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Centrifugal effects in rotating convection: nonlinear dynamics

Published online by Cambridge University Press:  01 June 2009

J. M. LOPEZ  and
F. MARQUES
J. M. LOPEZ*
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
F. MARQUES
Affiliation:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, Barcelona 08034, Spain
*
†Email address for correspondence: [email protected]
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Abstract

Rotating convection in cylindrical containers is a canonical problem in fluid dynamics, in which a variety of simplifying assumptions have been used in order to allow for low-dimensional models or linear stability analysis from trivial basic states. An aspect of the problem that has received only limited attention is the influence of the centrifugal force, because it makes it difficult or even impossible to implement the aforementioned approaches. In this study, the mutual interplay between the three forces of the problem, Coriolis, gravitational and centrifugal buoyancy, is examined via direct numerical simulation of the Navier–Stokes equations in a parameter regime where the three forces are of comparable strengths in a cylindrical container with the radius equal to the depth so that wall effects are also of order one. Two steady axisymmetric basic states exist in this regime, and the nonlinear dynamics of the solutions bifurcating from them is explored in detail. A variety of bifurcated solutions and several codimension-two bifurcation points acting as organizing centres for the dynamics have been found. A main result is that the flow has simple dynamics for either weak heating or large centrifugal buoyancy. Reducing the strength of centrifugal buoyancy leads to subcritical bifurcations, and as a result linear stability is of limited utility, and direct numerical simulations or laboratory experiments are the only way to establish the connections between the different solutions and their organizing centres, which result from the competition between the three forces. Centrifugal effects primarily lead to the axisymmetrization of the flow and a reduction in the heat flux.

JFM classification

Convection: Convection Geophysical and Geological Flows: Rotating flows Nonlinear Dynamical Systems: Bifurcation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 269 - 297
Copyright
Copyright © Cambridge University Press 2009

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References

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Lopez and Marques supplementary movie

Movie 1. Isotherms at mid-height of QP at Ra=15,500 and Fr=0.30.

Download Lopez and Marques supplementary movie(Video)
Video 11.3 MB

Lopez and Marques supplementary movie

Movie 2. Isotherms at mid-height of QP (locked) at Ra=17,000 and Fr=0.30.

Download Lopez and Marques supplementary movie(Video)
Video 11.3 MB

Lopez and Marques supplementary movie

Movie 3. Isotherms at mid-height of QP at Ra=18,500 and Fr=0.30.

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Video 15.1 MB

Lopez and Marques supplementary movie

Movie 4. Isotherms at mid-height of QP at Ra=20,000 and Fr=0.30.

Download Lopez and Marques supplementary movie(Video)
Video 7.6 MB

Lopez and Marques supplementary movie

Movie 5. Isotherms at mid-height of T3 at Ra=20,000 and F=0 (frame rate is half that of movies 1 to 4).

Download Lopez and Marques supplementary movie(Video)
Video 30.1 MB