Scattering Cross Section of Arrays of Rigid Pressure-Release and Resonant Elements

Abstract

The scattering cross section of orderly arrays of identical elements is discussed. Emphasis is placed on spherical scattering elements which are small in terms of wavelengths. In this range, pressure-release elements exhibit a relatively large, frequency-independent, omnidirectional scattering cross section which makes it necessary to consider cross coupling between elements, i.e., to account for the contributions to the wave incident on one element by the waves scattered by other elements. Cross-coupling need not be taken into account in an array of rigid elements because of their much smaller scattering cross section, which stands as (ka)4: 1 to the cross section of a pressure-release element. The two scatterers differ further in that the scattered field of the rigid element comprises a dipole component comparable in magnitude to the omnidirectional component. Finally, the effect of resonances of spherical scatterers is explored. If the resonance occurs at small ka, and in the absence of structural damping, a resonant mode raises the scattering cross section to a value proportional to (ka)−2. In practice, radiation damping is the limiting factor for the breathing mode only. In this case, it can be so large as to exclude resonant amplification. The directivity pattern of 20 equidistant spherical elements arranged in a spherical surface array was computed for pressure-release and rigid scatterers. In contrast to the single spherical scatterer, arrays are markedly directive, and become more so as the radius of the scattering elements is decreased. (This work was supported by BuShips under direction of U. S. Navy Underwater Sound Laboratory.)