Inverse cascade and symmetry breaking in rapidly-rotating Boussinesq convection

TL;DR

This study uses numerical simulations to explore how rapid rotation influences convection, revealing the formation of large-scale vortices, inverse energy cascades, and persistent cyclonic dominance, with flow characteristics dependent on Rayleigh number.

Contribution

It demonstrates the emergence of large-scale vortices and inverse cascades in rapidly-rotating convection, highlighting the role of symmetry breaking and flow regime transitions.

Findings

Large-scale depth-invariant flow forms at moderate Rossby and high Rayleigh numbers.

Inverse energy cascade observed alongside direct cascade in turbulent flow.

Cyclonic structures dominate small-scale turbulence and persist at large scales.

Abstract

In this paper we present numerical simulations of rapidly-rotating Rayleigh-B\'enard convection in the Boussinesq approximation with stress-free boundary conditions. At moderately low Rossby number and large Rayleigh number, we show that a large-scale depth-invariant flow is formed, reminiscent of the condensate state observed in two-dimensional flows. We show that the large-scale circulation shares many similarities with the so-called vortex, or slow-mode, of forced rotating turbulence. Our investigations show that at a fixed rotation rate the large-scale vortex is only observed for a finite range of Rayleigh numbers, as the quasi-two-dimensional nature of the flow disappears at very high Rayleigh numbers. We observe slow vortex merging events and find a non-local inverse cascade of energy in addition to the regular direct cascade associated with fast small-scale turbulent motions. Finally, we show that cyclonic structures are dominant in the small-scale turbulent flow and this symmetry breaking persists in the large-scale vortex motion.