# Scaling regimes in spherical shell rotating convection

@article{Gastine2016ScalingRI, title={Scaling regimes in spherical shell rotating convection}, author={Thomas Gastine and Johannes Wicht and Julien Aubert}, journal={Journal of Fluid Mechanics}, year={2016}, volume={808}, pages={690 - 732} }

Rayleigh–Bénard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use three-dimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning $3\times 10^{-7}\leqslant E\leqslant 10^{-1}$ , Rayleigh numbers within the range $10^{3}<Ra<2\times 10^{10}$ and a Prandtl number of…

## 66 Citations

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## References

SHOWING 1-10 OF 100 REFERENCES

Turbulent Rayleigh–Bénard convection in spherical shells

- PhysicsJournal of Fluid Mechanics
- 2015

We simulate numerically Boussinesq convection in non-rotating spherical shells for a fluid with a Prandtl number of unity and for Rayleigh numbers up to $10^{9}$ . In this geometry, curvature and…

Scaling behaviour in Rayleigh–Bénard convection with and without rotation

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract Rotating Rayleigh–Bénard convection provides a simplified dynamical analogue for many planetary and stellar fluid systems. Here, we use numerical simulations of rotating Rayleigh–Bénard…

Toroidal and poloidal energy in rotating Rayleigh–Bénard convection

- PhysicsJournal of Fluid Mechanics
- 2014

Abstract We consider rotating Rayleigh–Bénard convection of a fluid with a Prandtl number of $\mathit{Pr}=0.8$ in a cylindrical cell with an aspect ratio ${\it\Gamma}=1/2$ . Direct numerical…

Heat transport in the geostrophic regime of rotating Rayleigh-Bénard convection.

- Physics, Environmental SciencePhysical review letters
- 2014

We report experimental measurements of heat transport in rotating Rayleigh-Bénard convection in a cylindrical convection cell with an aspect ratio of Γ=1/2. The fluid is helium gas with a Prandtl…

Experiments on highly supercritical thermal convection in a rapidly rotating hemispherical shell

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 2003

We report experimental results on highly supercritical thermal convection in a rapidly rotating hemispherical shell with parabolic gravity. Using silicone oil as the working fluid and an Ekman number…

The onset of thermal convection in rotating spherical shells

- PhysicsJournal of Fluid Mechanics
- 2004

The correct asymptotic theory for the linear onset of instability of a Boussinesq fluid rotating rapidly in a self-gravitating sphere containing a uniform distribution of heat sources was given…

Nonlinear dynamics of boussinesq convection in a deep rotating spherical shell-i

- Physics
- 1977

Abstract Convection in a rotating spherical shell has wide application for understanding the dynamics of the atmospheres and interiors of many celestial bodies. In this paper we review linear results…

The quasi-geostrophic model for rapidly rotating spherical convection outside the tangent cylinder

- PhysicsJournal of Fluid Mechanics
- 2006

Rapidly rotating convection in spherical geometry outside the tangent cylinder is investigated using the quasi-geostrophic approximation. The validity of the approximation is discussed, and numerical…

Zonal flow driven by strongly supercritical convection in rotating spherical shells

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 2002

Thermal convection in a rotating spherical shell with free-slip boundaries can excite a dominant mean zonal flow in the form of differentially rotating cylinders concentric to the principal rotation…

Heat transfer by rapidly rotating Rayleigh–Bénard convection

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 2012

Abstract Turbulent, rapidly rotating convection has been of interest for decades, yet there exists no generally accepted scaling law for heat transfer behaviour in this system. Here, we develop an…