The objective of this project is to develop laboratory, theoretical and numerical research of self-organization in rotating shallow water shear flows as simulation of astrophysical, atmospheric and plasma vortical structures in Russia, using improved experimental tools and renewed theoretical ideas. The project is divided into the following three scientific parts: (1) simulation of astrophysical disc objects; (2) simulation of vortical structures of atmospheres and magnetised plasmas; and (3) development of diagnostics. The simulation of astrophysical disc is one of the main aims of this project, but the results are also of interest for atmospheric dynamics, when hydraulic jumps or fronts are encountered. The particular goals of this simulation are: to carry out a laboratory simulation with a shallow water layer for studying gaseous disc stability at differential rotation with an arbitrary (variable) velocity profile (including Keplerian, "sub-Keplerian" and "super-Keplerian" ones); in parallel and in comparison with the laboratory experiment, to carry out a theoretical investigation and numerical simulation of the object above; to make numerical experiments in the line of the scheme, extending it to the range of steeper velocity profiles and higher Mach numbers of the leap so that the numerical results can be compared with the existing data of the laboratory simulation. The simulation of vortical structures of atmospheres and magnetised plasmas is focussed on regimes with a strong background rotation, relevant for atmospheric vortices, and also magnetised plasmas. The particular goals of this simulation are: to carry out a laboratory and numerical investigation of generation and stability of large-scale vortices in the polar regions of the Earth as well as their interactions with surrounding flows; using all varieties of the approaches above, to study vortices of the size both larger and smaller than the Rossby-Obukhov radius, both barotropic and baroclinic ones. The particular goal of the development of diagnostics are: to develop diagnostic tools, unified for the project, for obtaining velocity and depth fields on the basis of a commercial scientific general purpose image processor.