Entropy and energy spectra in low-Prandtl-number convection with rotation

Abstract

We present results for entropy and kinetic energy spectra computed from direct numerical simulations for low-Prandtl-number ($Pr<1$) turbulent flow in Rayleigh-Bénard convection with uniform rotation about a vertical axis. The simulations are performed in a three-dimensional periodic box for a range of Taylor number ($0\le Ta\le 10^8$) and reduced Rayleigh number $r=Ra/R{a}_{\circ }(Ta,Pr)$ ($1.0\times 10^2\le r\le 5.0\times 10^3$). The Rossby number $Ro$ varies in the range $1.34\le Ro\le 73$. The entropy spectrum $E_{\theta }(k)$ shows bi-splitting into two branches for lower values of wave number $k$. The entropy in the lower branch scales with $k$ as $k^{-1.4\pm 0.1}$ for $r>10^3$ for the rotation rates considered here. The entropy in the upper branch also shows scaling behavior with $k$, but the scaling exponent decreases with increasing $Ta$ for all $r$. The energy spectrum $E_v(k)$ is also found to scale with the wave number $k$ as $k^{-1.4\pm 0.1}$ for $r>10^3$. The scaling exponent for the energy spectrum and the lower branch of the entropy spectrum vary between $-1.7$ to $-2.4$ for lower values of $r$ ($<10^3$). We also provide some simple arguments based on the variation of the Kolmogorov picture to support the results of simulations.

12 pages, 8 postscript figures, 1 table, A slightly modified version is to appear in Physical Review E

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