G. C. Gaunaurd
H. Huang
Naval Surface Warfare Ctr., White Oak Detachment, Silver Spring, MD 20903-5640
Sound scattering by an air bubble in a boundless fluid is an old classical
problem [i.e., R. Y. Nishi, Acustica 33, 65--74 (1975)]. If the air bubble is
near, and strongly interacting with the surface of a liquid half-space, then
the scattering cross section (SCS) of the bubble is quite different from its
value far away from the boundary. The exact solution for this scattering
problem is given which is valid for any incidence direction of the (plane)
sound waves, and for any bubble depth, obtained by the method of images. This
benchmark solution is found by means of the addition theorems for the spherical
wave functions. The resulting SCS contains contributions from the interface,
the bubble, and from its image, and it is expressible in terms of coupling
coefficients containing products of Wigner 3-j symbols. The formulation is
illustrated with many computed plots and it is finally extended to the case of
a round, low-concentration cloud of equal size bubbles, just beneath the sea
surface. This generalization is possible by replacing the individual bubble
properties by those of an ``effective medium'' describing the bubble cloud just
as we found them earlier [i.e.,