Destabilization of free convection by weak rotation

TL;DR

This paper investigates how weak rotation can destabilize free convective flows by analyzing models where centrifugal forces oppose main circulation, revealing mechanisms involving vortex splitting and thermal stratification.

Contribution

It provides a detailed explanation of destabilization mechanisms in rotating convection flows, including effects at different Prandtl numbers and applications to magnetic and crystal growth flows.

Findings

Destabilization occurs when centrifugal force opposes main circulation.

Low Prandtl numbers lead to vortex splitting and instability.

High Prandtl numbers cause thermal stratification steepening, triggering Rayleigh-Bénard instability.

Abstract

This study offers an explanation of a recently observed effect of destabilization of free convective flows by weak rotation. After studying several models where flows are driven by a simultaneous action of convection and rotation, it is concluded that the destabilization is observed in the cases where centrifugal force acts against main convective circulation. At relatively low Prandtl numbers this counter action can split the main vortex into two counter rotating vortices, where the interaction leads to instability. At larger Prandtl numbers, the counter action of the centrifugal force steepens an unstable thermal stratification, which triggers Rayleigh-B\'enard instability mechanism. Both cases can be enhanced by advection of azimuthal velocity disturbances towards the axis, where they grow and excite perturbations of the radial velocity. The effect was studied considering a combined convective/rotating flow in a cylinder with a rotating lid and a parabolic temperature profile at the sidewall. Next, explanations of the destabilization effect for rotating magnetic field driven flow and melt flow in a Czochralski crystal growth model were derived.