Multiple scattering theory for modeling sonic booms in atmospheric turbulence.

Sonic booms are often modeled using Burgers equations accounting for dominant propagation effects. Scattering effects of turbulence, however, have not been incorporated into such equations, although these effects are ubiquitous in measured sonic booms. This paper formulates the mean scattering effects, including backscattering, using multiple scattering theory and ensemble averaging. It obtains an acousto-turbulence interaction energy representing the interaction of an acoustic wavefield with a turbulence field. The interaction energy gives rise to a scattering wavenumber, a complex-valued correction to the free-space wavenumber. The scattering wavenumber leads to a dispersion and attenuation of the mean waveform due to backscattering, and can be obtained from a derived exact solution. An existing Burgers equation is extended to include the scattering effects of turbulence as an additional linear term. Numerical simulations of an N-wave and a low boom show that the mean scattering effects lead to shock thickening in the mean waveforms as well as reduce the peak amplitudes and total energy contents. The energy reduction is less severe in the low boom than in the N-wave and is dependent on the variance, correlation length, and thickness of the turbulence field.

Numerical prediction of loudness metrics for N-waves and shaped sonic booms in kinematic turbulence.

The effects of a kinematic field of velocity fluctuations on the loudness metrics of two waveforms are examined with a three-dimensional one-way propagation solver. The waveforms consist of an N-wave and a simulated low-boom from NASA's X-59 QueSST aircraft. The kinematic turbulence is generated using a von Kármán composite spectrum, which is dependent on a root mean square (rms) velocity and outer scale of the turbulence. A length scale is proposed to account for the effect of the rms velocity and integral scale on the focusing and defocusing of the sonic boom waveform. The probability density function of the location of the first caustic attains a maximum value when the propagation distance is equal to the proposed length scale. Simulation results indicate that for small values of the nondimensional propagation distance, the standard deviation of the loudness metrics increases linearly. The loudness metrics follow a normal distribution within a given range of the nondimensional propagation distance. Results indicate the potential to parameterize the loudness metric distributions by the rms velocity and integral length scale.

Time reversal for localization of sources of infrasound signals in a windy stratified atmosphere.

Time reversal is used for localizing sources of recorded infrasound signals propagating in a windy, stratified atmosphere. Due to the convective effect of the background flow, the back-azimuths of the recorded signals can be substantially different from the source back-azimuth, posing a significant difficulty in source localization. The back-propagated signals are characterized by negative group velocities from which the source back-azimuth and source-to-receiver (STR) distance can be estimated using the apparent back-azimuths and trace velocities of the signals. The method is applied to several distinct infrasound arrivals recorded by two arrays in the Netherlands. The infrasound signals were generated by the Buncefield oil depot explosion in the U.K. in December 2005. Analyses show that the method can be used to substantially enhance estimates of the source back-azimuth and the STR distance. In one of the arrays, for instance, the deviations between the measured back-azimuths of the signals and the known source back-azimuth are quite large (-1° to -7°), whereas the deviations between the predicted and known source back-azimuths are small with an absolute mean value of <1°. Furthermore, the predicted STR distance is off only by <5% of the known STR distance.

A theoretical relation between the celerity and trace velocity of infrasonic phases.

This paper presents a relationship between the celerity and trace velocity of infrasound signals propagating in a stratified, windy atmosphere. Despite their importance, known celerity values have only been determined empirically. An infrasonic phase (I-phase) diagram is developed which is useful in identifying different I-phases. Such an I-phase diagram allows for the prediction of the range of values of the celerity and trace velocity for each I-phase. The phase diagram can easily be extended to underwater acoustic and acoustic-gravity waves. An I-phase diagram is compared with data obtained from a ground-truth event where qualitative agreement is obtained.

Suppression of an acoustic mode by an elastic mode of a liquid-filled spherical shell resonator.

The purpose of this paper is to report on the suppression of an approximately radial (radially symmetric) acoustic mode by an elastic mode of a water-filled, spherical shell resonator. The resonator, which has a 1-in. wall thickness and a 9.5-in. outer diameter, was externally driven by a small transducer bolted to the external wall. Experiments showed that for the range of drive frequencies (19.7-20.6 kHz) and sound speeds in water (1520-1570 m/s) considered in this paper, a nonradial (radially nonsymmetric) mode was also excited, in addition to the radial mode. Furthermore, as the sound speed in the liquid was changed, the resonance frequency of the nonradial mode crossed with that of the radial one and the amplitude of the latter was greatly reduced near the crossing point. The crossing of the eigenfrequency curves of these two modes was also predicted theoretically. Further calculations demonstrated that while the radial mode is an acoustic one associated with the interior fluid, the nonradial mode is an elastic one associated with the shell. Thus, the suppression of the radial acoustic mode is apparently caused by the overlapping with the nonradial elastic mode near the crossing point.

Uniformly valid solution for acoustic propagation in weakly tapered circular waveguides: liquid jet example.

The propagation of ultrasound down laminar liquid jets has potential applications to the stimulation of liquid drop production [J. B. Lonzaga, C. F. Osterhoudt, D. B. Thiessen, and P. L. Marston, J. Acoust. Soc. Am. 121, 3323-3330 (2007)] as well as to the coupling of ultrasound to objects through contact with a jet. In normal gravity, a jet issuing from a nozzle becomes tapered as the jet accelerates downward. A uniformly valid solution for the acoustic propagation in a weakly tapered, liquid jet waveguide in air with a turning point is derived using Langer's transformation and the method of multiple scales. The loss of energy from transmission into the air and from thermal viscous absorption is neglected. A solvability condition is used to obtain the leading-order correction due to the taper of the waveguide. This asymptotic solution is validated using finite-element numerical calculations. The ultrasonic wave amplitude is enhanced in the region of the jet close to the cutoff of the excited mode.

Liquid jet response to internal modulated ultrasonic radiation pressure and stimulated drop production.

Experimental evidence shows that a liquid jet in air is an acoustic waveguide having a cutoff frequency inversely proportional to the jet diameter. Ultrasound applied to the jet supply liquid can propagate within the jet when the acoustic frequency is near to or above the cutoff frequency. Modulated radiation pressure is used to stimulate large amplitude deformations and the breakup of the jet into drops. The jet response to the modulated internal ultrasonic radiation pressure was monitored along the jet using (a) an optical extinction method and (b) images captured by a video camera. The jet profile oscillates at the frequency of the radiation pressure modulation and where the response is small, the amplitude was found to increase in proportion to the square of the acoustic pressure amplitude as previously demonstrated for oscillating drops [P.L. Marston and R.E. Apfel, J. Acoust. Soc. Am. 67, 27-37 (1980)]. Small amplitude deformations initially grow approximately exponentially with axial distance along the jet. Though aspects of the perturbation growth can be approximated from Rayleigh's analysis of the capillary instability, some detailed features of the observed jet response to modulated ultrasound are unexplained neglecting the effects of gravity.