Turbulent jet noise: Shear noise, self-noise and other contributions

Using a previously validated simulation database of a Mach 0.9 cold jet, we examine the components of Lighthill's analogous noise source that are linear (shear noise terms) and quadratic (self-noise terms) in velocity fluctuations, as well as components that are deviations from ρ' = a²∞ ρ'. It is found that the shear noise is highly directional, with an angle of extinction near α = 90°, measured from the downstream axis, which is consistent with Ribner's theory 1 that I ~ cos⁴ α + cos² α. Its spectrum broadens at larger a. In contrast, the self-noise is more uniform. Is is fit by five inverse Doppler factors, (1 - Mc cos α)^-5, but only provided that Mc is dropped below its typically assumed values of Mc ≈ 0.6U_j/α∞ = 0.5 to Mc ≈ 0.3. In previous work it was found that M_c ≈ 0.3 was indeed the dominant phase velocity for the Lighthill source in this same jet. The spectral shape of the self-noise is relatively independent of angle, in contrast to the shear noise. The shear noise and self-noise are correlated, especially at small angles where their mutual correlation coefficient reaches as low as -0.4, casting doubt on models that treat these terms as distinct. The ρ' = α²∞ρ' contribution is relatively small, not negligible as expected for a cold jet, but it is so well correlated with the shear noise (correlation coefficient of -0.6 at small angles) that it should not be neglected. The total radiated power of the com-ponent quadratic in the velocity fluctuations is nearly the same as that of all components combined. Examining turbulence statistics relevant to jet noise, we see that two-point correlations statics are well fitted by exponential functions, as is typical of turbulence at all but the lowest Reynolds numbers, but integrated fourth-order space/retarded-time covariances, which are directed related to the radiated acoustic intensity, are instead very well fitted by Gaussian functions of different widths for different components, which is counter to conventional modeling practice.