Single-point nonlinearity indicators for the propagation of high-amplitude jet noise

Prediction schemes based on linear acoustics are often insufficient to describe the character of the noise radiated from a jet engine. Nonlinear evolution of jet noise is usually identified using linear extrapolation and spectral comparisons. Because it requires measurements at multiple locations, this method is susceptible to errors in the presence of ground reflections or meteorological effects, when the location of the source is uncertain, and in the near-field of the jet. Thus, an indicator of nonlinearity that can be derived from a measurement at a single point is desirable. This work introduces one such indicator based on a quantity found in a spectral Burgers equation derived by Morfey and Howell [AIAA J. 19, 986-992 (1981)]. The quantity, denoted Q _p2p and commonly referred to as the QSD, is related to the nonlinear evolution of the signal. The indicator discussed here is a normalization of the QSD that assesses the relative importance of nonlinear, absorption, and spreading effects. For this reason, it is referred to as the spectral Gol'dberg number and is denoted Γ_s. It is applied to model-scale jet signatures and is shown to have larger values for higher jet Mach numbers and peak radiation angles relative to the jet axis.