Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-19T06:51:41.379Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Borg, S. F. 1957 Some contributions to the wedge-water entry problem Proc. Am. Soc. Civil Engrs, J. Engng Mech. Div. 83, no.Google Scholar
Borg, S. F. 1959 The maximum pressures and total force on straight-sided wedges with small dead-rise J. Am. Soc. Naval Engrs, 71, 559–561.Google Scholar
Cumberbatch, E. 1960 The impact of a water wedge on a wall J. Fluid Mech. 7, 353–374.Google Scholar
Dobrovol'’kaya, Z. N. 1965 Some non-linear problems of the similarity flow of incompressible fluid with free surface (in Russian). In: Applications of the Theory of Functions in Continuum Mechanics, vol. 2, pp. 150–170. Moscow.
Dobrovol'’kaya, Z. N. 1966 Numerical solution of integral equation of a two-dimensional problem of the similarity flow with free surface (in Russian) J. Comput. Math. and Math. Phys. 6, 934–941.Google Scholar
Garabedian, P. R. 1953 Oblique water entry of a wedge Comm. Pure and Appl. Math. 6, 157–165.Google Scholar
Grigoryan, S. S. 1956 Some problems of the hydrodynamics of slender bodies (in Russian). Thesis, Moscow Univ.
Mackie, A. G. 1962 A linearized theory of the water entry problem Quart. J. Mech. and Appl. Math. 15, 137–151.Google Scholar
Moiseev, N. N., Borisova, E. P. & Koriavov, P. P. 1959 Plane and axially symmetrical automodel (similarity) problems of stream impact. Appl. Math. and Mech. (PMM) 23, 490–507.Google Scholar
Pierson, J. D. 1950 The penetration of a fluid surface by a wedge. Stevens Inst. Technol., Expt. Towing Tank Rep. no. 387.Google Scholar
Sagomonyan, A. Y. 1956 Wedge entry into a compressible fluid (in Russian). Vestnik Moscow Univ. no. 2, 13–18.Google Scholar
Wagner, H. 1932 Über Stoss- und Gleitvorgänge an der Oberfläche von Flüssigkeiten Z. angew. Math. und Mech. 12, 193–215.Google Scholar
Supplementary material: PDF

Dobrovol'skaya supplementary material

Supplementary Material

Download Dobrovol'skaya supplementary material(PDF)
PDF 683.5 KB