Acoustic scattering by density gradients

Questions related to an underestimation of the noise of aircraft engines at low jet Mach numbers in the relations of Lighthill's (1952, 1954) theory of aerodynamic sound generation are considered, taking into account experiments on model jets conducted by Hoch et al. (1973) and Tanna et al. (1975) which show that at low Mach numbers an increase in the jet temperature results in an increase in the radiated sound. It is shown that scattering by density gradients does not induce a monopole source. Model problems are examined to illustrate that no 'monopole splash' occurs though density gradients can scatter the near field of quadrupoles and enhance their radiation efficiency to that of dipoles. The field of a monopole located close to a discontinuity in the fluid density or speed of sound is found to be the same regardless of whether the monopole is just above or just below the interface. Similar conclusions hold for a dipole with axes parallel to the discontinuity but not for one with axis perpendicular to it.