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

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 Coriolis forces in the fluid. However, owing to the curved surface of the bubble, the buoyancy and Coriolis forces vary with latitude on the bubble, giving rise to rich flow behaviour. 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 , and large-scale mean circulations that are strongly influenced by rotation. We then consider quantities that reveal the multiscale nature of the flow, including spectra and spectral fluxes of kinetic and thermal energy, enstrophy and structure functions of velocity and temperature. The fluxes show that just as for non-buoyant 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, owing to strong intermittency in the temperature field.