Toroidal and poloidal energy in rotating Rayleigh-B\'enard convection

TL;DR

This study investigates how energy is distributed between toroidal and poloidal components in rotating Rayleigh-Bénard convection, identifying four distinct flow regimes across a range of rotation rates and Rayleigh numbers.

Contribution

It introduces a novel method to analyze regime transitions by decomposing the velocity field into toroidal and poloidal parts in rotating convection.

Findings

Four distinct flow regimes identified based on energy decomposition.

Regime transitions depend on the balance between toroidal and poloidal energies.

The method captures the influence of rotation on convective flow structures.

Abstract

We consider rotating Rayleigh-B\'enard 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 $10^5 \leq Ra \leq 10^9$ and the inverse Rossby number range $0 \leq 1/Ro \leq 20$. 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, $e^0_{tor}$. Second, a rotation influenced regime, starting at rotation rates where $e_{tor} > e^0_{tor}$ and ending at a critical inverse Rossby number $1/Ro_{cr}$ 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 $e^0_{tor}$. Fourth, a geostrophic turbulence regime for high rotation rates where the toroidal energy drops below the value of non-rotating convection.