Remarks on the stability of the Navier-Stokes equations supplemented with stress-free boundary conditions

TL;DR

This paper investigates the long-term stability of Navier-Stokes equations with Coriolis force and stress-free boundary conditions, revealing that axisymmetry can lead to spurious stability depending on the Coriolis force's presence.

Contribution

It provides new insights into how axisymmetry and Coriolis force influence the stability of fluid flows under stress-free boundary conditions.

Findings

Spurious stability can occur in axisymmetric domains.

The presence or absence of Coriolis force affects stability behavior.

Long-term stability analysis depends on domain symmetry and external forces.

Abstract

The purpose of this note is to analyze the long term stability of the Navier-Stokes equations supplemented with the Coriolis force and the stress-free boundary condition. It is shown that, if the flow domain is axisymmetric, spurious stability behaviors can occur depending whether the Coriolis force is active or not.