Low dimensional description of the axisymmetric jet mixing layer

The near field jet mixing layer is studied using a dynamical system model developed by Glauser et al. (1989). This model is similar to that applied by Aubry et al (1988) to the near wall region of the turbulent boundary layer. In this work the instantaneous velocity field is expanded in terms of the empirical eigenfunctions obtained by Glauser and George (1987). These eigenfunctions were extracted from the measured cross-spectral tensor by application of the proper orthogonal decomposition theorem (POD) suggested by Lumley (1967). Galerkin projection is then applied to the Navier Stokes equations in conjuction with this representation, resulting in low-dimensional sets or ordinary differential equations. In particular, a 18 equation model is developed where the neglected modes are accounted for by a Heisenberg type model. The methods of dynamical systems theory are then used to analyze this system of 18 equations in an attempt to further our understanding of the transfer of turbulent energy between various azimuthal modes and streamwise wavenumbers and relate this to the turbulence production phenomena in the jet mixing layer. With this model the sequence by several values of the bifurcation parameter which is introduced into the system of equations through the Heisenberg model. In this paper, however, the results for only one value of the bifurcation parameter are presented.