Propagation of Sound Waves through a Linear Shear Layer

On the applicability of high-frequency approximations to Lilley's equation

“…Adequate agreement between the exact source directivity and a high-frequency approximation for Strouhal numbers as small as one has been demonstrated in some limited circumstances by Tester and Morfey [7] using a ray-theory solution for polar angles outside the zone of silence of a round jet and by Scott [8] for a two-dimensional isothermal flow with a piecewise constant mean shear. The primary objective of the present paper is to determine the relative success of the above three high-frequency approximations for parallel round jets by comparing them to the exact order-one frequency solution over a wide range Strouhal numbers and far-field observation angles.…”

Aeroacoustics of Turbulent Shear Flows

“…However, Scott (1979) compared the exact and high-frequency solutions for fixed quadrupoles in a linear shear flow and fo und the results to be in close agreement, even at a Olsen & Friedmann (1974) plotted at constant source frequency n, where n/2rc is equal to the peak frequency of the spectrum at 90' fr om the jet axis.…”

“…(5) with y treated as a moving point source can be interpreted as corrections to the Lighthill (1952)/Ffowcs Williams (1963) result (8) that account for the effects of the nonuniform surrounding mean flow. A number of investigators (Mani 1976, Balsa 1976, Berman 1974, Goldstein 1975, 1976a, 1982, Tester & Morfey 1976, Scott 1979, Lilley 1974 have therefore calculated the acoustic radiation from point quadrupole sources moving through transversely sheared mean flows. Solutions must, in general, be obtained numerically, but relatively simple closed-form (or nearly closed form) solutions can be obtained in the low-and high-frequency limits OJDIUJ « 1 and OJDIUJ » 1, respectively, where D denotes the jet diameter (see Figure 1) and UJ denotes the jet velocity.…”

Sound source radiation in two-dimensional shear flow

“…6 " 9 A good synthesis of the results obtained in these studies is presented by Goldstein. 10 Further investigations have been carried out by Scott 11 and Koutsoyanis et al 12 Other studies pertinent to this problem are those of Refs. 13-17. In distinction with these previous studies our treatment is essentially numerical and does not rely on approximation techniques such as the method of steepest descent or the method of stationary phase.…”