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 projecting Navier–Stokes
equations onto an empirical basis set from the proper orthogonal decomposition
(POD) using a Galerkin method. To obtain this low-dimensional set of equations, a
truncation is performed that only includes the first POD mode for selected streamwise/spanwise
(k1/k3) modes. The initial truncations
are for k3 = 0; however, once
these truncations are evaluated, 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 feedback between
the turbulent and mean flows. The results of the numerical simulations show a
strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the
correct energy distributions in the cross-stream direction. These models also indicated
that the events associated with the centre of the mixing layer lead the temporal
dynamics. For truncations involving both spanwise and streamwise wavenumbers,
the reconstructed velocity field exhibits the main spanwise and streamwise vortical
structures known to exist in this flow. The streamwise aligned vorticity is shown to
connect spanwise vortex tubes.
Study of photoluminescence and energy transfer properties of an organic dye salt doped thin films
