The Dynamics of a Simple Baroclinic Model of the Wind-Driven Circulation

Abstract

The authors study the dynamics of a two-layer approximation to the steadily forced baroclinic circulation in a closed ocean basin with the aim of understanding its temporal variability and the onset of low-frequency variability. It is found that, for a range of dissipation that includes values used in a number of ocean modeling studies in the past five years, if one waits a sufficient length of time, the asymptotic behavior of the system is characterized by only a very small number of degrees of freedom. By varying the dissipation as a control parameter, the authors identify abrupt transitions in the form of the long-term circulation exhibited by the model. One type of transition, from a time-varying circulation dominated by two frequencies to a chaotic circulation, is accompanied by the appearance of low-frequency variability. This constitutes an internal mechanism for the production of variability at climatological timescales. The model used is a two-layer, quasigeostrophic model forced by a steady wind stress with a uniform cyclonic curl. Dissipation is modeled by a lateral diffusion of momentum with a uniform eddy viscosity. In two sets of experiments with two internal deformation radii and layer depth ratios, the eddy viscosity is varied and the types of circulation that result are reported. The stable steady circulation seen in the viscous limit gives way to time-dependent circulations of increasing temporal complexity. Spatially, the circulations fall into two types, those dominated by large recirculating gyres in the western part of the basin and those with a strong (and strongly meandering) peripheral current reminiscent of that seen in the Black Sea. From an examination of the linear eigenmodes of the steady circulation, the initial transition to time dependence may be characterized as a baroclinic instability of the western recirculation gyre.