear PDE system similar to the 2-D Prandtl system and proving its well-posedness in analytic function spaces.

Contribution

It introduces a new boundary layer model for parallel rotation axes and establishes well-posedness results, extending understanding beyond the classical Ekman layer case.

Findings

Derived a nonlinear PDE system for the boundary layer with parallel rotation.

Proved well-posedness of the boundary layer system in analytic function spaces.

Identified similarities to the 2-D Prandtl system in the boundary layer dynamics.

Abstract

It is well known that, for fast rotating fluids with the axis of rotation being perpendicular to the boundary, the boundary layer is of Ekman-type, described by a linear ODE system. In this paper we consider fast rotating fluids, with the axis of rotation being parallel to the boundary. We show that the corresponding boundary layer is describe by a nonlinear, degenerated PDE system which is similar to the 2-D Prandtl system. Finally, we prove the well-posedness of the governing system of the boundary layer in the space of analytic functions with respect to tangential variable.