Identification of coherent wavy motion in round turbulent jets

Large-scale coherent vortical structures are at the heart of free-shear turbulent flows, such as wakes, mixing layers and jets. These structures are involved in intensive mixing, entrainment and generation of aeroacoustic noise. We analyze direct numerical simulation data of a turbulent jet, performed with an in-house high-order finite-difference/pseudo-spectral code that solves the compressible Navier-Stokes equations. Using appropriate statistical tools we show that the jet dynamics can be represented as a superposition of propagating helical waves. We apply a snapshot-based Proper Orthogonal Decomposition to the azimuthally Fourier decomposed velocity fields for five cylindrical subdomains chosen at different downstream positions over a sufficiently long ensemble. We note that the main eigenfunctions with low non-zero azimuthal amplitudes come in pairs of (virtually) equal amounts of energy, taking the shape of helical vortices. Further decomposition of complex-valued temporal coefficients provides a convenient framework to analyze wavy motion downstream of the identified helical vortices and corresponding phase speed of these structures. The results show good agreement with the linear local stability analysis.