Sound Radiation by Instability Wavepackets in a Boundary Layer

Sound radiation by instability wavepackets evolving from general initial conditionsin a low‐Mach‐number, slightly unstable boundary layer is studied. The formulation can be viewed as an exact instance of Lighthill's [13] acoustic analogy. The original disturbance may be line‐ or point‐centered with an infinitesimal amplitude. The sound field is confined within an expanding sphere. The directivity of sound is beamed and points upstream. This “superdirectivity” is slowly enhanced in time whereas the sound level is slowly attenuated. Nonlinear processes, once they come into play, reverse the temporal behavior of the sound level and sound directivity. For the boundary‐layer profiles studied, nonlinearity causes a “burst,” in a finite time, of the sound field in the form of a dipole.