**Titre/Title :**

Transitions in turbulent thermal convection, seen from the mechanical energy budget.

**Contact :**

Joel Sommeria

**Résumé/Abstract :**

The dynamics of turbulent convection are examined by considering the mechanical energy budget. We present for the first time a decomposition of the flow into contributions having large and small length scales, or mean and turbulent components. Three-dimensional Direct Numerical Simulations and Large Eddy Simulations are used, and we compare Rayleigh-B´enard convection (in a fluid layer heated below and cooled above) to horizontal convection (in a long box with differential heating along its base), up to Rayleigh numbers never before simulated. At very large Rayleigh numbers most of the available potential energy goes into motion at large-scales, and the large-scale ’wind’ undergoes shear instabilities that sustain small-scale turbulence. This answers a question that has been particularly controversial for horizontal convection. We also, for the first time, explicitly include gravitational potential energy in the mechanical energy budget and show that there are two ’sinks’ of the available potential energy supplied by heating and cooling, viscous dissipation and irreversible mixing. The rate of mixing (relative to the total "dissipation" by mixing and viscosity) approaches 50% in Rayleigh-Benard convection and 100% in horizontal convection. Although viscous dissipation becomes predominantly turbulent, such a small viscous dissipation in horizontal convection suggests that this quantity is not a useful indicator of the style of flow.