On Plane, Steady, Creeping Flow, Generated Around an Arbitrary Cylinder by a Translating Flat Plate

Plane, steady, creeping flow around an arbitrary cylinder situated in vicinity of a flat plate is considered, the flow being generated by translation of this plate along itself with constant speed, perpendicular to generatrices. The stream function of the flow satisfies the biharmonic equation, so that all properties of the flow - such as velocity and pressure fields as well as fields of other stress tensor components - are expressed in terms of the Goursat functions. Hence, the problem of determination of the flow reduces to determination of these functions. The two-step approach is applied to the solution of this problem. The first step consists in conformal mapping of the original domain of solution onto an annulus - by means of a suitable set of mapping functions. The second step consists in development of the two Goursat functions in Laurent series extended by two logarithmic terms each. Unknown coefficients of the series have to satisfy a system of linear algebraic equations, following from boundary conditions. The system is arrived at by means of the pseudospectral method. The so obtained velocity field is applied to generation of streamline patterns. Such a pattern is presented in the paper, and compared with an analogous one, corresponding to potential flow.