广义流函数表示的不可压缩无粘流体的流体动力学方程
Hydrodynamic equations for incompressible inviscid fluid in terms of generalized stream function
摘要：
理想不可压缩流体的流体动力学方程用广义流函数表示。这些方程的二维版本被转换为一个动态方程的形式的流函数。该方程包含由边界上给定的入流条件确定的任意函数。为了确定唯一解，必须在边界上给出速度和涡量（而不仅仅是速度本身）。这种意想不到的情况可以解释为流体具有比所认为的更多的自由度。此外，涡度是比速度更不容易观测到的量。结果表明，Clebsch势基本上用于描述旋涡流动。
英文摘要：
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.
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