Reply to "Comments on 'Acoustic Scattering by an Air Bubble Near the Sea Surface'"

Abstract

Ahtruct- The paper’s paradoxical result that the scattering form function of a bubble increases with decreasing distance from a pressurerelease surface is discussed. In this paper,’ Gaunaurd and Huang describe calculations of the effect of a nearby pressure-release surface on the spherical pulsation frequency of a gas bubble submerged in a liquid, and indicate good agreement between their values and those published by me some years ago [I]. Their comparison with my somewhat obscure data is gratifying; but a minor correction is required. The frequencies listed in their Table I1 as my “measurements” are actually calculated values. My paper does, indeed, list measured frequencies that are in reasonable agreement with the calculations, but those are not the ones cited by them. It is instructive to note that my simple calculation of the frequency of resonance of a bubble, which assumes that the surrounding liquid is incompressible, agrees with their more exact and complicated theory, at least for bubbles much closer than a wavelength from the surface. The values of the bubble “form function” shown in their Figs. 2 and 3(a) indicate that its peak value at resonance increases as the bubble moves closer to the free surface. This seems contrary to what might intuitively be expected, since a nearby free surface converts the bubble monopole into an acoustic dipole which radiates less efficiently. The apparent paradox is explained by noting that their theory does not take account of any mechanism limiting the magnitude of bubble pulsations at resonance except radiation damping, which is smaller for a dipole than for a monopole. In the absence of other sources of damping, the reduction in radiation damping due to a free surface might lead to a sufficiently large increase in the bubble pulsation amplitude at resonance, for constant incident sound pressure, to overcompensate for the reduced radiation efficiency, and thus result in a net increase in their calculated values of the form function for some directions. In a real gas bubble, however, thermal damping is much larger than radiation damping above 1 kHz; see, e.g., Devin [2]. If the resonant response of a bubble is controlled by thermal damping, its pulsation amplitude will not be affected by the presence of a free surface. Accordingly, the peak form function would then be expected to decrease with decreasing distance from the surface, contrary to the trend shown in their figures.