Effects of Compressibility on the Radiation and Viscous Damping Terms in the Scattering and Extinction Cross-Sections 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 571-576], the authors described a discrepancy between the radiation damping coefficients in the models due to Weston and to Medwin describing the scattering cross-section of a single spherical bubble. The resolution of that discrepancy [M. A. Ainslie & T. G. Leighton, J. Acoust. Soc. Am. 126, 2163-2175 (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 cross-section