Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

Abstract

We present numerical simulations, using two complementary setups, of rotating Boussinesq thermal convection in a three-dimensional Cartesian geometry with misaligned gravity androtation vectors. This model represents a small region at a non-polar latitude in the convection zone of a star or planet. We investigate the effects of rotation on the bulk properties of convection at different latitudes, focusing on determining the relation between the heat flux andtemperature gradient. We show that our results may be interpreted using rotating mixing lengththeory (RMLT). The simplest version of RMLT (due to Stevenson) considers the single mode that transports the most heat. This works reasonably well in explaining our results, but there is a systematic departure from these predictions (up to approximately 30% in the temperature gradient) at mid-latitudes. We develop a more detailed treatment of RMLT that includes the transport afforded by multiple modes, and we show that this accounts for most of the systematic differences. We also show that convectively-generated zonal flows and meridional circulations are produced in our simulations, and that their properties depend strongly on the dimensionsof the box. These flows also affect the heat transport, contributing to departures from RMLT at some latitudes. However, we find the theoretical predictions of the multi-mode theory for the mid-layer temperature gradient, the root-mean-square (RMS) vertical velocity, the RMS temperature fluctuation, and the spatial spectrum of the heat transport at different latitudes ,are all in reasonably good agreement with our numerical results when zonal flows are small.