Steady Rayleigh--B\'enard convection between stress-free boundaries
| Autor: | Matthew LeDuc, Charles R. Doering, David Goluskin, Gregory P. Chini, Baole Wen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Convection
Materials science Mechanical Engineering Mechanics Physics - Fluid Dynamics Condensed Matter Physics 01 natural sciences Isothermal process 010305 fluids & plasmas Physics::Fluid Dynamics Mechanics of Materials 0103 physical sciences 010306 general physics Stress free Rayleigh–Bénard convection |
| Popis: | 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 $\pi/5\le\Gamma\le4\pi$, where $\Gamma$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $10^3\le Ra\le10^{11}$, and four orders of magnitude in the Prandtl number, $10^{-2}\le Pr\le10^2$. 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|