An Examination of the Axisymmetric Jet Mixing Layer using Coherent Structure Detection Techniques

Abstract

The Proper Orthogonal Decomposition (POD) [12] and Linear Stochastic Estimation (LSE) [1] are used to identify structure in the axisymmetric jet mixing layer. Cole et al [4] found that the POD produces a better global representation of the structures, whereas the LSE yields better results on a local scale (relative to the integral length scale of the flow). In this paper we will briefly discuss the application of each method, then focus on a novel technique which employs the strengths of each. This complementary technique is composed of three main steps. First, the eigenfunctions and eigenvalues are obtained from direct application of the POD to the two-point spectral tensor (see Glauser et al [7], [8] and [10]). Second, the LSE is applied to the cross-correlation tensor and multipoint estimates of the random vector field are computed as described by Cole et al [3]. Third, the eigenfunctions obtained from step one are projected onto the estimated velocity field obtained from step two to obtain estimated random coefficients. The estimated random coefficients are then used in conjunction with the POD eigenfunctions to reconstruct the random velocity field. A qualitative comparison between the first POD mode representation of the estimated random velocity field and that obtained utilizing the full field indicates that the two are remarkably similar. In order to quantitatively assess the technique, the root mean square (RMS) energies are computed and compared for both cases. The RMS kinetic energy captured using the first POD mode of the estimated field is very close to that obtained from the first POD mode of the unestimated original field. These results show that the complementary technique, which combines LSE and POD, allows one to obtain time dependent information from the POD while greatly reducing the amount of instantaneous data required. That is, it is not necessary to have the instantaneous data at all points in space simultaneously, but only at a few select positions.