Aerodynamic sound from a high-speed modulated transitory wave: Application to screech

Abstract

Screech occurs in supersonic jets characterized by a periodic cell structure (cell length s) in which the jet velocity varies periodically in the downstream direction. The transitory wave (Mach number M, wavelength Λ) consequently becomes space-modulated, upsetting the otherwise high degree of cancellation and yielding a stationary phased array, resolvable into long and short propagating waves, of wavelengths Λs/(Λ−s) and Λs/(Λ+s). The radiation of the latter is comparatively very weak. The former radiates with a single peak in the upstream direction, maximizing with perfect reinforcement when Λ/s=(1+M), the peak shifting away from the axis for higher Mach numbers. Plausible assumptions yield realistic screech intensity estimates (that exceed those of the downstream radiation of the unmodulated wave). The first harmonic of the cell structure interacts with that of the transitory wave to produce another single directional maximum, at near normal to the jet direction, again in accordance with experiment. In this treatment the simplest of assumptions have been used. In particular, the cell structure has been taken to be fixed, whereas Schlieren photographs reveal that sometimes very large displacements occur. This nonlinear refinement is now being investigated.