TY - JOUR

T1 - Centrifugal effects in rotating convection

T2 - Nonlinear dynamics

AU - Lopez, Juan

AU - Marques, F.

N1 - Funding Information:
This work was supported by the National Science Foundation grant DMS-05052705, the Spanish Government grant FIS2007-61585 and Catalonian Government grant SGR-00024.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

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U2 - 10.1017/S0022112009006193

DO - 10.1017/S0022112009006193

M3 - Article

AN - SCOPUS:67650924883

VL - 628

SP - 269

EP - 297

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -