Thermal effects on the dynamics of vortex breakdown in spherical Couette flow

Abstract

This study investigates the effect of heating on the topology of vortex breakdown in spherical Couette flow under unstable thermal stratification. A three-dimensional spectral direct numerical solver is employed to solve the non-dimensionalised Navier–Stokes and energy equations. The inner sphere is rotated with constant angular velocity, while the outer sphere remains stationary. A constant temperature difference is maintained between the inner and outer spheres. The rotational effects are characterized by the Reynolds number (Re), while buoyancy-driven forces are quantified by the Rayleigh number (Ra). At low Ra, rotational forces dominate, resulting in steady, axisymmetric flow with well-defined vortex-detection bubbles and an equatorial jet. As Re increases, centrifugal instabilities lead to periodic oscillations and the formation of complex bubble structures. For higher Ra values, buoyancy-induced convection destabilizes the flow, transitioning it to nonaxisymmetric and chaotic states dominated by convective cells and large-scale circulation. The evolution of the vortex breakdown topology is characterized using streamlines and velocity magnitude distributions. Time series and their fast Fourier transform illustrate the transition from periodic oscillations to high-frequency complex unsteady flow. Dynamic mode decomposition analysis reveals the dominant spatiotemporal modes, providing insight into the interplay between rotational and buoyancy-driven instabilities. Thermal plumes, driven by buoyancy forces, enhance radial mixing and heat transfer, with their coherence and complexity increasing with Ra and Re.