Chaos in a simple model of the three-dimensional, salt-dominated ocean circulation |
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| Authors: | G van der Schrier L R M Maas |
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| Institution: | (1) Netherlands Institute for Sea Research, PO Box 59, 1790 AB Texel, The Netherlands E-mail: schrier@nioz.nl, NL |
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| Abstract: | A simple moments model used in studying the large-scale thermally driven ocean circulation, in one hemisphere, is extended
with a set of evolution equations for the basin-averaged salinity gradients. Natural formulations of the boundary conditions
for the heat flux and the (virtual) salt flux are given, the latter based on the SST-evaporation feedback. Stommel’s box model
result, a coexisting thermal and saline solution, is retrieved in the limit of no rotation. Including rotation in a salt-dominated
setting, a steady circulation is found which bifurcates for higher Rayleigh numbers in a periodic solution which becomes chaotic
through a cascade of subharmonic bifurcations. Periodic motion results from two different mechanisms. First, the stable stationary
state bifurcates into a periodic solution where anomalously saline water is advected by the overturning circulation. Second,
this periodic solution bifurcates into a state which is dominated, during the larger part of the cycle, by diffusion and inertia,
characterized by a decreasing overturning rate, and, during the subsequent shorter part of the cycle, by rapid advection and
restratification of the entire basin. The basin-averaged vertical density field is stably stratified in the steady and the
periodic regimes and remains statically stable in the chaotic regime.
Received: 16 July 1996 / Accepted: 29 December 1997 |
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