The process of formation of azimuthal flows generated by a mass source-sink system in a shallow water layer on the surface of a rotating paraboloid is investigated theoretically and experimentally. The calculations are carried out within the framework of the shallow-water equations with allowance for bottom friction. Asymptotic solutions describing the process of establishment of steadystate azimuthal flows which takes place after instantaneous initiation of the source-sink system are constructed. It is shown that theory and experiment are in satisfactory agreement.As follows from theory of hyperbolic equations, if we take the plus sign in Eq. (2.2) (source at the center), the boundary condition (2.3) must be imposed at the left end r = r 1 of the interval considered, if the minus