Numerical simulations of thermalof two-dimensional hemispherical turbulence

The two-dimensional Navier Stokes equations are often used as a model for describing turbulence in the atmosphere.
Indeed, atmospheric phenomena are confined in a layer of fluid whose 
dimensions are only a few kilometers in the vertical direction and thousands of kilometers in the horizontal directions. Even if this model cannot completely describethe complexity of the atmosphere, two dimensional simulations can still be used to mimic large-scale structures motionin the atmosphere. Quite recently H. Kellay et. al designed a new physical experiment: a thermal convection cell
composed by a half soap bubble heated at the equator. This device 
allowed them to study thermal convection and the movement of vortices on the surface of the bubble. The purpose of this talk is to present the mathematical model and the numerical simulations of this
hemispherical bubble heated at the equator and to compare the results to known behavior in classical Rayleigh-Benard
convection in three (or two) dimensional containers.