Resonant scatterer configurations near elastic boundaries

Abstract

Systems of precisely spaced bubbles, air‐filled shells or balloons in water, insonified at frequencies near their intrinsic radial resonance ω0 exhibit true resonant modes. For resonant wavenumber kR (in water) and scatterer radius a, this leads to amplification factors (kRa)−1 above and beyond the similar classical factor due to single scatter, and thus to net pressure amplification of order (kRa)−2 relative to the incident field (i.e., over 120 dB on the intensity scale, on or inside the scatterer). This effect is predicted by formulas for the equivalent source strength B of each scatterer of the system, account being taken of multiple scatter interaction. Whereas for pairs of scatterers, or periodic lattices, B is known to exhibit relatively modest maxima for selected values of x = kl (l being the spacing between scatterers), which had been called resonances [V. Twersky, J. Opt. Soc. Am. 52, 145–171 (1962)], one can show that, under certain conditions, true resonances exist— i.e., in the absence of attenuation, B exhibits real poles. This phenomenon is much enhanced for systems near elastic boundaries for which coupling between scatterers is mediated by surface waves, and doublet or triplet configurations develop spectra of resonant configurations xn at frequencies ωn (the latter being all close to ω0 for a spectrum of scatterer sizes an). [Work supported by ONR.]