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Symmetry, sidewalls, and the transition to chaos in baroclinic systems

Published online by Cambridge University Press:  26 April 2006

Michael D. Mundt ,
John E. Hart  and
Daniel R. Ohlsen
Michael D. Mundt
Affiliation:
Program in Atmospheric and Oceanic Sciences, Box 311, University of Colorado, Boulder, CO 80309, USA Present address: Institute of Marine Science, University of California at Santa Cruz, Santa Cruz, CA 95064, USA.
John E. Hart
Affiliation:
Program in Atmospheric and Oceanic Sciences, Box 311, University of Colorado, Boulder, CO 80309, USA Department of Astrophysical, Planetary, and Atmospheric Sciences, Box 391, University of Colorado, Boulder, CO 80309, USA
Daniel R. Ohlsen
Affiliation:
Program in Atmospheric and Oceanic Sciences, Box 311, University of Colorado, Boulder, CO 80309, USA
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Abstract

A high-resolution, quasi-geostrophic numerical model is utilized to examine two-layer baroclinic flow in a cylinder. Particular attention is given to the role of horizontal shear of the basic state induced by viscosity near the cylinder wall, and to the desymmetrization brought about by the cylindrical geometry, in the transition to baroclinic chaos. Solutions are computed for both f-plane and β-plane situations, and the results are compared to previous laboratory experiments. Agreement in the former case is found to be good, although the onset of chaos occurs at slightly lower forcing in the laboratory when its basic flow is prograde, and at higher forcing amplitude when the experimental basic azimuthal currents are retrograde. This suggests that the modest discrepancies may be attributable to computationally neglected ageostrophic effects in the interior fluid and Ekman boundary layers. When β ≠ 0, the numerical and laboratory results are in excellent agreement. The computational simulations indicate that the viscous sidewall boundary layer plays a pivotal role in the dynamics. Moreover, in contrast to previous studies performed in a periodic, rectilinear channel, the route to chaos is largely temporal and involves relatively few spatial modes. The reduction in symmetries upon going from f-plane channel to either f-plane or β-plane cylinder models leads to fewer secondary instabilities and fewer spatial modes that are active in the dynamics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 300 , 10 October 1995 , pp. 311 - 338
Copyright
© 1995 Cambridge University Press

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