Numerical simulations of turbulent thermal convection on the surface of a soap bubble

I present in this paper an unusual method to implement cartesian computations to solve a CFD spherical problem. The problem consists in performing the numerical simulations of a half bubble of soap located on a heated ring. The gradient of temperature between the base and the top of the bubble generates plumes at the base that move up their surfaces. These plumes give rise to eddies that survive for several minutes eventually creating a two-dimensional turbulent thermal convective flow. Our method consists in defining an appropriate stereographic projection in order to use classical numerical scheme defined for two-dimensional Navier-Stokes equations. The results are then analyzed and compared to real soap bubble experiments data and cyclones data.