Infinite Prandtl Number Convection with Navier-Slip Boundary Conditions
Abstract
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 $$\textit{Nu}$$ Nu in terms of the Rayleigh number $$\textit{Ra}$$ Ra , 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, $$\textit{Nu}\lesssim \textit{Ra}^{1/3}$$ Nu ≲ Ra 1 / 3 ; for relatively large slip lengths, we recover scaling estimates for free-slip boundaries, $$\textit{Nu}\lesssim \textit{Ra}^{5/12}$$ Nu ≲ Ra 5 / 12 .
Fields of Study & Subjects
Fluid Dynamics and Turbulent Flows
Navier-Stokes equation solutions
Gas Dynamics and Kinetic Theory
Publication details
- Journal / source
- Communications in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 407
- Issue
- 6
- Publication date
- 2 May 2026
- Language
- EN