An Analysis of Laminar Wake behind a Symmetrical Two-Dimensional Body in a Uniform Shear Flow

Abstract

An apsect of laminar wake of a symmetrical two-dimensional body placed in a uniform shear flow is described theoretically within the framework of the second-order boundary layer theory. The effect of the external vorticity involved in the oncoming flow is treated as a small perturbation to the case of uniform flow. An analytical solution for the far wake is obtained together with an approximate numerical solution for the near wake behind a flat plate aligned parallel to the oncoming flow, showing the overall development of the wake in the uniform shear flow.The analysis shows that the spreading of the wake is greater towards the side of smaller velocity than the side of larger one. However, the width of the wake defined as the distance between two points at which the streamwise velocity defect amounts to one-half of the maximum defect is found to be little affected by the presence of the external vorticity.In the present flow configuration, the displacement effect also appears as another second-order term which is found to be less significant in the far wake region than the effect of the external vorticity.