Infinite Prandtl number convection with Navier-slip boundary conditions

Seis, Christian

Abstract

We are concerned with infinite Prandtl number Rayleigh–Bénard convection with Navier-slip boundary conditions. The goal of this work is to estimate the average upward heat flux measured by the non-dimensional Nusselt number in terms of the Rayleigh number, which is a non-dimensional quantity measuring the imposed temperature gradient. We derive bounds on the Nusselt number that coincide for relatively small slip lengths with the optimal Nusselt number scaling for no-slip boundaries; for relatively large slip lengths, we recover scaling estimates for free-slip boundaries.