Coherent structure in a turbulent jet via a vector implementation of the proper orthogonal decomposition

Abstract

The coherent structure in the near-field of an axisymmetric turbulent jet at a Reynolds number of 3.8 × 105 and Mach number of 0.3 is experimentally characterized by a vector implementation of the proper orthogonal decomposition (POD). The POD eigenfunctions and associated eigenvalues are extracted at several selected streamwise locations in the initial region. The focus on the near-field is motivated by its importance in numerous technical applications. Results show a rapid energy convergence with POD mode number. Examination of the relative energy contained in the combined azimuthal and radial components of the POD modes reveals that it is comparable to that in the streamwise component. The streamwise evolution of the eigenvalue spectra is characterized by a remarkable variation in the azimuthal mode number energy distribution, leading to the dominance of azimuthal mode m = 1 beyond the end of the jet core. In contrast, a scalar implementation using only the streamwise component shows the dominance of mode m = 2 which is consistent with previous scalar implementations of the POD. For a given azimuthal mode number, the eigenvalue spectra exhibit a broad peak which occurs at a constant value of Strouhal number based on local shear layer momentum thickness and local jet maximum velocity. The phase information required for a local reconstruction of the jet structure is obtained by projecting the POD eigenmodes onto instantaneous realizations of the flow at fixed streamwise locations. The instantaneous realizations are obtained by utilizing cross-stream arrays of multi-sensor probes in conjunction with linear stochastic estimation (LSE). Results clearly show the local dynamic behaviour of each component of the jet structure.