LOW-DIMENSIONAL DESCRIPTION OF FREE-SHEAR-FLOW COHERENT STRUCTURES AND THEIR DYNAMICAL BEHAVIOR

The snapshot form of the Karhunen-Loeve (K-L) expansion has been appli ed to two-dimensional, two-component hot-wire data from the region of a weakly perturbed free shear layer that includes the first pairing pr ocess. Low-level external perturbation was provided by a loudspeaker d riven by a computer-generated signal composed of two sine waves of equ al amplitude at the frequencies of the naturally developing fundamenta l instability wave and its first subharmonic, separated by a controlla ble initial phase angle difference. It was found that a large fraction of the fluctuation energy is carried by the first few modes. A low-di mensional empirical eigenfunction space is obtained which describes th e shear-flow coherent structures well. Galerkin projection of the Navi er-Stokes equations onto this basis set of principal eigenfunction mod es results in a low-order system of dynamical equations, and solution of this system of equations describes the dynamics of the coherent str uctures associated with eigenfunctions. Finally the simulation, as obt ained from the system of dynamical equations, is shown to compare reas onably well with the experiments.