Wave propagation through a thin bubbly layer

Abstract

The shielding effects of a thin bubbly layer submerged in pure liquid on the propagation of acoustic waves are analyzed. By using the method of matched asymptotics, conditions across the bubbly layer are derived. They are: (1) that the pressure is continuous and (2) that the jump of normal velocity is related to the temporal derivative of pressure times a parameter representing the bulk property of the bubbly layer. This parameter is the product of a small number and a large number. The former is the wavenumber times the integral of the gas volume fraction β across the layer and the latter is the ratio of the density times the square of the speed of sound for the liquid phase to that for the gas phase. When the thin bubbly layer is adjacent to a rigid surface, their combined effect is described by an impedance boundary condition.

Scattering of acoustic waves by a nonlinear resonant bubbly screen

“…Next, a more significant result is the derivation of the term of bubble-bubble interaction in the RP equation dictating the nonlinear dynamics of the array. This contribution was absent from the analysis of Caflisch et al (1985a,b) for a bubbly liquid and its extension to a bubbly screen (Ng & Ting 1986;Miksis & Ting 1989); indeed its derivation requires the analysis to be conducted one order further than the dominant one considered in these references. Our result generalizes the findings of Leroy et al (2009) to the nonlinear regime and to the time domain.…”

“…This contribution was absent from the analysis of Caflisch et al. (1985 a , b ) for a bubbly liquid and its extension to a bubbly screen (Ng & Ting 1986; Miksis & Ting 1989); indeed its derivation requires the analysis to be conducted one order further than the dominant one considered in these references. Our result generalizes the findings of Leroy et al.…”

“…In contrast, the model of Leroy et al (2009) shows that bubbles within a screen experience a radiative damping much larger than an isolated bubble does; also that the resonant frequency of the screen is higher than that of an isolated bubble due to bubble-bubble interactions. A different approach has been proposed by Ng & Ting (1986) and Miksis & Ting (1989) who use the effective wave equation derived in Caflisch et al (1985a,b) for a bubbly liquid. By considering the limiting case of a thin layer, they derive transmission conditions through an effective screen in the nonlinear regime and in the time domain.…”

“…(2009) shows that bubbles within a screen experience a radiative damping much larger than an isolated bubble does; also that the resonant frequency of the screen is higher than that of an isolated bubble due to bubble–bubble interactions. A different approach has been proposed by Ng & Ting (1986) and Miksis & Ting (1989) who use the effective wave equation derived in Caflisch et al. (1985 a , b ) for a bubbly liquid.…”