Internal heating in rapidly rotating convection is not a shortcut to geostrophic turbulence
Abstract
Convective turbulence in planets and stars is often driven by internal heating. This forcing mechanism has also been proposed as a means of accessing the diffusion-free scalings of the geostrophic turbulence (GT) regime at modest forcing. We test this with the asymptotically reduced quasi-geostrophic model, which is formally valid in the limit of vanishing Ekman number, Ek → 0, and retains the Prandtl number as an independent parameter. We find no such shortcut: the Nusselt and Reynolds numbers are no closer to their diffusion-free predictions than in the boundary-heated case, and at Pr = 7 they are further from them; the predicted Pr−1/2 collapse fails; and the prefactor depends on the form of the heating. Our no-slip/stress-free cases track the radiatively driven simulations of Hadjerci et al. (2024) case by case, yet a 25% variation in Nu persists between sweeps that share the same reduced Rayleigh and Prandtl numbers but differ in Ekman number. Those data span only the narrow range of forcing over which the compensated Nusselt number is stationary; across the wider range accessible to the reduced model it rises to a maximum and then falls. We argue that bulk transport scalings are incomplete diagnostics of GT, whereas the saturation of the interior mean temperature gradient and of the vertical velocity kurtosis remain reliable indicators.
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BibTeX
@misc{nicoski2026internal,
title = {{Internal heating in rapidly rotating convection is not a shortcut to geostrophic turbulence}},
author = {Justin A. Nicoski and Tobias G. Oliver and Stefano Maffei and Michael A. Calkins},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28756},
eprint = {2608.28756},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28756},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Internal heating in rapidly rotating convection is not a shortcut to geostrophic turbulence
AU - Justin A. Nicoski
AU - Tobias G. Oliver
AU - Stefano Maffei
AU - Michael A. Calkins
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28756
UR - https://arxiv.org/abs/2608.28756
AB - Convective turbulence in planets and stars is often driven by internal heating. This forcing mechanism has also been proposed as a means of accessing the diffusion-free scalings of the geostrophic turbulence (GT) regime at modest forcing. We test this with the asymptotically reduced quasi-geostrophic model, which is formally valid in the limit of vanishing Ekman number, Ek → 0, and retains the Prandtl number as an independent parameter. We find no such shortcut: the Nusselt and Reynolds numbers are no closer to their diffusion-free predictions than in the boundary-heated case, and at Pr = 7 they are further from them; the predicted Pr^−1/2 collapse fails; and the prefactor depends on the form of the heating. Our no-slip/stress-free cases track the radiatively driven simulations of Hadjerci et al. (2024) case by case, yet a 25% variation in Nu persists between sweeps that share the same reduced Rayleigh and Prandtl numbers but differ in Ekman number. Those data span only the narrow range of forcing over which the compensated Nusselt number is stationary; across the wider range accessible to the reduced model it rises to a maximum and then falls. We argue that bulk transport scalings are incomplete diagnostics of GT, whereas the saturation of the interior mean temperature gradient and of the vertical velocity kurtosis remain reliable indicators.
ER -