Scale-by-scale kinetic energy flux calculations in simulations of rotating convection

TL;DR

This paper compares two methods for measuring scale-by-scale kinetic energy fluxes in rotating convection, revealing a dominant direct cascade with localized inverse cascades near boundaries, advancing understanding of turbulence in geophysical flows.

Contribution

It introduces and validates two techniques for measuring energy fluxes in anisotropic, confined rotating convection domains, enabling better analysis of energy transfer processes.

Findings

Bulk flow dominated by direct cascade

Inverse cascade prominent near top and bottom plates

Methods effectively measure fluxes in complex domains

Abstract

Turbulence is an out-of-equilibrium flow state that is characterised by nonzero net fluxes of kinetic energy between different scales of the flow. These fluxes play a crucial role in the formation of characteristic flow structures in many turbulent flows encountered in nature. However, measuring these energy fluxes in practical settings can be challenging as soon as one moves away from unrestricted turbulence in an idealised periodic box. Here, we focus on rotating Rayleigh-B\'enard convection, being the canonical model system to study geophysical and astrophysical flows. Owing to the effect of rotation, this flow can yield a split cascade, where part of the energy is transported to smaller scales (direct cascade), while another fraction is transported to larger scales (inverse cascade). We compare two different techniques for measuring these energy fluxes throughout the domain: one based on a spatial filtering approach and an adapted Fourier-based method. We show how one can use these methods to measure the energy flux adequately in the anisotropic, aperiodic domains encountered in rotating convection, even in domains with spatial confinement. Our measurements reveal that in the studied regime, the bulk flow is dominated by the direct cascade, while significant inverse cascading action is observed most strongly near the top and bottom plates, due to the vortex merging of Ekman plumes into larger flow structures.