The turbulent near wake at a sharp trailing edge

Abstract

The problem of a turbulent boundary layer that evolves into a wake flow at the sharp trailing edge of a thin flat plate is considered; the formal structure of the near-wake flow is investigated using matched expansions in the limit of infinite Reynolds number. The symmetric turbulent near wake is shown to develop a two-layer structure which is independent of turbulence model. The general asymptotic analysis shows that a thin layer at the wake centreline grows linearly with distance from the trailing edge while the centreline velocity varies logarithmically in a manner that is supported strongly by experimental measurements. The relatively thick outer layer of the near-wake flow is undisturbed by the evolution of the inner layer to leading order. An additional region near the trailing edge is required to resolve a non-uniformity in transverse velocity. The general asymptotic results are used to guide the development of a zonal turbulence model for the near wake in the form of a simple eddy viscosity formula. Analytic profiles for velocity and Reynolds stress are obtained for the near-wake region; these profiles are shown to provide accurate representations of available near-wake experimental data.