Bound on vertical heat transport at large Prandtl number
نویسنده
چکیده
We prove a new upper bound on the vertical heat transport in Rayleigh-Bénard convection of the form c Ra 1 3 (lnRa) 2 3 under the assumption that the ratio of Prandtl number over Rayleigh number satisfies Pr Ra ≥ c0 where the non-dimensional constant c0 depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) Ra 1 3 bound (modulo logarithmic correction) on vertical heat transport for the infinite Prandtl number model for convection due to Constantin and Doering [6] and Doering, Otto and Reznikoff [10]. It also improves a uniform (in Prandtl number) Ra 1 2 bound for the Nusselt number [5] in the case of large Prandtl number. keywords: Rayleigh-Bénard convection, Boussinesq equations, Prandtl number, Rayleigh number, Nusselt number
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