Studies of Von Karman's Similarity Theory and Its Extension to Compressible Flows. A Similarity Theory for Turbulent Boundary Layer Over a Flat Plate in Compressible Flow.

摘要

As an application of the concepts in NACA TN 2541, the problem of turbulent boundary layer over a flat plate in compressible flow is treated. The dissipation term in the energy equation, often neglected, is first carefully studied and found to be of importance. In the differential equations governing the fluctuations, the lower-frequency components of all quantities are regarded to participate in an equilibrium in accordance with the similarity concept. After proper linearization, a set of differential equations containing only the lower-order-frequency fluctuations is obtained. In parallel with Von Karman's theory in incompressible flow, the similarity scales for all the flow variables are derived. Two possible length scales are found, and the significance of this possibility is discussed.