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Hydrodynamic equations for incompressible inviscid fluid in terms of Clebsch potentials

Hydrodynamic equations for ideal incompressible fluid are written in terms of Clebsch potentials. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation contains arbitrary function which is determined by inflow conditions given on the boundary. To determine unique solution, velocity and vorticity (but not only velocity itself) must be given on the boundary. This unexpected circumstance may be interpreted in the sense that the fluid has more degrees of freedom, than it was believed. Besides, the vorticity is less observable quantity as compared with the velocity. It is shown that the dynamic equation for incompressible fluid do not contain time derivatives essentially, and the problem of nonstationary flow for incompressible fluid is reduced to the problem of stationary flow with the time as a parameter of boundary conditions.