The Streamwise Evolution of Coherent Structures in the Axisymmetric Jet Mixing Layer

Abstract

The dynamical equations governing the streamwise evolution of coherent structures in the axisymmetric jet shear layer are derived. The method utilized is similar to that used by Aubry et al (1988) and Glauser et al (1989). This method consists of performing a Galerkin projection, using the basis functions obtained from application of the proper orthogonal decomposition (POD), onto the Navier Stokes equations. In this study, however, the so called random coefficients are written as a function of the streamwise direction, and not time as in the previous studies. This results in a boundary value problem and not an initial value problem as was the case in the afore mentioned work. This type of an approach is important from an experimentalist’s point of view. The two-point correlation tensor (needed for application of the POD) can be measured much easier at one streamwise location as a function of time difference rather than at many streamwise separations. The basic idea is to measure the two-point correlation at one streamwise location and infer the evolution of the coherent structures in the streamwise direction from the dynamical equations. These equations and some ideas on how to solve them numerically will be discussed.