Amplitude scaling of turbulent-jet wavepackets

Wavepackets modelling large-scale coherent structures are related to the peak noise radiation by subsonic jets. Such wavepacket models are well developed in the literature, and are often based on a linearization of the Navier-Stokes system; solutions of the resulting linear problem have a free amplitude, which can be obtained by comparison with experiments or simulations. In this work we determine amplitudes of turbulent-jet wavepackets by comparing large-eddy simulation (LES) data from Br`es et al. of a Mach 0.9 jet and fluctuation fields using the parabolized stability equations (PSE) model (Sasaki et al.). Projection of the leading mode from spectral proper orthogonal decomposition (SPOD), applied to the LES data, onto the PSE model solutions is a way to determine the free amplitude, and by analyzing such amplitudes for different Strouhal numbers and azimuthal modes of the turbulent jet, it is possible to notice a clear pattern of the scaling factor with varying St. Azimuthal wavenumbers m = 0, 1 and 2 show an exponential dependence of wavepacket amplitude with Strouhal number. This sheds light on how wavepackets amplitudes behave and how they are excited upstream.