The radiation of sound by the instability waves of a compressible plane turbulent shear layer

Abstract

The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near-and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.

The role of instability waves in predicting jet noise

“…, because the second order solution 14 (which is a generalization of the second order instability wave solution considered by Tam and Morris) now decays more slowly with x 2 as x 2 → ± ∞ than the first order solution. But an "outer" solution can be constructed by using the WKBJ method to solve the reduced stationary (or uniformly moving) media wave equation that governs the flow in that region This result can be used to form a "composite" solution 17 that remains uniformly valid everywhere within and outside the shear layer.…”

Nonlinear mechanisms of sound generation in a perturbed parallel jet flow

“…Recent experimental work has provided evidence that instability waves are present in fully turbulent jets at high Reynolds number: Suzuki & Colonius (2006) used a nearfield microphone array to extract the instability-wave pressure signature and found remarkably good agreement with linear theory. A model for the production of sound based on linear instability waves was developed by Tam & Morris (1980), assuming a slowly spreading base flow, which resulted in the spatial growth and decay of linear eigenmodes. The approach has been of most use in supersonic flows, where the instability waves responsible for the sound radiation are amongst the most unstable.…”

Beamformed Flow-Acoustic Correlations in a Supersonic Jet

“…Of primary interest is noise in the peak radiation direction that arises from the supersonic motion of largescale turbulent structures, which have been shown to be modeled well as instability waves [1][2][3][4][5][6]. The approach involves flow-acoustic correlations using simultaneous multipoint measurements of turbulent fluctuations in the jet and pressure fluctuations in the acoustic far field.…”