Inertial oscillations over the background of shear currents in the ocean

Inertial oscillations observed in the seas and oceans are frequently characterized by various hodographs of current velocities different from circular anticyclonic motion as follows from the simplest model. It is supposed in [1] on the basis of the data analysis of measurements carried out on the shelf near Gelendzhik in the autumn of 2009 that the observed distortions of hodographs of inertial currents are the consequences of superposition of inertial oscillations and background shear current. In this work we construct a simple model of inertial oscillations over the background of a shear current based on the exact solution of shallowwater equations, which generally confirms the hypothesis suggested in [1].