AVERAGE ECHOES FROM RANDOMLY ORIENTED RANDOM-LENGTH FINITE CYLINDERS - ZOOPLANKTON MODELS

By heuristically extending the previously developed ray solution [Stan ton et al. J. Acoust. Soc. Am. 94, 3454-3462 (1993)] to predict the sc attering by cylinders over all angles of incidence, approximate expres sions are derived which describe the echo energy due to sound scattere d by finite cylinders averaged over orientation and length. Both strai ght and bent finite length cylinders of high aspect ratio are consider ed over the full range of frequencies (Rayleigh through geometric scat tering). The results show that for a sufficiently broad range of orien tation, the average echo is largely independent of the degree of bend- that is, the results are essentially the same for both the straight an d bent cylinders of various radii of curvature (provided the bend is n ot too great). Also, in the limit of high frequency (i.e., the acousti c wavelength is much smaller than the cross-sectional radius of the ob ject), the averages are independent of frequency. The resultant formul as derived herein are useful in describing the scattering by elongated zooplankton whose shape may not necessarily be known in the natural o cean environment. The average echo is shown to depend directly upon st andard deviation (s.d.) of the angle of orientation as well as size. I f independent measurements of size are made (such as from trawling sam ples), then the properties of the angle distribution and hence behavio r may be inferred from the data. Averages over both angle and a narrow distribution of size are shown to only partially smooth out deep null s in the scatter versus frequency curves. The formulas compare favorab ly with laboratory data involving aggregations of animals and a broad range of frequencies (38 kHz to 1.2 MHz).