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- W3095248049 abstract "Steady two-dimensional Rayleigh--B'enard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios $pi/5leGammale4pi$, where $Gamma$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $10^3le Rale10^{11}$, and four orders of magnitude in the Prandtl number, $10^{-2}le Prle10^2$. At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $Ra rightarrow infty$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $Ra^{1/3}$ uniformly in $Pr$. The prefactor of this scaling depends on $Gamma$ and is largest at $Gamma approx 1.9$. The Reynolds number $Re$ for large-$Ra$ rolls scales as $Pr^{-1} Ra^{2/3}$ with a prefactor that is largest at $Gamma approx 4.5$. All of these large-$Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox (2009). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $Gamma$ is smaller." @default.
- W3095248049 created "2020-11-09" @default.
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- W3095248049 date "2020-11-04" @default.
- W3095248049 modified "2023-09-27" @default.
- W3095248049 title "Steady Rayleigh–Bénard convection between stress-free boundaries" @default.
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- W3095248049 doi "https://doi.org/10.1017/jfm.2020.812" @default.
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