Thursday, May 24, 20122:00 PM - 3:00 PMCNLS Conference Room (TA-3, Bldg 1690)|
Ultimate State of Two-Dimensional Rayleigh-Benard Convection Between Free-Slip Fixed-Temperature Boundaries
Jared WhiteheadCCS-2 and CNLS
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