Turbulence and heat transfer on a rotating, heated half soap bubble

TL;DR

This study uses direct numerical simulations to analyze the complex flow and heat transfer phenomena on a rotating, heated half soap bubble, revealing rich multiscale behaviors influenced by buoyancy, rotation, and curvature effects.

Contribution

It provides a detailed analysis of flow properties on a curved, rotating surface, highlighting the interplay of buoyancy and Coriolis forces and their impact on turbulence and heat transfer.

Findings

Non-monotonic dependence of flow properties on Rossby number

Large-scale circulations are strongly affected by rotation

Kinetic energy spectrum follows Bolgiano-Obukhov scaling at certain scales

Abstract

We use Direct Numerical Simulations to study the two-dimensional flow of a rotating, half soap bubble that is heated at its equator. The heating produces buoyancy and rotation generates a Coriolis forces in the fluid. However, due to the curved surface of the bubble, the buoyancy and Coriolis forces vary with latitude on the bubble, giving rise to rich flow behavior. We first explore the single-point properties of the flow, including the Reynolds and Nusselt numbers, mean fields, and Reynolds stresses, all as a function of latitude. For a given Rayleigh number, we observe a non-monotonic dependence on the Rossby number Ro, and large scale mean circulations that are strongly influenced by rotation. We then consider quantities that reveal the multiscale nature of the flow, including spectrums and spectral fluxes of kinetic and thermal energy, and enstrophy, and structure functions of velocity and temperature. The fluxes show that just a for nonbuoyant two-dimensional turbulence on a flat surface, there is an upscale flux of kinetic energy at larger scales (fed by buoyancy injection of turbulent kinetic energy at smaller scales), and a downscale flux of enstrophy at smaller scales. The kinetic energy spectrum and velocity structure functions are well described by Bolgiano-Obukhov (BO) scaling at scales where the effects of rotation are weak. The temperature structure functions do not, however, satisfy BO scaling in general, due to strong intermittency in the temperature field.