Effect of turbulence on the risetime of sonic booms and spark generated N waves

Abstract

The risetime of acoustic pulses, such as sonic booms and electric spark generated N waves, is affected by propagation through turbulence. Risetime increases with increasing propagation distance and turbulence intensity. Data from electric spark propagation through turbulence show that Pierce’s wave front folding theory (1971) correctly describes the dependence of risetime τ on propagation distance x, i.e., τ∝x11/7, and turbulence kinetic energy dissipation rate ε, i.e., τ∝ε4/7. More recently, Pierce (AIAA-95-105) also derived a dispersion relation for acoustic pulse propagation through turbulence. The dispersion relation leads to an extra term in the propagation equation and takes into account the averaged contribution of all or part of the turbulence spectrum. A review of the dispersion theory is presented. Then a Van Kármán turbulent kinetic energy spectrum is used to obtain an accurate representation of both very large and very small turbulence structures. New results are compared with previous results obtained with a Kolmogorov spectrum.