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On some problems of similarity flow of fluid with a free surface

Published online by Cambridge University Press:  29 March 2006

Z. N. Dobrovol'skaya
Z. N. Dobrovol'skaya
Affiliation:
Computing Centre of the Academy of Sciences of the USSR, Moscow
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Abstract

The paper presents the method of solving a class of two-dimensional problems of the similarity flow of an incompressible fluid with a free surface. The fluid is assumed to be non-viscous and weightless. We consider two-dimensional irrotational similarity flows with dimensionless hydrodynamic characteristics depending only on the ratios x/v0t, y/v0t, where x, y are Cartesian co-ordinates, t is time and v0 is a constant of the velocity dimension.

The proposed method is based upon using the function introduced by Wagner (1932) and can be applied to the problems where the flow region is bounded by free surfaces and uniformly moving (or fixed) rectilinear impermeable boundaries. Introduction of Wagner's function makes it possible to reduce each of the problems under consideration to a non-linear singular integral equation for the real function.

The method is illustrated by solving the classical problem of the uniform symmetrical entry of a wedge into a half-plane of a fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 36 , Issue 4 , 19 May 1969 , pp. 805 - 829
Copyright
© 1969 Cambridge University Press

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References

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