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Linear and nonlinear baroclinic instability with rigid sidewalls

Published online by Cambridge University Press:  26 April 2006

Michael D. Mundt ,
Nicholas H. Brummell  and
John E. Hart
Michael D. Mundt
Affiliation:
Department of Astrophysical, Planetary, and Atmospheric Sciences, Campus Box 391, University of Colorado at Boulder, Boulder, CO 80309-0391, USA
Nicholas H. Brummell
Affiliation:
Department of Astrophysical, Planetary, and Atmospheric Sciences, Campus Box 391, University of Colorado at Boulder, Boulder, CO 80309-0391, USA
John E. Hart
Affiliation:
Department of Astrophysical, Planetary, and Atmospheric Sciences, Campus Box 391, University of Colorado at Boulder, Boulder, CO 80309-0391, USA
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Abstract

The behaviour of baroclinic waves growing from instability in a two-layer channel flow with rigid (no-slip) sidewalls is described and contrasted with that for the more traditional free-slip boundary conditions. The linear theory for the onset of small-amplitude disturbances shows that the change in lateral boundary conditions has only a modest effect for typical laboratory parameter values, although the no-slip case is slightly more unstable at very small values of bottom friction. On the other hand, the nonlinear evolution of no-slip modes is completely different. While the free-slip case becomes aperiodic only at large values of the supercriticality (F–Fc)/Fc, the rigid wall case can be subcritically chaotic. Aperiodic, highly nonlinear wave motions are possible for external control values set in the linearly stable region of parameter space. Weakly nonlinear analysis shows that the no-slip case has a negative Landau constant for moderately small values of bottom friction, and it is in this regime that high-resolution numerical simulations exhibit subcritical chaos. At larger values of bottom friction, the rigid-wall simulations undergo a supercritical quasi-periodic transition to chaos at modest, order one, supercriticality, which is substantially smaller than that required for chaos in the free-slip case.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 291 , 25 May 1995 , pp. 109 - 138
Copyright
© 1995 Cambridge University Press

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