Chaos and nonlinear resonances in the problems of geophysical fluid

Abstract

In the framework of background currents, we examine a dynamically consistent model of a periodic flow over an isolated submerged obstacle of Gaussian shape. Chaotic advection of passive scalars in the ocean is studied from the viewpoint of the dynamic system theory. Much attention is given to the nonlinear resonance role. The relationship between the rotation frequency of an unperturbed fluid particle and the appearance and disappearance of a nonlinear resonance is established. So, the frequency gives us the opportunity to explain the trajectories' chaotization via the Chirikov criteria. This simple estimation is verified by numerical calculations. A simplified model is used for more exact reasoning. The distance between nonlinear resonance and its width was established for large action, and accurate estimation of chaotic region boundary was calculated. Also, numerically and analytically, there are studied chaotization dependencies from some other flow parameters.