Super-resonant scatter under ice sheets and in full spaces

Abstract

Systems of monopole scatterers interacting through multiple scatter may develop normal modes, i.e., true resonant behavior at certain frequencies (the equivalent source coefficients of each scatterer have real poles). This occurs when the single scatter cross sections are large enough to give significant interaction. This happens for highly tuned scatterers, e.g., gas-filled balloons, bubbles, and thin shells in water, insonified at frequencies near their characteristic “bubble” frequencies. This kind of super-resonance (SR) occurs when the system is at or near the interface with an elastic medium, e.g., a thin elastic plate [I. Tolstoy, J. Acoust. Soc. Am. 80, 282–294 (1986)]. Energy transport between scatterers is then mediated by boundary modes excited by the scatterers acting as point sources (e.g., the flexure waves of a thin plate). The case of two and three bubble systems at an ice-water or lucite-water interface is explored, with particular reference to the parameters ka, kl (k is the acoustic wavenumber, a the scatterer radius, l the spacing between scatterers) and the plate elastic constants. For a pair (doublet) the pressure amplification re: the free-field value is ≅ 2 × 103 for kl values as small as 0.5, with a directionality factor of 30: This is a passive, highly tuned, high magnification, strongly directional compact array (≅λ/12 size). A 30-Hz system would consist of two ballons of 10-cm radius near an ice boundary, with a discrete set of permissible l values ranging from about 5–20 m. Optimum spacings and magnifications depend upon the ice thickness (≅5 m). In an acoustic full space, energy exchange between scatterers is mediated less effectively by volume waves, and the scatter coefficient poles vanish: Bona-fide SR does not take place. Nevertheless, strong peaks may occur, giving magnifications ≅103. This quasiresonant behavior is discussed for simple two-, three-, four-, and six-element plane and polyhedral configurations. However, true SR behavior is reintroduced in full spaces by partially blocking selected pathways between scatterers. [Work supported by ONR.]