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

Abstract

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.

Acoustic field characterization of the Duolith: Measurements and modeling of a clinical shock wave therapy device

“…Dissipation at the shock front is very strong, therefore once the shock is formed prefocally, its propagation is accompanied by energy losses that lead to reduction of the focusing gain of the peak positive pressure. 41,43,[50][51][52] In these previous simulation studies it was shown that the maximum focusing gain of the peak positive pressure is reached at an output level when the shock starts to develop at the focus. Here, additional simulations were performed to determine if a shock would develop if higher pressures were achieved.…”

“…[49][50][51] A method of fractional steps with an operator splitting procedure was used to march the solution over the axial coordinate z. A combined time and frequency domain solution was used.…”

Two-Point Measurements of Post-shock Overpressure Past a Grid Turbulence

“…Lee et al and Hasegawa & Noguchi showed deformation and smearing of a shock wave due to isotropic turbulence [7], [8]. Averiyanov et al [9] modeled finite amplitude acoustic wave through atmospheric turbulence using Khokhlov-Zabolotskaya-Kuznetsov type equation, thereby demonstrating production of focusing and defocusing regions and evaluating statistical behavior, time-of-flight, peak pressure and rise time, of Nwaves. However, experimental data of the same kind is far from sufficient.…”

Turbulent jet interaction with a long rise-time pressure signature

“…In the general turbulence interaction with the short rise-time pressure signature, the shock wave focusing/diffracting at a shock wave front are caused by the shock wave propagating to various direction resulting from the distortion of the shock wave front [27,28]. Salze et al [29] showed a shock propagation distance relates to a transverse shock focusing region and experimentally estimated its shock focal region.…”

“…Salze et al [29] showed a shock propagation distance relates to a transverse shock focusing region and experimentally estimated its shock focal region. Averiyanov et al [28,30] showed that an overpressure decrease and the arrival time are governed by the large scale of a velocity fluctuation, and the small scales of a velocity fluctuation mainly cause increasing the rise time. In the typical model experiments [10,29,30], in order to simulate the N-shaped sonic boom propagation in the real atmosphere, the characteristic length scales, such as a wavelength, a turbulent interaction distance, and the geometrical turbulence length scales, were adjusted.…”