Improved Linearized Velocity Profiles for Turbulent Free Shear Layers

Abstract

The longitudinal motion equation for turbulent boundary layers is linearized in a manner which retains the spirit of Reichardt’s inductive theory. The resulting approximate velocity profiles for isobaric free shear layers are found to be functions of the density field as well as the velocity of the secondary stream. Using the amount of transverse shift, which is required to satisfy the momentum integral equation, as a figure of merit, it is shown that the alternate profiles are generally better representations of the flow field than distributions obtained with the classic Oseen linearization for both developing and fully developed free layers. The alternate velocity distributions, in combination with integral conservation equations, are shown to yield characteristic velocities in the midpart of the profile which are in agreement with those obtained from more elaborate nonlinear analyses.