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## Section: New Results

### Thermal convection on a hemisphere

Hamid Kellay (LOMA) performs a physical experiment using a half soap bubble heated at the equator. This device allows to study thermal convection and the movement of large scale structures on the surface of the bubble. The results show strong similarities with atmospheric flows on the earth. In particular large vortical structures on the half bubble and tropical cyclones in the atmosphere have the same dynamics.

Using a stereographic transform we solve Navier-Stokes equations on the half bubble and get very good agreement with the experiment. In addition we find that the Nusselt and Reynolds numbers varify scaling laws quite close to the scaling law given in the literature for Rayleigh-Bénard convection: $\mathrm{Nu}\propto {\mathrm{Ra}}^{0.31}$ and $\mathrm{Re}\propto {\mathrm{Ra}}^{1/2}$. Finally a Bolgieno regime is found with scaling as $R{a}^{-1/4}$.

Figure 8. Temperature (left) and vorticity (right) fields at the stationary state for $Ra=3.{10}^{8}$ and $Pr=7$. Plumes move upward and interact with each other.

Adding the rotation like on the earth we show that the rotation changes the nature of turbulent fluctuations and a new scaling regime is obtained for the temperature field.