107 research outputs found
Hydrodynamic equations for incompressible inviscid fluid in terms of generalized stream function
Hydrodynamic equations for ideal incompressible fluid are written in terms of
generalized stream function. 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 Clebsch potentials
are used essentially at the description of vortical flow.Comment: 31 pages, 0 figures, The paper is reduced. Consideration of
nonstationary flow has been remove
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