Impact of domain anisotropy on the inverse cascade in geostrophic turbulent convection

TL;DR

This paper examines how domain anisotropy influences the inverse energy cascade in geostrophic turbulence within rapidly rotating Rayleigh-Bénard convection, revealing different large-scale flow structures depending on domain shape.

Contribution

It demonstrates the impact of domain shape on flow states in geostrophic turbulence and connects these findings to statistical mechanics principles and inviscid invariants.

Findings

Square domains favor a domain-filling dipole state.

Rectangular domains produce jet and vortex structures.

Flow structures are linked to inviscid invariants and statistical mechanics.

Abstract

The effect of domain anisotropy on the inverse cascade occurring within the geostrophic turbulence regime of rapidly rotating Rayleigh-B\'enard convection (RRBC) is investigated. In periodic domains with square cross-section in the horizontal a domain-filling dipole state is present. For rectangular periodic domains a Kolmogorov-like flow consisting of a periodic array of alternating unidirectional jets with embedded vortices is observed, together with an underlying weak meandering transverse jet. Similar transitions occurring in weakly dissipative two-dimensional flows driven by externally imposed small amplitude noise as well as in classical hydrostatic geostrophic turbulence are a consequence of inviscid conservation of energy and potential enstrophy and can be understood using statistical mechanics considerations. RRBC represents an important three-dimensional system with only one inviscid invariant that nonetheless exhibits large-scale structures driven by intrinsically generated fluctuations.