Abstract
Instability waves in shear flows are believed to play an important role in noise generation. The mechanisms are by no means obvious because instability modes usually attenuate exponentially in the transverse direction. The acoustic analogy is not suited for identifying the mechanisms since it does not probe into sound generation process. The asymptotic approach has therefore been developed to describe, on the basis of first principles, how sound is radiated by instability waves in several canonic shear flows, including super- and sub-sonic jets, and boundary layers.
In supersonic jets, supersonically propagating modes exist, and emit, in the course of their amplification and attenuation, directly intense sound in the form of Mach waves. The asymptotic approach allows the Mach wave field to be described explicitly in terms of the envelope of the instability wavetrain. In contrast, instability modes in subsonic jets propagate subsonically and do not radiate sound directly. However, a spatially and temporally modulated wavetrain generates, through nonlinear interactions, a mean-flow distortion, which is slowly modulated on the long time and length scales of the envelope. This mean-flow field acts as a
non-compact source to radiate low-frequency sound.
Strong sound may be generated when a Tollmien-Schlichting wave in boundary layer is scattered by a local surface roughness. Asymptotic analysis of the scattering shows that the sound may produce an appreciate back effect on th source. Furthermore, when another roughness element is present, the sound generated at the downstream element propagates upstream to regenerate the instability wave at the upstream element. It is found that such a global acoustic coupling may lead to global instability, characterised by a self-sustained oscillation at discrete frequencies, whose dependence on the parameters (the Reynolds number and the distance between the two roughness elements) exhibits the familiar `ladder structure’.