Green's function and a semi-analytical method for the channel turbulent flow

Abstract

The work offers a semi-analytical method for solving a classical problem of dynamics of viscous fluid in the flow of a turbulent homogeneous current in the channel of a constant width (a 2D problem). In the standard iteration interpretation of incremental motion along a temporary variable, we obtain certain linear elliptical forth-order problem in the band. This work provides an explicit solution in quadratures. To do this, we at first construct the Green's function along the channel with the use of the integral Fourier transform. This function satisfies the necessary boundary conditions for the stream function on the channel borders. Then the solution of the problem is described in an explicit form in terms of this Green's function.