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The Boussinesq approximation in rapidly rotating flows

Published online by Cambridge University Press:  15 November 2013

Jose M. Lopez ,
Francisco Marques  and
Marc Avila
Jose M. Lopez
Affiliation:
Departament de Física Aplicada, Univ. Politècnica de Catalunya, Barcelona 08034, Spain
Francisco Marques*
Affiliation:
Departament de Física Aplicada, Univ. Politècnica de Catalunya, Barcelona 08034, Spain
Marc Avila
Affiliation:
Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
*
†Email address for correspondence: marques@fa.upc.edu
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Abstract

In commonly used formulations of the Boussinesq approximation centrifugal buoyancy effects related to differential rotation, as well as strong vortices in the flow, are neglected. However, these may play an important role in rapidly rotating flows, such as in astrophysical and geophysical applications, and also in turbulent convection. Here we provide a straightforward approach resulting in a Boussinesq-type approximation that consistently accounts for centrifugal effects. Its application to the accretion-disc problem is discussed. We numerically compare the new approach to the typical one in fluid flows confined between two differentially heated and rotating cylinders. The results justify the need of using the proposed approximation in rapidly rotating flows.

JFM classification

Convection: Buoyancy-driven instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , pp. 56 - 77
Copyright
©2013 Cambridge University Press 

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