Scaling behaviour in Rayleigh–Bénard convection with and without rotation

Abstract

Abstract Rotating Rayleigh–Bénard convection provides a simplified dynamical analogue for many planetary and stellar fluid systems. Here, we use numerical simulations of rotating Rayleigh–Bénard convection to investigate the scaling behaviour of five quantities over a range of Rayleigh ( $1{0}^{3} \lesssim \mathit{Ra}\lesssim 1{0}^{9} $ ), Prandtl ( $1\leq \mathit{Pr}\leq 100$ ) and Ekman ( $1{0}^{- 6} \leq E\leq \infty $ ) numbers. The five quantities of interest are the viscous and thermal boundary layer thicknesses, ${\delta }_{v} $ and ${\delta }_{T} $ , mean temperature gradients, $\beta $ , characteristic horizontal length scales, $\ell $ , and flow speeds, $\mathit{Pe}$ . Three parameter regimes in which different scalings apply are quantified: non-rotating, weakly rotating and rotationally constrained. In the rotationally constrained regime, all five quantities are affected by rotation. In the weakly rotating regime, ${\delta }_{T} $ , $\beta $ and $\mathit{Pe}$ , roughly conform to their non-rotating behaviour, but ${\delta }_{v} $ and $\ell $ are still strongly affected by the Coriolis force. A summary of scaling results is given in table 2.