In the framework of the linear barotropic hydrodynamical model an expression is derived for the transfer function of the dynamical atmosphere-ocean system within the synoptical frequency range. As input processes the air pressure and the shear stress of the wind were considered, and the sea level was the output. Numerical experiments were made relating to the elementary modes of the gradient-vortex waves: Rossby waves, current waves and topographical waves. The resonance wavelengths were determined at the periods of 3, 10 and 30 days, and the resonance areas were located.