Exact solutions of fluid equations on a sphere

TL;DR

This paper derives exact solutions to the Navier-Stokes and Euler equations on a spherical surface, highlighting a unique vortex flow pattern under specific assumptions.

Contribution

It presents the first exact solutions of fluid equations on a sphere, identifying a unique vortex flow with zero convection term.

Findings

Exact solutions for Navier-Stokes and Euler equations on a sphere

Unique vortex flow with oppositely rotating point vortices at poles

Flow solution valid under zero convection assumption

Abstract

Exact solutions of both the Navier-Stokes and Euler equations are found on the surface of a sphere. Under the assumption of a vanishing convection term, the flow of two oppositely rotating point vortices at the poles turns out to be the unique common solution.