Three kinds of results have been described in this paper. Firstly, an experimental study of the Rossby vortex meridional drift on the rotating shallow water has been carried out. Owing to the stringent physical analogy between the Rossby vortices and drift vortices in the magnetized plasma, the results obtained have allowed one to make a conclusion that the transport rate of the plasma, trapped by the drift vortices, across the magnetic field is equivalent to the “gyro-Bohm” diffusion coefficient. Secondly, a model of big vortices of the type of the Great Red Spot of Jupiter, dominating in the atmospheres of the outer planets, has been produced. Thirdly, the rotating shallow water modeling has been carried out of the hydrodynamical generation mechanism of spiral structures in galaxies. Trailing spiral waves of various azimuthal modes, generated by a shear flow between fast rotating “nucleus” and slow rotating periphery, were produced. The spirals are similar to those existing in the real galaxies. The hydrodynamical concept of the spiral structure formation in galaxies has been substantiated. Strong anticyclonic vortices between the spiral arms of the structures under study have been discovered for the first time. The existence of analogous vortices in real galaxies has been predicted. (This prediction has been reliably confirmed recently in special astronomical observations, carried out on the basis of the mentioned laboratory modeling and the prediction made – see the paper by A. Fridman et al. (Astrophysics and Space Science, 1997, 252, 115.)