A STUDY OF THE FINE-SCALE MOTIONS OF INCOMPRESSIBLE TIME-DEVELOPING MIXING LAYERS

The geometry of dissipating motions in direct numerical simulations (D NS) of the incompressible mixing layer is examined. All nine partial d erivatives of the velocity field are determined at every grid point in the flow, and various invariants and related quantities are computed from the velocity gradient tensor. Motions characterized by high rates of kinetic energy dissipation and high enstrophy density are of parti cular interest. Scatter plots of the invariants are mapped out and int eresting and unexpected patterns are seen. Depending on initial condit ions, each type of shear layer produces its own characteristic scatter plot. In order to provide more detailed information on the distributi on of invariants at intermediate and large scales, scatter plots are r eplaced with more useful number density contour plots. These essential ly represent the unnormalized joint probability density function of th e two invariants being cross-plotted. Plane mixing layers at the same Reynolds number, but with laminar and turbulent initial conditions, ar e studied, and comparisons of the rate-of-strain topology of the dissi pating motions are made. The results show conclusively that, regardles s of initial conditions, the bulk of the total kinetic energy dissipat ion is contributed by intermediate scale motions, whose local rate-of- strain topology is characterized as unstable-node-saddle-saddle (two p ositive rate-of-strain eigenvalues, one negative). In addition, it is found that, for these motions, the rate-of-strain invariants tend to a pproximately follow a straight line relationship, characteristic of a two-dimensional flow with out of plane straining. In contrast, fine-sc ale motions, which have the highest dissipation, but which only contri bute a small fraction of the total dissipation tend toward a fixed rat io of the principal rates of strain.