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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. Introduction. – Wave transport in a multiple scattering environment has been a subject of intense research, demonstrating a large variety of behaviors, from the dis-persive propagation of a coherent wave [1, 2] to the existence of a diffusive regime, sometimes leading to local-ization [3, 4]. On the other hand, the nonlinear propagation of waves also comes with many intriguing phenomena , such as self-induced transparency [5] or second-harmonic generation [6], for instance. The question arises of how waves propagate when both strong multiple scattering and nonlinearities are present. For mechanical waves, this question has been addressed in granular media [7, 8], with the complication that both scattering and nonlin-earities are strongly dependent on the contact between the grains. Gas bubbles appear as perfect candidates for looking at nonlinear acoustic propagation in a multiple scattering regime: they are efficient acoustic scatter-ers, as well as strong nonlinear sources. Bubbly liquids have already been shown to exhibit substantial acoustic nonlinearities [9–12]. But an important limitation of the previous studies was the lack of quantitative comparison between the theoretical predictions and the experimental measurements, often due to a weak knowledge of the structure of the bubbly liquids used for the experiments.
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Olivier Lombard, Christophe Barrière, Valentin Leroy. Nonlinear multiple scattering of acoustic waves by a layer of bubbles. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2015, ⟨10.1209/0295-5075/112/24002⟩. ⟨hal-01527080⟩

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