Generation of sound and instability waves due to unsteady suction and injection

This paper analyses the generation of sound and Tollmien-Schlichting (T-S) waves in a compressible boundary layer that is subject to unsteady suction and injection. An asymptotic approach based on the triple-deck formulation has been developed to calculate the sound field. It is shown that in addition to the three familiar asymptotic regions that govern the near-field hydrodynamic motion, an extra outer region controlling the sound radiation must be introduced. The near-field solution is sought via an asymptotic expansion in ascending powers of epsilon = R-1/8, where R is the global Reynolds number. The first three terms in the asymptotic series are found to act as quadrupole, dipole and monopole sources respectively, and make equal order-of-magnitude contributions to the acoustic far field. The analysis also allows the amplitude of the excited T-S waves to be determined to O(epsilon) accuracy. It is believed that the flow structure and solution procedure may be used to solve a range of aeroacoustic problems.