Dynamics of gas bubbles in viscoelastic media accounting for high amplitude pulses and second harmonic emissions

Abstract

More than three decades ago, Anderson and Hampton [1980a, 1980b] (A&H) presented the theories for wave propagation in gassy water, saturated sediments and gassy sediments in their two-part review, which has been cited by many researchers in the geoacoustics and underwater acoustics areas. They gave an empirical formulation based on the theory of Spitzer [1943] for the wave propagation in gassy water by adapting that for a viscoelastic, lossy medium, though without providing a detailed derivation. Following Leighton [2007], this paper presents a theory based on non-stationary nonlinear dynamics of spherical gas bubbles and extends that 2007 paper to include liquid compressibility and thermal damping effects. The paper then shows how that nonlinear formulation can be reduced to the linear limit, and from this it derives the expressions for the damping coefficients, the scattering cross section, the speed of sound and the attenuation, and compares these with the A&H theory. The current formulation has certain advantages over A&H theory such as implementing an energy conservation based, nonlinear model for the gas pressure inside the bubble, having no sign ambiguity for the speed of sound formula (which is important when estimating the bubble void fraction in marine sediments) and correcting the ambiguity on the expression for scattering cross section, as identified in the recent work of Ainslie and Leighton [2011].

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Identifiers

ORCID for Timothy G. Leighton: orcid.org/0000-0002-1649-8750

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