Abstract

Bounds are derived for rotating Rayleigh–Bénard convection with free slip boundaries as a function of the Rayleigh, Taylor and Prandtl numbers ${\textit {Ra}}$ , {Ta}}$ {Pr}}$ . At infinite {Ta}} > 130$ Nusselt number {Nu}}$ obeys {Nu}} \leqslant \frac {7}{36} \left ({4}/{{\rm \pi} ^2} \right )^{1/3} {\textit {Ra}} {Ta}}^{-1/3}$ whereas kinetic energy density $E_{kin}$ $E_{kin} ({7}/{72 {\rm...

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) ...