Finite amplitude acoustic wave propagation through atmospheric turbulence is modeled using a Khokhlov–Zabolotskaya–Kuznetsov (KZK)-type equation. The equation accounts for the combined effects of nonlinearity, diffraction, absorption, and vectorial inhomogeneities of the medium. A numerical algorithm is developed which uses a shock capturing scheme to reduce the number of temporal grid points. The inhomogeneous medium is modeled using random Fourier modes technique. Propagation of N-waves through the medium produces regions of focusing and defocusing that is consistent with geometrical ray theory. However, differences up to ten wavelengths are observed in the locations of fist foci. Nonlinear effects are shown to enhance local focusing, increase the maximum peak pressure (up to 60%), and decrease the shock rise time (about 30 times). Although the peak pressure increases and the rise time decreases in focal regions, statistical analysis across the entire wavefront at a distance 120 wavelengths from the source indicates that turbulence: decreases the mean time-of-flight by 15% of a pulse duration, decreases the mean peak pressure by 6%, and increases the mean rise time by almost 100%. The peak pressure and the arrival time are primarily governed by large scale inhomogeneities, while the rise time is also sensitive to small scales.

/pdf/nonlinear-and-diffraction-effects-in-propagation-of-n-waves-4d5lo2gz7f.pdf

Nonlinear and diffraction effects in propagation of N-waves in randomly inhomogeneous moving media.

A laboratory experiment was conducted to study the propagation of short duration (25 μs) and high amplitude (1000 Pa) acoustic N-waves in turbulent flow. Turbulent flows with a root-mean-square value of the fluctuating velocity up to 4 m/s were generated using a bidimensional nozzle (140 × 1600 mm2). Energy spectra of velocity fluctuations were measured and found in good agreement with the modified von Karman spectrum for fully developed turbulence. Spherical N-waves were generated by an electric spark source. Distorted waves were measured by four 3 mm diameter microphones placed beyond the turbulent jet. The presence of turbulence resulted in random focusing of the pulse; more than a threefold increase of peak pressures was occasionally observed. Statistics of the acoustic field parameters were evaluated as functions of the propagation distance and the level of turbulence fluctuations. It is shown that random inhomogeneities decrease the mean peak positive pressure up to 30% at 2 m from the source, double the mean rise time, and cause the arrival time about 0.3% earlier than that for corresponding conditions in still air. Probability distributions of the pressure amplitude possess autosimilarity properties with respect to the level of turbulence fluctuations.

https://acoustique.ec-lyon.fr/publi/averiyanov_jasa11b.pdf

Random focusing of nonlinear acoustic N-waves in fully developed turbulence: laboratory scale experiment.

This paper describes ground-level measurements of sonic boom signatures made as part of the SR-71 sonic boom propagation experiment recently completed at NASA Dryden Flight Research Center, Edwards, California. Ground level measurements were the final stage of this experiment which also included airborne measurements at near and intermediate distances from an SR-71 research aircraft. Three types of sensors were deployed to three station locations near the aircraft ground track. Pressure data were collected for flight conditions from Mach 1.25 to Mach 1.60 at altitudes from 30,000 to 48,000 ft. Ground-level measurement techniques, comparisons of data sets from different ground sensors, and sensor system strengths and weaknesses are discussed. The well-known N-wave structure dominated the sonic boom signatures generated by the SR-71 aircraft at most of these conditions. Variations in boom shape caused by atmospheric turbulence, focusing effects, or both were observed for several flights. Peak pressure and boom event duration showed some dependence on aircraft gross weight. The sonic boom signatures collected in this experiment are being compiled in a data base for distribution in support of the High Speed Research Program.

/pdf/ground-based-sensors-for-the-sr-71-sonic-boom-propagation-32fsv4m6el.pdf

Ground-based sensors for the SR-71 sonic boom propagation experiment

Theoretical approach for the description of nonlinear acoustic waves transmitted through randomly inhomogeneous thin layer (phase screen) is presented An exact analytical solutions of governing equations are obtained both for the spatial structure of the field behind the screen and for the temporal waveform Using this model statistical characteristic of a single N-pulse having passed through the screen is studied The influence of the random focusing and defocusing effect on the statistical properties of N-wave behind the screen is analyzed Distribution functions for the shock amplitude, overpressure probability density, and ray convergency are presented It is shown that the spatial modulation of the phase front affects the average characteristics of the field and causes the strong variations of the wave field parameters

J. M. Downing

Papers

Sonic booms produced by US Air Force and US Navy aircraft: Measured data