Application of a modified Prandtl mixing length model to the turbulent far wake with a variable mainstream flow

Abstract

A modified version of Prandtl’s mixing length closure model is applied to the two-dimensional turbulent classical far wake with a variable mainstream flow. This modified version of Prandtl’s mixing length model has been previously applied to the two dimensional turbulent classical wake where the mainstream speed is constant. The model is able to address some of the serious criticisms on the applicability of Prandtl’s mixing length model to free shear flows. For instance, the model is complete in that the mixing length is derived in a systematic way and a wake boundary extending to infinity is predicted. In this work, the effect of a variable mainstream flow on the expression for the mixing length and the effective width of the wake is examined. For variable mainstream flows, it is shown that the effective width is not only proportional to the mixing length but also inversely proportional to the slip velocity. For this problem, the power is conserved. The invariant solution corresponding to the conserved quantity is obtained. The flow behavior is analyzed for a constant, a decelerating, and an accelerating ideal slip-flow.