Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet

Abstract

Recent studies have shown that while linear wavepacket models accurately reproduce experimentally observed, low azimuthal-wavenumber pressure fluctuations in the near field of turbulent jets, they significantly under-predict the intensity of the acoustic radiation produced in the subsonic case. In a linear context, "jittering" of the wavepackets, which can arise due to both stochastic and nonlinear interactions that force the wavepackets, has been hypothesized as a mechanism by which the radiation efficiency of wavepackets is greatly increased. We use data from a carefully validated large-eddy-simulation of a Mach 0.9 turbulent jet to explore this hypothesis. We analyze the LES data in frequency space using windowed segments of a set of snapshots spanning two thousand acoustic time units. We apply the linearized Navier-Stokes operator to this data in order to compute the non-linear forcing field that occurred in the LES simulations, and propose several techniques for educing the relation between the forcing and the observed flow fields. In particular, we employ empirical techniques to identify high energy modes (via proper orthogonal decomposition) in both the flow and acoustic fields, as well as a set of empirical resolvent modes that maximize either the gain between the forcing and flow fields, or the gain between the forcing and acoustic fields. The high gain modes are similar to the high energy modes in both cases, suggesting that the forcing fields are nearly uncorrelated in each realization. Both flow and acoustic fields appear to be driven by largely incoherent forcing corresponding to turbulence in the region of strong shear and, in particular, close to the critical layer. With the caveat that we have thus far only analyzed the axisymmetric mode of the disturbance fields, the results suggest that accurate linear wavepacket models that capture both the coherent flow and acoustic fields can be constructed if appropriate parameterizations of the stochastic forcing can be found, i.e. such forcings will excite the high gain modes to produce the observed coherent structures in both the near and far field.