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Updated: May 30, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries
Jared P Whitehead1, Charles R Doering
1Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1034, USA. jaredwh@umich.edu
Abstract:
Rigorous upper limits on the vertical heat transport in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number Nu is bounded in terms of the Rayleigh number Ra according to Nu≤0.2891Ra(5/12) uniformly in the Prandtl number Pr. This scaling challenges some theoretical arguments regarding asymptotic high Rayleigh number heat transport by turbulent convection.
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