Gust-Shock Interaction in Transonic Small-Disturbance Flow
The sound generated by interaction of small-amplitude convected disturbances with an attached shock wave in transonic small-disturbance flow is analyzed using Goldstein's decomposition of unsteady compressible flow. The equations obtained by linearizing the Euler equations about the nonuniform mean flow provide a framework that enables the calculation of the vortical, entropic, and acoustic waves generated by the gust-shock interaction. The lateral stretching of disturbances that is characteristic of transonic small-disturbance flow implies that the shock wave is long relative to the O(1) or smaller gust wavelength and that its strength and obliqueness angle vary slowly along its length. This leads to inner regions near the shock where the jump relations are solved and to an outer region where the shock's finite length and variation in strength determine the far-field acoustic radiation. The theory is applied to obtain numerical results for the radiated acoustic power and directivity patterns for a shock wave attached to an infinite curved surface