Similarity of the Outer Region of the Turbulent Boundary

摘要

New similarity criteria are obtained for the velocity profile and the Reynolds stress terms by a stream function approach using the transformed x- momentum balance equation and the transformed Reynolds stress transport equation. The similarity criteria are similar to earlier results but are developed without a priori assumptions as to the velocity or Reynolds stress term scaling variables. Using the criteria, eleven experimental datasets for turbulent flow on a wedge are found. Scaling results indicate that the displacement thickness, the momentum thickness, the ninety-nine percent thickness, and the Rota-Clauser thickness all work as the outer region similarity thickness scale. The experimental and theoretical evidence indicates the free stream velocity works well as the velocity scaling parameter. For the Reynolds stress scaling. experimental evidence is for the most part ambiguous. However. recent DNS results clearly indicate that the friction velocity squared is the proper scaling but this result is seemingly at odds with the new theoretical criteria. Resolution of the conflict is made by the observation that similarity like behavior of the velocity profile and the Reynolds stress terms are only obtained for the flow datasets where the ratio of the free stream velocity to the friction velocity is almost constant.