# Scalar wave scattering by random semicylindrical bosses

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## Abstract

The theoretical and experimental study of the total acoustic field reradiated from two quasi-rigid model surfaces emersed in a water medium was undertaken. These models consisted of periodic arrays of circular semicylindrical bosses with either constant or random radii on a plane surface. The radii of these bosses were large compared to the wavelength of a 7 MHz incident field,and the separation between bosses was taken to be large in order to reduce multiple reflections. The model surfaces were machined from 3/8 inch thick aluminum plate. The selection of the size of the radii, separation distances between bosses and number of illuminated bosses, was based on a compromise to obtain the best approximation to a plane incident wave over the target. Since most of the surface insonified had radius of curvature much larger than the wavelength, the total field reradiated from these models was calculated using the Kirchhoff method of physical acoustics. This approach neglects shadow effects, diffraction and multiple reflections; therefore, in order to correct for some of these deficiencies, a geometric shadow approximation was made in the case of the random radii model. The total field expression was utilized to obtain the specular reflection coefficient and the backscattering cross-section for each model. The theoretical and experimental reflection coefficient curves obtained for the constant and random radii models without the geometric shadow correction were in general agreement for angles of incidences ([angle of incidence]) from 0 to 50 degrees. The discrepancy for the case of the constant radii for [angle of incidence] varying from 50 to 70 degrees was explanable on the basis of the shadow effect, etc. The inclusion of the shadow correction in the case of random radii made the two curves practically identical for values of [angle of incidence] up to 75 degrees. In the case of backscattering cross-sections, the theoretical and experimental results for both the constant radii array and the random radii array were in good agreement for off normal angles of incidence. The inclusion of the geometric shadow correction did not improve the off normal agreement between the two curves. This establishes the act that the scalar Kirchhoff theory is reasonably well adequate for near vertical incidence to high grazing angles of 50 to 60 degrees, after which correction for serious shadow effects must be included. The three-dimensional scattering ([angle of incidence],[scatter angle],[scatter angle out of plane of incidence]) apparatus was specially designed, constructed for this work and it is believed to be the only underwater acoustic facility of its type in existence. The experimental set-up used for this study with some improvement in position read-out and signal processing may be used to obtain much experimental data from model surfaces of considerable theoretical and practical applications; especially the randomly spaced constant radii circular semicylindrical models considered by Burke and Twersky and the rectangularly corrugated surface analyzed by Deryugin and Myakishev. Another such model requiring further work is the hemispherical boss array with fixed or random spacing.