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Boundary layer control of rotating convection systems

Abstract

Turbulent rotating convection controls many observed features of stars and planets, such as magnetic fields, atmospheric jets and emitted heat flux patterns1,2,3,4,5,6. It has long been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force7,8,9,10,11,12. Here, however, we present results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. We formulate a predictive description of the transition between the two regimes on the basis of the competition between these two boundary layers. This transition scaling theory unifies the disparate results of an extensive array of previous experiments8,9,10,11,12,13,14,15, and is broadly applicable to natural convection systems.

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Figure 1: Iso-surfaces of vertical velocity, from numerical experiments.
Figure 2: Nusselt number versus Rayleigh number.
Figure 3: The transition from rotationally controlled to non-rotating heat transfer behaviour.
Figure 4: Nusselt number versus the convective Rossby number for laboratory experiments in water (Pr ≈ 7) with 3 × 10-6E ≤ 10-2.

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Acknowledgements

Salary support for E.M.K., J.N. and J.M.A. was provided by the US National Science Foundation Earth Sciences Division Geophysics Program and the NASA Planetary Atmospheres Program. Support for S.S. and U.H. was provided by the German Research Foundation and for S.S. by the NASA Solar and Heliospheric Physics Program. Support for laboratory experiment fabrication was provided by the US National Science Foundation Instrumentation & Facilities Program. Computational resources were provided by the John von Neumann-Institut für Computing. E.M.K., J.N. and J.M.A. would like to thank J. Frydman, J. Neal, A. Yaghmaei and R. M. Aurnou for engineering support in experimental development. E.M.K. and J.M.A. would like to thank H. T. Rossby for making his thesis data available to them, J. McWilliams for discussion and S. R. Dickman for introducing them to geophysics.

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Correspondence to Eric M. King.

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King, E., Stellmach, S., Noir, J. et al. Boundary layer control of rotating convection systems. Nature 457, 301–304 (2009). https://doi.org/10.1038/nature07647

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