Turbulent flow of fluid near trailing edge of plate in stream at zero angle of attack

The problem of turbulent flow at the trailing edge of a plate, in a stream of incompressible fluid at zero angle of attack, is solved by the method of asymptotic expansions and their collocation. Boundary conditions of adhesion are replaced with the condition of axial symmetry in the wake, which results in a different gradient of the displacement thickness and a longitudinal pressure gradient so large as to invalidate the boundary-layer approximation. A theory is constructed that describes the interaction of wake and boundary layer, with the former assumed to be the only source of perturbations in the latter. The velocity field, its longitudinal and transverse components, as well as the pressure field and the turbulent shearing stress are calculated from the corresponding differential equation of momentum for the appropriate boundary conditions, taking into account that the flow function is antisymmetric in the wake region and assuming a power-law velocity profile in the unperturbed state. The solution is sought in self-adjoint form, with a Fourier integral, and found to contain Gauss's hypergeometric function, which can be evaluated with the aid of the GOURSAT quadratic transformation.