Toroidal and poloidal energy in rotating Rayleigh-Bénard convection

Abstract

We consider rotating Rayleigh-Bénard convection of a fluid with a Prandtl number of $Pr=0.8$ in a cylindrical cell with an aspect ratio $\Gamma =1/2$. Direct numerical simulations were performed for the Rayleigh number range $10^5\le Ra\le 10^9$ and the inverse Rossby number range $0\le 1/Ro\le 20$. We propose a method to capture regime transitions based on the decomposition of the velocity field into toroidal and poloidal parts. We identify four different regimes. First, a buoyancy dominated regime occurring as long as the toroidal energy $e_{tor}$ is not affected by rotation and remains equal to that in the non-rotating case, $e_{tor}^0$. Second, a rotation influenced regime, starting at rotation rates where $e_{tor}>e_{tor}^0$ and ending at a critical inverse Rossby number $1/R{o}_{cr}$ that is determined by the balance of the toroidal and poloidal energy, $e_{tor}=e_{pol}$. Third, a rotation dominated regime, where the toroidal energy $e_{tor}$ is larger than both, $e_{pol}$ and $e_{tor}^0$. Fourth, a geostrophic turbulence regime for high rotation rates where the toroidal energy drops below the value of non-rotating convection.

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