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Multiple equilibria in two-dimensional thermohaline circulation

Published online by Cambridge University Press:  26 April 2006

Paola Cessi  and
W. R. Young
Paola Cessi
Affiliation:
Istituto FISBAT-CNR, I-40126 Bologna, Italy
W. R. Young
Affiliation:
Scripps Institution of Oceanography, La Jolla, CA 92093, USA
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Abstract

As a model of the thermohaline circulation of the ocean we study the two-dimensional Boussinesq equations forced by prescribing the surface temperature and the surface salinity flux. We simplify the equations of motion using an expansion based on the small aspect ratio of the domain. The result is an amplitude equation governing the evolution of the depth averaged salinity field. This amplitude equation has multiple, linearly stable equilibria. The simplified dynamics has a Lyapunov functional and this variational structure permits a simple characterization of the relative stability of the alternative steady solutions.

Even when the thermal and salinity surface forcing functions are symmetric about the equator there are asymmetric solutions, representing pole to pole circulations. These asymmetric solutions are stable to small perturbations and are always found in conjunction with symmetric solutions, also stable to small perturbations. Recent numerical solutions of the full two-dimensional equations have shown very similar flow patterns.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 241 , August 1992 , pp. 291 - 309
Copyright
© 1992 Cambridge University Press

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