Definitive scaling relations for rotating-convection length scales

Establish definitive scaling relations between the control parameters of geophysically relevant rapidly rotating convection and the characteristic length scales of temperature anomalies, to improve predictions of heat transport and magnetic induction in the fluid layers of stars, planets, and moons.

Background

The paper examines a thermally driven, rapidly rotating laboratory experiment in which centrifugal convection, baroclinic instability, and zonal jets coexist. The authors compare observed temperature structures with several predicted length scales, including the rotating-convection onset scale and a diffusivity-free convective Rhines scale.

Although these estimates identify the observed structures as convective, the authors state that the quantitative relationship between control parameters and the characteristic temperature-anomaly length scale is unresolved. A definitive scaling law would be important for predicting heat transport and magnetic induction in geophysical and astrophysical fluid layers.

References

Though the estimates for $\ell_{\text{onset}$ and $\ell_{\text{conv}$ adequately identify the structures in panels (d--f) as convective, the quantitative relationship between the control parameters and the characteristic temperature anomaly length-scale in this system requires further investigation. Definitive scaling relations for length-scales in geophysically-relevant regimes of rotating convection remain elusive \citep{guervilly_turbulent_2019,oliver_small_2023} and are essential to predictions of heat transport and magnetic induction in the fluid layers of stars, planets, and moons.

— Infrared imaging of thermally-driven jets and eddies in planetary-style laboratory turbulence  (2608.12694 - David et al., 13 Aug 2026) in Section 3, paragraph beginning “Whereas baroclinic instability involves the exchange...”