Tone excited jets, part V: A theoretical model and comparison with experiment†

Five papers have been submitted by Lockheed-Georgia Company to the Journal to appear successively in the same issue. Each paper describes a different facet of the outcome of a research program on jets excited by upstream discrete tones. In this last paper of the series, a mathematical model of tone-excited jets is developed. The model consists of two major components. The first component involves a mathematical description of the process by which the intrinsic instability waves of the jet are excited by upstream tones. This process is generally referred to as receptivity. The second component is the modeling of the non-linear interaction between the mean flow of the jet, the excited large-scale instability waves or turbulence structure and the fine-scale turbulence. In formulating this quasi-linear model it is assumed that each of these components of the jet flow can be characterized by a few parameters. These parameters are then related by conservation equations supplemented by closure models. The predicted results of the quasi-linear model are compared with experimental measurements. Very favorable agreement is found over a wide range of excitation frequencies and excitation levels. A limited parametric study of the effects of discrete tone excitation on jets predicted by using the present model is also carried out. This study covers parametric regions in which experimental measurements are not presently available. The effects of flight on the phenomenon of broadband noise amplification associated with tone excited jets are also discussed briefly.