Toroidal and poloidal energy in rotating Rayleigh–Bénard convection

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 Γ=1/2 . Direct numerical simulations (DNS) were performed for the Rayleigh number range 10⁵ Ra 10⁹ and the inverse Rossby number range 0 1/Ro 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 while the toroidal energy eₜₒᵣ is not affected by rotation and remains equal to that in the non-rotating case, eₜₒᵣ⁰ . Second, a rotation-influenced regime, starting at rotation rates where eₜₒᵣ>eₜₒᵣ⁰ and ending at a critical inverse Rossby number 1/Rocr that is determined by the balance of the toroidal and poloidal energy, eₜₒᵣ=eₚₒₗ . Third, a rotation-dominated regime, where the toroidal energy eₜₒᵣ is larger than both eₚₒₗ and eₜₒᵣ⁰ . Fourth, a geostrophic regime for high rotation rates where the toroidal energy drops below the value for non-rotating convection.