On the Role of Nonlinearity in Mach Wave Radiation in a Mach = 1.92 Jet

Mach wave radiation in a turbulent fully expanded supersonic jet is revisited. Our goal is to determine the extent to which predictions for the radiated sound that are based on linearized analysis agree with solution of the full nonlinear equations. To this end, we solve the linearized Navier-Stokes equations (LNS) with precisely the same mean flow and inflow disturbances as a previous direct numerical simulation (DNS) of a turbulent M = 1.92 jet. We restrict our attention to the first two azimuthal modes, n — 0 and n = 1, which constitute most of the acoustic field. The direction of peak radiation and the peak Strouhal number matches the DNS reasonably well, which is in accord with previous experimental justification of the linear theory. However, it is found that the sound pressure level predicted by LNS is significantly lower than that from DNS. Thus, linear theory misses a substantial component of the noise. In order to investigate the discrepancy, the behavior of individual frequency components of the solution are examined. Near the peak Strouhal number, particularly for the azimuthal mode n = 1, the amplification of disturbances in the LNS closely matches those from the DNS data. However, away from the peak frequency (and generally for the azimuthal mode n — 0), the DNS data shows amplification rates roughly comparable to those at the peak Strouhal number, while those from the linear computations are damped.