A thermal convection limit of spiral state in wide-gap spherical Couette flow

TL;DR

This paper investigates the stability and transition of spiral flow states in spherical Couette flow when thermal stratification is introduced, revealing how mechanical and thermal effects influence flow structures and their stability.

Contribution

It demonstrates the homotopy of spiral states from mechanical to thermal systems and identifies mode transitions in spherical harmonics under thermal effects.

Findings

The rotating wave state connects smoothly to thermal stratification systems.

Mode transition from $m=4$ to $l=4$ and $m=3$ in spherical harmonics.

Residual torque and circulation are analyzed at the thermal limit.

Abstract

The symmetries of flow structures are often prescribed by their mechanical instability and geometry. Here, as an example, we present the homotopy of the rotating 3-fold spiral state that is robust in a spherical Couette flow towards the hybrid system with a thermal stratification effect. It has not yet been confirmed that the rotating wave state smoothly connects to the thermal stratification system. Through continuation, the most dangerous mode at a purely spherical Couette flow of $m=4$ modes of spherical harmonics is replaced by $l=4$ and $m=3$ in a purely thermal convective system. For the state obtained at the limit under only the thermal effect, the residual quantities of both the torque to the outer sphere and meridional circulation are discussed in detail.