# Numerical study on the axisymmetric state in spherical Couette flow under unstable thermal stratification

## TL;DR

This numerical study explores how thermal stratification influences the transition from axisymmetric to non-axisymmetric flow in spherical Couette flow, revealing that thermal effects can both promote and suppress flow transitions depending on conditions.

## Contribution

It extends the understanding of spherical Couette flow by analyzing the combined effects of shear and thermal stratification, especially in wide gap geometries, through detailed numerical simulations.

## Key findings

- Thermal buoyancy lowers the critical Reynolds number for transition.
- Transition patterns connect to classical spherical Bénard convection states.
- Thermal effects can both facilitate and inhibit flow state changes.

## Abstract

This paper numerically investigates the shear flow between double concentric spherical boundaries rotating differentially, so-called spherical Couette flow, under unstable thermal stratification, focusing on the boundary of the axisymmetric/non-axisymmetric transition in wide gap cases where the inner radius is comparable to the clearance width. While the transition of SCF has been confirmed experimentally in cases without thermal factor, insufficient knowledge on SCF subject to thermal instability, related to geophysical problems especially in wide gap cases, has been accumulated mainly based on numerical analysis; our motivation is to bridge the knowledge gap by a parameter extension. We reconfirm that the transition under no thermal effect is initiated by a disturbance visualised as a spiral pattern with n arms extending from the equatorial zone to the pole in each hemisphere, at the critical Reynolds number, Recr, as previously reported. With increasing thermal factor, the buoyancy effect assists the system rotation to trigger a transition towards non-axisymmetric states, resulting in a relative decrease of Recr. This is in contrast with the result that the system rotation apparently suppresses via Coriolis effect the transition to the thermally convective states at low Reynolds numbers. The present study elucidates that the existence of the axisymmetric state is restricted within a closed area in the extended parameter space, along the boundary of which the spiral patterns observed experimentally in SCF continually connect to the classical spherical Benard convective states.