A note on nonlinear aspects of large-scale atmospheric instabilities



A barotropic model with momentum transport, a simple baroclinic model with transports of heat only and a baroclinic model with both momentum and heat transports are used to illustrate the instabilities and the nonlinear longer term behavior of barotropic, baroclinic and mixed barotropic-baroclinic processes in models without forcing and frictional dissipations. While the instabilities of such models are well known through analytical studies of the linear perturbation equations, it is obvious that these studies give no information on the long term behavior which can be studied only by nonlinear equations. Numerical integrations of low order nonlinear equations will be used to illustrate the long term behavior of the two models. The main aspects of the observed atmospheric energy processes may be reproduced by the most general low-order model used in this study. This model contains meridional transports of sensible heat and momentum by the eddies which are included in the model. To reproduce the atmospheric energy diagram based on observational studies it is necessary to include heating and frictional dissipations. The latter two processes will be excluded in the present study in order to obtain the long term behavior in non-forced models. The integrations of the various models will indicate that a long-term almost periodic behavior is observed with rather large time scales. The almost periodic variations are obtained from initial states with moderate values of the zonal parameters.

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