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Numerical Study of Rotating Thermal Convection on a Hemisphere

Institut de Mathématiques de Bordeaux (IMB), Université de Bordeaux, CNRS UMR 5251, F-33400 Talence, France
Laboratoire Ondes et Matiere d’Aquitaine (LOMA), Université de Bordeaux, CNRS UMR 5798, F-33400 Talence, France
Author to whom correspondence should be addressed.
Fluids 2020, 5(4), 185;
Received: 29 September 2020 / Revised: 10 October 2020 / Accepted: 12 October 2020 / Published: 20 October 2020
(This article belongs to the Special Issue Thermal Flows)
Numerical simulations of rotating two-dimensional turbulent thermal convection on a hemisphere are presented in this paper. Previous experiments on a half soap bubble located on a heated plate have been used for studying thermal convection as well as the effects of rotation on a curved surface. Here, two different methods have been used to produce the rotation of the hemisphere: the classical rotation term added to the velocity equation, and a non-zero azimuthal velocity boundary condition. This latter method is more adapted to the soap bubble experiments. These two methods of forcing the rotation of the hemisphere induce different fluid dynamics. While the first method is classically used for describing rotating Rayleigh–Bénard convection experiments, the second method seems to be more adapted for describing rotating flows where a shear layer may be dominant. This is particularly the case where the fluid is not contained in a closed container and the rotation is imposed on only one side of it. Four different diagnostics have been used to compare the two methods: the Nusselt number, the effective computation of the convective heat flux, the velocity and temperature fluctuations root mean square (RMS) generation of vertically aligned vortex tubes (to evaluate the boundary layers) and the energy/enstrophy/temperature spectra/fluxes. We observe that the dynamics of the convective heat flux is strongly inhibited by high rotations for the two different forcing methods. Also, and contrary to classical three-dimensional rotating Rayleigh–Bénard convection experiments, almost no significant improvement of the convective heat flux has been observed when adding a rotation term in the velocity equation. However, moderate rotations induced by non-zero velocity boundary conditions induce a significant enhancement of the convective heat flux. This enhancement is closely related to the presence of a shear layer and to the thermal boundary layer just above the equator. View Full-Text
Keywords: computational fluid dynamics; turbulence; rotating thermal convection; Rayleigh–Bénard computational fluid dynamics; turbulence; rotating thermal convection; Rayleigh–Bénard
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MDPI and ACS Style

Fischer, P.; Bruneau, C.-H.; Kellay, H. Numerical Study of Rotating Thermal Convection on a Hemisphere. Fluids 2020, 5, 185.

AMA Style

Fischer P, Bruneau C-H, Kellay H. Numerical Study of Rotating Thermal Convection on a Hemisphere. Fluids. 2020; 5(4):185.

Chicago/Turabian Style

Fischer, Patrick, Charles-Henri Bruneau, and Hamid Kellay. 2020. "Numerical Study of Rotating Thermal Convection on a Hemisphere" Fluids 5, no. 4: 185.

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