ON THE DYNAMICS OF ELLIPTIC VORTEX WITH A FREE-SURFACE

The homogeneous eddy-like lens is considered to have elliptical isobaths and streamlines and parabolic vertical section. The eddy dynamics is defined by geometry and mutual orientation of the height ellipse and the streamfunction ellipse (hyperbola) and, also, by the Lagrangian function of dilatation of the lens. By the satisfaction of geostrophic balance with respect to modified Coriolis parameter in the rotating systems of reference and initial alignment of axes with each other there are vacillation with inertial period. By the disturbance of these conditions regime becomes more complicate, that so there exist the resonant and unresonant ways. The asymptotic solutions are obtained with the method of multiple scales for both these cases.