Coriolis-driven fluid motion on spherical surfaces

TL;DR

This paper studies the behavior of viscous fluids on spherical surfaces under Coriolis effects, proving global existence of solutions and their exponential convergence to aligned states.

Contribution

It establishes the existence of global solutions for incompressible viscous fluids on spheres with Coriolis force and shows their exponential convergence to rotation-aligned states.

Findings

Global solutions exist for divergence-free initial conditions.

Solutions converge exponentially to states aligned with sphere rotation.

The analysis incorporates Coriolis effects on spherical fluid motion.

Abstract

We consider the motion of an incompressible viscous fluid on a sphere, incorporating the effects of the Coriolis force. We demonstrate that global solutions exist for any divergence-free initial condition with finite kinetic energy. Furthermore, we show that each solution converges at an exponential rate to a state that is aligned with the rotation of the sphere.