Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers vs Interior Dynamics

TL;DR

This study combines simulations, experiments, and modeling to understand heat transfer in rapidly rotating convection, revealing the significant role of boundary layers and multiple dynamical regimes affecting heat transfer scaling.

Contribution

It demonstrates the impact of Ekman boundary layers on heat transfer and introduces an analytical parameterization that aligns simulations with experimental results.

Findings

Ekman boundary layers significantly influence heat transfer.

Adding Ekman transport parameterization improves simulation accuracy.

Multiple dynamical regimes exist in rapidly rotating convection.

Abstract

Rapidly rotating Rayleigh-B\'enard convection is studied by combining results from direct numerical simulations (DNS), laboratory experiments and asymptotic modeling. The asymptotic theory is shown to provide a good description of the bulk dynamics at low, but finite Rossby number. However, large deviations from the asymptotically predicted heat transfer scaling are found, with laboratory experiments and DNS consistently yielding much larger Nusselt numbers than expected. These deviations are traced down to dynamically active Ekman boundary layers, which are shown to play an integral part in controlling heat transfer even for Ekman numbers as small as $10^{-7}$. By adding an analytical parameterization of the Ekman transport to simulations using stress-free boundary conditions, we demonstrate that the heat transfer jumps from values broadly compatible with the asymptotic theory to states of strongly increased heat transfer, in good quantitative agreement with no-slip DNS and compatible with the experimental data. Finally, similarly to non-rotating convection, we find no single scaling behavior, but instead that multiple well-defined dynamical regimes exist in rapidly-rotating convection systems.