Infinite Prandtl number convection with Navier-slip boundary conditions

Christian Seis

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arXiv · 2504.11051

Infinite Prandtl number convection with Navier-slip boundary conditions

Christian Seis

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Abstract

We are concerned with infinite Prandtl number Rayleigh--B\'enard 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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Christian Seis. 2025-04-15. Infinite Prandtl number convection with Navier-slip boundary conditions. https://arxiv.org/abs/2504.11051

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