1 

The Influence of Radiation Damping on ThroughResonance Variation in the Scattering CrossSection of Gas Bubbles
When a gas bubble in water undergoes forced pulsations, sound is radiated at the forcing frequency, and the scattering crosssection exhibits a resonance peak when the forcing frequency passes through the bubble’s natural frequency. At resonance, the amplitude of the scattered spherical wave is determined by the amount of damping associated with the bubble dynamics. In his 1967 article, ‘Sound propagation in the presence of bladder fish’, Weston describes a model for the throughresonance frequency dependence of the scattering and extinction crosssections, based on the work of Andreeva (1964). In Weston’s model, if all damping terms other than radiation damping are omitted, the resonance peak is skewed, with a tendency for the scattering crosssection to increase with increasing frequency through resonance. In 1977, Medwin published ‘Acoustical determination of bubblesize spectra’, based on Eller (1970), in which he describes a similar model, according to which the predicted resonance peak is also skewed, but in the opposite direction to that predicted by Weston. If Medwin’s model turns out to be valid, this would have little impact, as his curves are already in widespread use. However, if the AndreevaWeston model is correct, a small adjustment becomes necessary to Medwin’s curves. A possible experiment designed to establish the true frequency dependence is described, involving the ensonification of a single spherical bubble with a broadband pulse, through the bubble’s resonance frequency. If the radiation damping can be separated form other effects, the correct frequency dependence can be established by measuring the spectrum of the scattered sound.

[Abstract]

2 

Sonar Equations for Planets and Moons
A set of equations to describe the performance of sonar systems, collectively known as the “sonar equations”, was developed during and after the Second World War. These equations assumed that both the sonar equipment and the object to be detected (usually a submarine) would be submerged in one of Earth’s seas or oceans, and the efficacy of the sonar equations is long established for this situation. Looking ahead into the 21st century, the proposed use of sonar in the exotic oceans of Europa, Ganymede or Titan demands a fresh look at the 50yearold sonar equations to assess their suitability for this new purpose. Examples are given for Europa’s icy ocean, one of Titan’s hydrocarbon lakes, and Jupiter’s dense gaseous atmosphere.

[Abstract]

3 

Near resonant bubble acoustic crosssection corrections, including examples from oceanography, volcanology, and biomedical ultrasound
The scattering crosssection σs of a gas bubble of equilibrium radius R0 in liquid can be written in the form σs =4π R02 / [(ω12 / ω2 1)2 + δ2], where ω is the excitation frequency, ω1 is the resonance frequency, and δ is a frequencydependent dimensionless damping coefficient. A persistent discrepancy in the frequency dependence of the contribution to δ from radiation damping, denoted δrad, is identified and resolved, as follows. Wildt's [Physics of Sound in the Sea (Washington, DC, 1946), Chap. 28] pioneering derivation predicts a linear dependence of δrad on frequency, a result which Medwin [Ultrasonics 15, 713 (1977)] reproduces using a different method. Weston [Underwater Acoustics, NATO Advanced Study Institute Series Vol. II, 5588 (1967)], using ostensibly the same method as Wildt, predicts the opposite relationship, i.e., that δrad is inversely proportional to frequency. Weston's version of the derivation of the scattering crosssection is shown here to be the correct one, thus resolving the discrepancy. Further, a correction to Weston's model is derived that amounts to a shift in the resonance frequency. A new, corrected, expression for the extinction crosssection is also derived. The magnitudes of the corrections are illustrated using examples from oceanography, volcanology, planetary acoustics, neutron spallation, and biomedical ultrasound. The corrections become significant when the bulk modulus of the gas is not negligible relative to that of the surrounding liquid. © 2009 Acoustical Society of America.

[Abstract]

4 

Effects of Compressibility on the Radiation and Viscous Damping Terms in the Scattering and Extinction CrossSections of a Single Spherical Bubble: A Puzzle Solved and a Puzzle Posed
In [M. A. Ainslie & T. G. Leighton, Underwater Acoustic Measurements (Heraklion, Crete, 2007), pp 571576], the authors described a discrepancy between the radiation damping coefficients in the models due to Weston and to Medwin describing the scattering crosssection of a single spherical bubble. The resolution of that discrepancy [M. A. Ainslie & T. G. Leighton, J. Acoust. Soc. Am. 126, 21632175 (2009)] is summarised, and a new question posed related to viscous damping, as follows. The usual derivation of bubble damping due to viscosity assumes an incompressible medium; in that derivation, dilatational viscosity is neglected on the grounds that there is no compression. Modern theoretical treatments of scattering and attenuation through bubble clouds permit a compressible medium for radiation damping, but do not revisit the effect of this compressibility on the viscous damping. This raises as yet unanswered questions about the validity of the currently accepted expressions for the viscous damping factor used for calculating scattering and extinction crosssections

[PDF]
[Abstract]

5 

Review of scattering and extinction crosssections, damping factors, and resonance frequencies of a spherical gas bubble
Perhaps the most familiar concepts when discussing acoustic scattering by bubbles are the resonance frequency for bubble pulsation, the bubbles' damping, and their scattering and extinction crosssections, all of which are used routinely in oceanography, sonochemistry, and biomedicine. The apparent simplicity of these concepts is illusory: there exist multiple, sometimes contradictory definitions for their components. This paper reviews expressions and definitions in the literature for acoustical crosssections, resonance frequencies, and damping factors of a spherically pulsating gas bubble in an infinite liquid medium, deriving two expressions for resonance frequency that are compared and reconciled with two others from the reviewed literature. In order to prevent errors, care is needed by researchers when combining results from different publications that might have used internally correct but mutually inconsistent definitions. Expressions are presented for acoustical crosssections associated with forced pulsations damped by liquid shear and (oftneglected) bulk or dilatational viscosities, gas thermal diffusivity, and acoustic reradiation. The concept of a dimensionless damping coefficient is unsuitable for radiation damping because different crosssections would require different functional forms for this parameter. Instead, terms based on the ratio of bubble radius to acoustic wavelength are included explicitly in the crosssections where needed. © 2011 Acoustical Society of America.

[Abstract]

6 

Sonar equations for planetary exploration
The set of formulations commonly known as “the sonar equations” have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and ocalize objects submerged in seawater. The efficacy of the sonar equations, with individualterms evaluated in decibels, is well established in Earth’s oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake highfidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan’s hydrocarbon lakes, and for the gaseous atmospheres of (for

[Abstract]
