Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model

The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by project ing Navier-Strokes equations onto an empirical basis set from the proper or thogonal decomposition (POD) using a Galerkin method. To obtain this low-di mensional set of equations, a truncation is performed that only includes th e first POD mode for selected streamwise/spanwise (k(1)/k(3)) modes. The in itial truncations are for k(3) = 0; however, once these truncations are eva luated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedb ack between the turbulent and mean flows. The results of the numerical simu lations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-strea m direction. These models also indicated that the events associated with th e centre of the mixing layer lead the temporal dynamics. For truncations in volving both spanwise and streamwise wavenumbers, the reconstructed velocit y field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connec t spanwise vortex tubes.