Infinite Prandtl number convection with Navier-slip boundary conditions

2025/04/15 by Seis, Christian
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.11051

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 nondimensional Nusselt number Nu in terms of the Rayleigh number Ra, which is a nondimensional 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, Nu\lesssim Ra^1/3; for relatively large slip lengths, we recover scaling estimates for free-slip boundaries, Nu\lesssim Ra^5/12.

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