THE DEVELOPMENT OF FREE TURBULENT SHEAR LAYERS

Abstract
The development of a two-dimensional, free turbulent shear layer from an arbitrary initial velocity profile is analyzed theoretically. Included in the analysis are effects of both heat transfer and compressibility. The mean flow is described by approximate velocity profiles containing an unknown position parameter which is dependent upon the development length. Integral forms of the continuity and momentum equations are utilized to specify the flow characteristics along the streamline which separates the primary and secondary flow regions. By applying the Navier-Stokes equations to this dividing streamline, one is able to calculate the position parameter and thus complete the description of the developing flow field. Also presented are results of extensive calculations which show, for various external and initial flow conditions, the variation of the dividing streamline velocity, shear stress (Stanton number), and average eddy viscosity. The theory also enables one to estimate the effects of heat transfer and compressibility on the spread rate parameter for fully developed mixing zones. The theoretical results are shown to agree with experimental data from a number of sources.

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