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Center for Nonlinear Studies |
Rigorous upper limits on the vertical heat transport in two-dimensional Rayleigh- Benard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number Nu is bounded in terms of the Rayleigh number Ra according to Nu 0:2891Ra5=12 uniformly in the Prandtl number Pr. This scaling challenges some theoretical arguments regarding asymptotic high Rayleigh number heat transport by turbulent convection.
If time permits I will present an overview of additional results in three-dimensions but with restriction on the Prandtl number. Other cases of interest including mixed thermal and Navier-slip boundaries will be reviewed to indicate open problems and future work. The use of asymptotically motivated numerics, and the motivation said numerics provide will be emphasized.
Host: Kipton Barros, T-4 and CNLS