Quasi-geostrophic Rayleigh-B\'enard convection on the tilted $f$-plane

TL;DR

This study numerically investigates rapidly rotating quasi-geostrophic Rayleigh-Bénard convection on an f-plane, revealing how tilt influences large-scale flow structures, heat transport, and the persistence of temperature gradients in geophysically relevant regimes.

Contribution

It extends prior work by analyzing the effects of tilt on convection structures and heat transport using an asymptotically reduced quasi-geostrophic model applicable to rapid rotation.

Findings

Tilt causes a transition from vortices to zonal flows.

Global heat and momentum transport decrease with tilt angle.

Lateral thermal mixing maintains a persistent temperature gradient.

Abstract

Rapidly rotating Rayleigh-B\'enard convection on a $f$-plane at colatitude $\vartheta_f$ is investigated numerically using an asymptotically reduced equation set valid in the limit of very rapid rotation. The equations provide a non-hydrostatic but quasi-geostrophic description in a non-orthogonal coordinate system. The tilt changes the structure of the large-scale barotropic condensate from large-scale vortices to zonal flows as the colatitude of the $f$-plane increases, with bistable states present for certain parameter ranges, extending prior work to a geophysically significant parameter regime. This behaviour is understood through the impact of broken rotation symmetry on the barotropic source terms resulting from baroclinic vortical stresses and baroclinic torque. As the tilt angle $\vartheta_f$ increases, global heat and momentum transport is reduced relative to upright-polar convection, a result that is explained through linear theory and nonlinear power maps both of which demonstrate increased attenuation of the domain of dynamically active spatial scales as the convective modes depart from a North-South alignment in the horizontal plane. A key finding is that the predominance of lateral thermal mixing allows for the maintenance of a persistent unstable mean temperature gradient that saturates at increasing forcing levels and remains insensitive to the colatitude.