A note on the structure of the acoustic field emitted by a wave packet

The sound field created by wave packets has been subject to rigorous experimental, analytical and numerical research in the last two decades. It has been argued that the wave packet can model a large scale structure in the form of an instability wave, initially growing, then saturating and decaying. These structures were found to be dominant sound producers in the mixing region of forced jets [1, 2]. Several analytical models for analyzing the emitted sound by these structures have been offered over the years. Ffowcs Williams and Kempton [3] used Lighthill's analogy to determine the magnitude of the radiated sound. Tam and Burton [4, 5] used a linear stability analysis for calculating the sound field emitted by a slowly expanding supersonic shear layer and Crighton and Huerre [6] looked at the appearance of superdirectivity in the sound field of low subsonic shear layers. The purpose of this study is to produce simple analytical approximations for the sound field, which the previous studies seem to lack. There is a need for such approximations not just for the physical understanding of the sound field but also as a design and validation tool for computational and experimental aeroacoustics. The model suggested by Crighton and Huerre [5] seems to be the most appropriate for this aim. It treats the problem as a boundary value problem where the effect of the wave packet comes from the boundary condition. They have already succeeded in estimating the penetration distance of the transition region between the near field and the far field of a superdirective sound field of a low subsonic Gaussian wave packet. This study will give simple approximations for the near field and far field pressure for a subsonic and a supersonic wave packet. It will investigate the effect of the convective Mach number and different wave packet shapes on the penetration distance of the transition region in the transverse and longitudinal directions