On the problem of flow over a Zhukovskii sheet pile in an irrigated ground mass

Abstract

In the hydrodynamic formulation, the problem is solved of plane steady filtration under a Zhukovskii sheet pile through an irrigated ground mass underlain by a highly permeable pressure horizon, the left semiinfinite part of whose roof is modeled by an impermeable inclusion. Consideration is given to the case of motion where the flow velocity at the end of the sheet pile is equal to infinity, which leads to a multivalence of the relevant region of complex velocity. To study such flow, we formulate and solve, using the Polubarinova-Kochina method, a mixed multiparametric boundary-value problem of the theory of analytical functions. On the basis of this model, an algorithm of calculation of filtration characteristics is developed for the situations where in water filtration, one has to take account of infiltration onto the free surface. Numerical results and the analysis of the effects of all physical parameters on the flow picture are presented. Consideration is given to the limiting cases of motion associated with the absence of both an impermeable inclusion and the hydrostatic upthrust in the well-permeable underlying layer. The solution is compared with results for the case of a finite flow velocity at the end of the sheet pile.