Asymptotic Behavior in the Numerical Propagation of Finite-Amplitude Jet Noise

Abstract

One issue of interest pertaining to the development of a numerical model applicable to the nonlinear propagation of jet noise is the behavior of spectral predictions at large distances. In this study, a recorded noise waveform from a military jet aircraft is numerically propagated via a hybrid time-frequency domain solution to the generalized Burgers equation that incorporates spherical spreading and atmospheric absorption and dispersion. Numerical results show that the spatial rate of change of the difference between the nonlinearly-and linearlypredicted power spectra appears to approach constant nonzero behavior at high frequencies. This asymptotic relationship is analogous to that predicted by analytical theory for initiallysinusoidal plane and spherical waves.

Asymptotic behavior of a frequency-domain nonlinearity indicator for solutions to the generalized Burgers equation

“…Figures 2 and 3 of Ref. 16 show @NG=@r decreasing asymptotically to zero in the peak-frequency region, and for higher frequencies @NG=@r asymptotically converges to a successively larger value that is constant with distance. These trends seen for jet noise propagation are the same trends shown here for both planar and diverging waves in a lossy medium.…”

“…3 of Ref. 16, the actual ratios are 1.62, 2.50, and 3.71. The ratios from the data are very close to, but slightly less than the predicted ratios.…”

“…12,13 Similar trends have been predicted for noise propagation, 14,15 and the letter concludes by discussing the connections between the analytical behavior and that seen for jet noise. 16 …”

“…If the jet noise peak frequency in Ref. 16 is taken to be 113 Hz, the ratio of the asymptotic N values for 8, 10, and 12.5 kHz for an initial sinusoid in a thermoviscous medium should be 1.62, 2.54, and 3.97, respectively. Using the asymptotic values for numerically propagated jet noise in air from Fig.…”

“…In Ref. 16, experimental jet noise was numerically propagated to beyond 3 km-for atmospheric absorption and dispersion-and the nonlinear gain (NG), i.e., the change in sound pressure level due to nonlinearity, was calculated. The spatial derivative of the NG, @NG=@r, is essentially equivalent to N and was compared for various frequencies as a function of distance.…”