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 and rotation 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 and temperature gradient. We show that our results may be interpreted using rotating mixing length theory (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 dimensions of 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.

26 pages, 15 figures, accepted for publication in MNRAS

References in corpus (12)

• New evolutionary models for pre-main sequence and main sequence low-mass stars down to the hydrogen-burning limit
• Evolution of low-mass star and brown dwarf eclipsing binaries
• Solar differential rotation and meridional flow: The role of a subadiabatic tachocline for the Taylor-Proudman balance
• Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers vs Interior Dynamics
• Scaling regimes in spherical shell rotating convection
• Inverse cascade and symmetry breaking in rapidly-rotating Boussinesq convection
• Large-scale vortices in rapidly rotating Rayleigh-Bénard convection
• The Emergence of Solar Supergranulation as a Natural Consequence of Rotationally-Constrained Interior Convection
• Theory and simulations of rotating convection
• Heat transport in rotating convection without Ekman layers
• The magnitude of viscous dissipation in strongly stratified two-dimensional convection
• Predicting the Rossby number in convective experiments

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