Experimental and Theoretical Study of the Propagation of N Waves Through a Turbulent Medium

An experimental and theoretical study of the propagation of N waves through a turbulent medium is performed. The experiment is a model experiment that simulates the propagation of sonic booms through a turbulent atmosphere. Because the annoyance to sonic booms is related to the rise time and peak pressure of the booms, it is important to investigate the effect of atmospheric turbulence on sonic boom rise time and waveform. A review is presented of past research on the effect of turbulence on sonic boom propagation. In the model experiment, the N waves are generated by a spark -source, and the turbulence is produced by a plane jet. The characteristics of the plane jet turbulence are measured by hot-wire anemometry. The goal of this investigation is (1) to perform experiments to study the effect of turbulence on N wave waveform, (2) to use the model experiment data to test various sonic boom theories, and (3) to develop a new analytical model for the propagation of plane N waves through a turbulent medium. The results of this research are as follows. First, the model experiment is successful in simulating the propagation of sonic booms through the atmosphere. The waveform distortion of actual sonic booms is reproduced, both in scale and in character, in the model study. An important observation from the model study is that turbulence almost always increases rise time, and that, on average, peak pressure decays. Second, when used to test previous models of the effect of turbulence on rise time and waveform distortion, the data show that only Pierce's model, based on the wavefront folding mechanism, yields a fairly accurate prediction for rise time. Results from other models are not confirmed by the model experiment data. Third, a new theoretical model is developed, in which discrete realizations of a turbulent velocity field are generated. A linear acoustic wave equation is developed that describes propagation of plane N waves through turbulence. A perturbation scheme is used to solve the equation, and the results are confirmed by the measurements.