Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries

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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≤0.2891Ra5/12 uniformly in the Prandtl number Pr. This scaling challenges some theoretical arguments regarding asymptotic high Rayleigh number heat transport by turbulent convection. © 2011 American Physical Society.

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Whitehead, J. P., & Doering, C. R. (2011). Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries. Physical Review Letters, 106(24). https://doi.org/10.1103/PhysRevLett.106.244501

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