Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-30T18:39:24.526Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, D. A., Tannehill, J. C. & Pletcher, R. H. 1984 Computational Fluid Mechanics and Heat Transfer Hemisphere.
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics Springer.
Cattaneo, F. & Hart, J. E. 1990 Multiple states for quasi-geostrophic channel flows. Geophys. Astrophys. Fluid Dyn. 54, 1–33.Google Scholar
Hart, J. E. 1972 A laboratory study of baroclinic instability. Geophys. Fluid Dyn. 3, 181–209.Google Scholar
Hart, J. E. 1981 Wavenumber selection in nonlinear baroclinic instability. J. Atmos. Sci. 38, 400–408.Google Scholar
Hart, J. E. 1985 A laboratory study of baroclinic chaos on the f-plane. Tellus 37A, 286–296.Google Scholar
Hart, J. E. 1986 A model for the transition to baroclinic chaos. Physica D 20, 350–362.Google Scholar
Hart, J. E. & S. Kittelman 1986 A method for measuring interfacial fields in the laboratory. Geophys. Astrophys. Fluid Dyn. 36, 179–185.Google Scholar
Klein, P. & J. Pedlosky 1986 A numerical study of baroclinic instability at large supercriticality. J. Atmos. Sci. 43, 1243–1262.Google Scholar
Loeve, M. M. 1955 Probability Theory van Nostrand.
Lorenz, E. N. 1980 Noisy periodicity and reverse bifurcation. Ann. NY Acad. Sci. 357, 282–291.Google Scholar
Mansbridge, J. V. 1984 Wavenumber transition in baroclinically unstable flows. J. Atmos. Sci. 41, 925–930.Google Scholar
Mundt, M. & Hart, J. E. 1994 Secondary instability, EOF reduction, and the transition to baroclinic chaos. Physica D 78, 65–92.Google Scholar
Mundt, M., Brummell, N. H. & Hart, J. E. 1995 Linear and nonlinear baroclinic instability with rigid sidewalls. J. Fluid Mech. 291, 109–138.Google Scholar
Ohlsen, D. R. & Hart, J. E. 1989a The transition to baroclinic chaos on the β-plane. J. Fluid Mech. 203, 23–50.Google Scholar
Ohlsen, D. R. & Hart, J. E. 1989b Nonlinear interference vacillation. Geophys. Astrophys. Fluid Dyn. 45, 215–235.Google Scholar
Pedlosky, J. & Frenzen, C. 1980 Chaotic and periodic behaviour of finite-amplitude baroclinic waves. J. Atmos. Sci. 37, 1177–1196.Google Scholar
Pedlosky, J. 1981 The nonlinear dynamics of baroclinic wave ensembles. J. Fluid Mech. 102, 169–209.Google Scholar
Quartapelle, L. & Valz-Gris, F. 1981 Projection conditions on the vorticity in viscous incompressible flows. Intl J. Numer. Meth. Fluids 1, 129–144.Google Scholar
Sirovich, L. 1989 Chaotic dynamics of coherent structures. Physica D 37, 126–145.Google Scholar
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3, 17–26.Google Scholar
Yoshida, A. & Hart, J. E. 1986 A numerical study of baroclinic chaos. Geophys. Astrophys. Fluid Dyn. 37, 1–56.Google Scholar