HALINE CIRCULATION - BIFURCATION AND CHAOS

A highly idealized model for the oceanic haline circulation is studied . Specifically, loops filled with salty water and subjected to either the natural boundary condition, the virtual salt flux condition, or sa linity relaxation are considered. It is shown that the characteristics of the solutions, especially the transition between steady and unstea dy convection, depend critically on the applied boundary conditions. I t is found that the relaxation condition generally modifies the locati on of the Hopf bifurcation so highly that models based on it should al ways remain in the regime of steady convection. On the other hand, the Location of the Hopf bifurcation for models based on flux conditions is much less extreme. Thus, in these models, limit cycles or chaotic b ehavior can easily be excited. Further, the nature of the Hopf bifurca tion depends sensitively on the boundary condition. For example, if th e frictional parameter is gradually reduced, the model based on the na tural boundary condition goes through a supercritical Hopf bifurcation , while the model based on virtual salt flux goes through a subcritica l Hopf bifurcation. Similar dependencies are found when other paramete rs are varied. Beyond the Hopf bifurcations, windows of limit cycle so lutions alternate with windows of chaos. In addition, for a given set of parameters, the system can have multiple solutions, such as a limit cycle and a chaotic solution, or limit cycles which have distinctivel y different structure. These results comment on the types of behavior that more complicated three-dimensional models may exhibit.