The Zhukovskii problem of the flow around a sheet pile

✍ Scribed by E.N. Bereslavskii

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 542 KB
• Volume: 63
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(99)00072-6

✦ Synopsis

The solution of the Zhukovskii problem of the flow around a sheet pile is given using the principles of two-dimensional steadystate seepage in the case 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 using Polubarinova-Kochina's method, which is based on the application of the analytical theory of linear differential equations and, also, the method, developed by us, of the conformal mappings of circular polygons in polar meshes, which are extremely typical for the velocity hodograph domains of such flows. While reflecting the specific details and individual properties of such flows, the solution constructed below turns out to be expressed in closed form in terms of elementary functions and, consequently, it is the simplest and most convenient solution. In addition, it is the most general solution for the class of problems being considered. The well known results Zhukovskii, Vedemikov and others are obtained from it as special and limiting +ses. A detailed hydrodynamic analysis and the specific features of the seepage process being considered, as well as the effects of all the physical parameters of the model on the pattern of the phenomenon, are presented using this solution and by numerical calculations.