Nonlinear multiple scattering of acoustic waves by a layer of bubbles

Abstract

We present a theoretical and experimental study of the acoustic second-harmonic generation by a single layer of bubbles. This simple system allows us to investigate the subtle interplay between nonlinear effects and multiple scattering. A perturbative model is shown to give an excellent agreement with the experimental measurements, and we demonstrate the existence of an optimal concentration of bubbles, for which the harmonic generation is maximum. The potential of bubble screens as efficient subwavelength acoustic nonlinear sources is discussed.

Multiple scattering of an ultrasonic shock wave in bubbly media

“…However, multiple scattering effects are small at these frequencies. Finally, multiple scattering effects can be observed in nonlinear regime only if bubbles are excited around Minnaert frequency [29,30]. ***…”

Scattering of acoustic waves by a nonlinear resonant bubbly screen

“…The scalings are such that the resonance takes place in the low frequency regime, specifically ω M h/c = O(ε). Eventually, the scaling for the Mach number produces a linear propagation of waves at large scale in the liquid while keeping nonlinear responses of the bubbles, see Lombard, Barrière & Leroy (2015). The asymptotic analysis requires the use of the rescaled dimensionless coordinates x at the macroscopic scale of the wavelength, x m at the mesoscopic scale of the array spacing and x μ at the microscopic scale of the bubble radius (figure 13), with…”

Optimal subharmonic emission of stable bubble oscillations in a tube

“…From the results in Fig. 9(b) we can conclude that by increasing D/R 0 , (i) the transition distance from a spherical to a planar wave increases and (ii) the amplitude of the reflected wave decreases roughly as R 0 /D, which is the result of the reflection of bubble screens to linear pressure pulses [40]. In the following, to obtain a stable plane wave, the pressure is sampled at distance |x s |/R 0 = 15 in DNS and in order to compare the results with the predictions of the KM + Int model, we use a simple semiheuristic model described in Appendix A to relate the bubble response obtained from KM + Int equation with the pressure amplitude of the plane wave emitted by the bubble.…”