Toroidal and poloidal energy in rotating Rayleigh–Bénard convection

We consider rotating Rayleigh–Bénard convection of a fluid with a Prandtl number of in a cylindrical cell with an aspect ratio . Direct numerical simulations (DNS) were performed for the Rayleigh number range and the inverse Rossby number range . 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 while the toroidal energy is not affected by rotation and remains equal to that in the non-rotating case, . Second, a rotation-influenced regime, starting at rotation rates where and ending at a critical inverse Rossby number that is determined by the balance of the toroidal and poloidal energy, . Third, a rotation-dominated regime, where the toroidal energy is larger than both and . Fourth, a geostrophic regime for high rotation rates where the toroidal energy drops below the value for non-rotating convection.