Spatial Decompositions of a Fully-developed Turbulent Round Jet Sampled with Particle Image Velocimetry
Spatial decompositions of the turbulence in a far, axisymmetric jet at exit Reynolds number of 20, 000 have been performed. Equilibrium similarity
theory applied to the two-point Reynolds stresses has shown that the turbulence statistics in the far, fully developed region of an axisymmetric jet should be independent of origin in the streamwise direction when evaluated on the similarity coordinates system. The homogeneity was confirmed in a planar PIV experiment that measured the streamwise and radial velocity components in a (0.4m by 0.7 m) composite field-of-view intersecting the centerline. The homogeneity allowed for spatial spectra to be estimated in the streamwise direction. Radial Proper Orthogonal Decomposition was subsequently performed based on the two-point cross-spectral tensor elements. The obtained eigenspectra and eigenvectors reflect the highdimensional nature of the far jet as the rates of convergence to the available spectral density decreased with increasing wavenumber.
In addition, radial Proper Orthogonal Decomposition was performed on three-component stereoscopic PIV velocity data from cross-planes in the far turbulent jet. Fourier series expansion of the azimuthally homogeneous turbulence again highlighted the dynamic complexity of the far jet. In particular, it was shown that several azimuthal modes are needed to expand the primary Reynolds shear stress which is associated with the process by which the turbulence extracts kinetic energy from the mean flow gradient. This in turn implies that the far jet turbulence should not be expected to be dominated by any one azimuthal
mode, as has been inferred from linear stability analysis.
proper orthogonal decomposition
axisymmetric turbulent jet
spatial spectral analysis