Abstract
I the present note, a proof of the invariancy of the tota shear stress in free turbulent shear flows is given. It is pointed out that some of the more stringent restrictions imposed by other investigators are not necessary. The Howarth transformation is used to transform the compressible flow field to an incompressible field, and the invariancy of the stream function under this transformation is assumed. The analysis of compressible turbulent free shear flows is a complex problem. One of the main difficulties in transforming the compressible turbulent flow equations to the incompressible form lies in the transformation of the shear stress term. Some time ago, Mager showed that the Howarth transformation is valid for the compressible turbulent boundary-layer-type problems. However, in applying the transformation he made the assumption that the turbulent shear stresses are invariant under the transformation. Recently Burggraf relaxed the more stringent assumption of Mager by requiring only the y derivative of the turbulent shear to be invariant to permit the use of the transformation. In the present note, the authors show local in variance of the total shear stress .across sections perpendicular to the flow direction.
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