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Centrifugal effects in rotating convection: nonlineardynamics

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:lopez@math.asu.edu
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Abstract

Rotating convection in cylindrical containers is a canonical problem in fluiddynamics, in which a variety of simplifying assumptions have been used in orderto allow for low-dimensional models or linear stability analysis from trivialbasic states. An aspect of the problem that has received only limited attentionis the influence of the centrifugal force, because it makes it difficult or evenimpossible to implement the aforementioned approaches. In this study, the mutualinterplay between the three forces of the problem, Coriolis, gravitational andcentrifugal buoyancy, is examined via direct numerical simulation of theNavier–Stokes equations in a parameter regime where the three forces areof comparable strengths in a cylindrical container with the radius equal to thedepth so that wall effects are also of order one. Two steady axisymmetric basicstates exist in this regime, and the nonlinear dynamics of the solutionsbifurcating from them is explored in detail. A variety of bifurcated solutionsand several codimension-two bifurcation points acting as organizing centres forthe dynamics have been found. A main result is that the flow has simple dynamicsfor either weak heating or large centrifugal buoyancy. Reducing the strength ofcentrifugal buoyancy leads to subcritical bifurcations, and as a result linearstability is of limited utility, and direct numerical simulations or laboratoryexperiments are the only way to establish the connections between the differentsolutions and their organizing centres, which result from the competitionbetween the three forces. Centrifugal effects primarily lead to theaxisymmetrization of the flow and a reduction in the heat flux.

JFM classification

Convection: Convection Geophysical and Geological Flows: Rotating flows Nonlinear Dynamical Systems: Bifurcation

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Papers
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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.

Download Lopez and Marques supplementary movie(Video)
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