The Dynamics of Organized Structures in the Axisymmetric Jet Mixing Layer

Abstract

The near field jet mixing layer is modeled in a manner 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 conjunction with this representation, resulting in low-dimensional sets of ordinary differential equations. The methods of dynamical systems theory are then used to analyze these equations. This work consists of an attempt to utilize the dynamical systems model 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 which the various modes contribute in time can be examined.