Fourier-based Proper Orthogonal Decomposition of Fully Turbulent Round Jet

We use the Scanning-Tomographic Particle Image Velocimetry introduced by Casey et al. [1] to obtain time-resolved velocity field of a turbulent round jet with Re = 2640, 5280 and 10700, where the inlet turbulent jet is well-developed through a 100-diameter long pipe. A pulsed laser volume is scanned in 5-9 steps to obtain velocity vectors over a larger depth to span 100 mm-deep rectangular volume, centered in the self-similar region about 50 jet diameters downstream. This enables us to deduce polar velocity components in a cylindrical volume of radius 30-35 mm, and hence capture the large-scale azimuthal coherent structures. Casey et al. [1] observed azimuthal C-shaped coherent structures dominate at the lowest Re while observing smaller tubular structures at high Re using vorticity magnitude visualization criteria from the instantaneous reconstructions. By virtue of the jet’s symmetry, we decompose its velocity (u_r, u_θ, u_z) or vorticity (ω_r, ω_θ, ω_z) components into azimuthal Fourier modes. Then, we perform Proper Orthogonal Decomposition (POD) by taking the SVD of each Fourier mode to look at the evolution of coherent structures based on the dominant modes. The first azimuthal Fourier mode for all Re shows the appearance of azimuthal C-shaped structures from the inlet with different phases, which get broken down as they are advected by the mean flow. We characterize these structures by conditional averaging based on their phase, over many realizations.

[1] Casey T. A., et al. (2013) Phys. Fluids 025102.