Turbulent mixing in plane and axisymmetric shear layers

This paper considers two problems associated with turbulent mixing in high speed shear layers. In the first we extend a previous model by the authors for two-dimensional shear layers to consider axisymmetric shear layers. The model assumes that large scale coherent structures dominate the mixing process in free shear layers. These large structures are modeled locally as instability waves. Calculations are made for the development of the axisymmetric shear layer as a function of freestream Mach numbers, velocity and density ratios. The calculations for the axisymmetric case are compared with the two-dimensional calculations and experimental results. In the second part of the paper we consider the effect of confining walls on the development of a two-dimensional shear layer. The effects of changing the wall locations in both the spanwise and normal directions are considered. The various classes of instability waves that exist are examined. The relationship between the span-wise confined and unconfined shear layers is examined. It is shown that the growth rates of instabilities may be maximized by the correct choice of duct width to height ratio.