Turbulent mixing in compressible free shear layers

For almost twenty years it has been recognized that turbulent shear flows are dominated by large-scale structures. Yet the majority of models for turbulent mixing fail to distinguish the properties of the structures either explicitly or implicitly from the broad band turbulence. A new model for the large-scale structures in a turbulent shear layer is introduced. Two variations on the model are developed that describe the influence of large-scale motions on the turbulent mixing process. The first variation simulates the average behavior by calculating the development of the part of the turbulent spectrum related to the large-scale structures in the flow. The second variation simulates a single realization of the passage of a train of large scale-structures. In both of these treatments, the large scale structures are described by a superposition of instability waves. The local properties of these waves are determined from a quasi-linear, inviscid, stability analysis. The streamwise development of the mean flow is determined from an energy integral analysis. The models contain no empirical constants. The present turbulence models predict the effects of freestream velocity and density ratios and effects of compressibility on the growth of the shear layer. The predictions agree very well with the available experimental data. Calculations are also made for the time-dependent motion of the shear layer in the form of streaklines and iso-vorticity/density contours that agree qualitatively with experimental observations. A successful implementation of the present models requires an understanding of the characteristics of the various modes of instability in compressible shear layers. A detailed spatial stability analysis is performed to fulfill this requirement. Using the traditional normal mode analysis, the various modes of instability in compressible shear layers are characterized and the physical mechanisms that drive these instabilities are described. In addition, an initial value problem is formulated to calculate the development of wave packets in shear layers. The preliminary results obtained from this analysis indicate that the structure of the wave packet in a compressible shear layer depends on the duct aspect ratio and that its development is very different from that of an incompressible shear layer.