The Zhukovskii problem of the flow around a sheet pile

The solution of the Zhukovskii problem of the flow around a sheet pile is g iven using the principles of two-dimensional steady-state seepage in the ca se when, accompanying the motion of the seeping water, there is a layer of saline ground waters at a certain depth under the sheet pile and this layer is located above an impermeable thickness of rock salt. The mixed boundary -value problem of the theory of analytic functions which arises is solved u sing Polubarinova-Kochina's method, which is based on the application of th e analytical theory of linear differential equations and, also, the method, developed by us, of the conformal mappings of circular polygons in polar m eshes, which are extremely typical for the velocity hodograph domains of su ch flows. While reflecting the specific details and individual properties o f such flows, the solution constructed below turns out to be expressed in c losed form in terms of elementary functions and, consequently, it is the si mplest and most convenient solution. In addition, it is the most general so lution for the class of problems being considered. The well known results Z hukovskii, Vedernikov and others are obtained from it as special and limiti ng cases. A detailed hydrodynamic analysis and the specific features of the seepage process being considered, as well as the effects of all the physic al parameters of the model on the pattern of the phenomenon, are presented using this solution and by numerical calculations. (C) 1999 Elsevier Scienc e Ltd. All rights reserved.