Connections between Non-Rotating, Slowly Rotating, and Rapidly Rotating Turbulent Convection Transport Scalings

TL;DR

This paper establishes connections between different turbulent convection scaling laws across non-rotating, slowly rotating, and rapidly rotating regimes, unifying diverse community approaches through the convective Rossby number.

Contribution

It introduces a unified framework linking various convection scalings across rotation regimes using the convective Rossby number, bridging different scientific communities.

Findings

Rotating and non-rotating scalings are interconnected via the convective Rossby number.

Mappings between flux-based and non-flux-based scalings are established.

Different community approaches to turbulent convection are shown to be fundamentally related.

Abstract

Buoyancy-driven convection is likely the dominant driver of turbulent motions in the universe, and thus, is widely studied by physicists, engineers, geophysicists and astrophysicists. Maybe unsurprisingly, these different communities discuss the gross convective behaviors in different ways, often without significant cross-talk existing between them. Here, we seek to draw connections between these communities. We do so by carrying out a set of basic scale estimations for how heat and fluid momentum transport should behave in non-rotating, slowly rotating and rapidly rotating buoyancy-driven convective environments. We find that slowly and rapidly rotating scalings can be inter-related via one parameter, the so-called convective Rossby number $\RoC$, a dissipation-free parameter measuring the importance of buoyancy driving relative to rotation. Further, we map between non-flux-based and the flux-based, buoyancy-driven scalings used by different groups. In doing so, these scalings show that there are clean connections between the different communities' approaches and that a number of the seemingly different scalings are actually synonymous with one another.