Average echoes from randomly oriented random-length finite cylinders : zooplankton models

Abstract

By heuristically extending the previously developed ray solution [Stanton et al. J. Acoust. Soc. Am. 94, 3454–3462 (1993)] to predict the scattering by cylinders over all angles of incidence, approximate expressions are derived which describe the echo energy due to sound scattered by finite cylinders averaged over orientation and length. Both straight and bent finite length cylinders of high aspect ratio are considered over the full range of frequencies (Rayleigh through geometric scattering). The results show that for a sufficiently broad range of orientation, the average echo is largely independent of the degree of bend—that is, the results are essentially the same for both the straight and bent cylinders of various radii of curvature (provided the bend is not too great). Also, in the limit of high frequency (i.e., the acoustic wavelength is much smaller than the cross-sectional radius of the object), the averages are independent of frequency. The resultant formulas derived herein are useful in describing the scattering by elongated zooplankton whose shape may not necessarily be known in the natural ocean environment. The average echo is shown to depend directly upon standard deviation (s.d.) of the angle of orientation as well as size. If independent measurements of size are made (such as from trawling samples), then the properties of the angle distribution and hence behavior may be inferred from the data. Averages over both angle and a narrow distribution of size are shown to only partially smooth out deep nulls in the scatter versus frequency curves. The formulas compare favorably with laboratory data involving aggregations of animals and a broad range of frequencies (38 kHz to 1.2 MHz).