Bounds for rotating Rayleigh-Bénard convection at large Prandtl number

Abstract

Bounds are derived for rotating Rayleigh-Bénard convection with free slip boundaries as a function of the Rayleigh, Taylor and Prandtl numbers, and. At infinite and 130$]]>, the Nusselt number obeys, whereas the kinetic energy density obeys in the frame of reference in which the total momentum is zero, and. These three bounds are derived from the momentum equation and the maximum principle for temperature and are extended to general. The extension to finite is based on the fact that the maximal velocity in rotating convection at infinite is bound by.