Quantitative nonlinearity analysis of model-scale jet noise

The effects of nonlinearity on the power spectrum of jet noise can be directly compared with those of atmospheric absorption and geometric spreading through an ensemble-averaged, frequency-domain version of the generalized Burgers equation (GBE) [B. O. Reichman et al., J. Acoust. Soc. Am. 136, 2102 (2014)]. The rate of change in the sound pressure level due to the nonlinearity, in decibels per jet nozzle diameter, is calculated using a dimensionless form of the quadspectrum of the pressure and the squared-pressure waveforms. In this paper, this formulation is applied to atmospheric propagation of a spherically spreading, initial sinusoid and unheated model-scale supersonic (Mach 2.0) jet data. The rate of change in level due to nonlinearity is calculated and compared with estimated effects due to absorption and geometric spreading. Comparing these losses with the change predicted due to nonlinearity shows that absorption and nonlinearity are of similar magnitude in the geometric far field, where shocks are present, which causes the high-frequency spectral shape to remain unchanged.