Low Frequency Sound Scattering from Rough Bubbly Ocean Surface: Small Perturbation Theory Based on the Reformed Helmholtz-Kirchhoff-Fresnel Method

Abstract

Through the use of perturbation theory, Kuo has previously introduced a joint surface roughness/volumetric model in order to characterize bubbly sea surface reverberation based on volumetric wave spectra, surface roughness wave spectrum, and correlation of volumetric wave spectrum and surface roughness wave spectrum. Due to the lack of undetermined volumetric scattered wave number K n , Kuo obtained backscattering strengths using only PiersonMoskwitz wave spectrum. In this paper, the reformed integral equation of authentic Helmholtz-Kirchhoff-Fresnel is discussed in which volumetric scattering is involved. By applying the reformed Helmholtz-Kirchhoff-Fresnel, volumetric scattered acoustic pressure field P n is obtained. Using Helmholtz wave equation and the obtained pressure field P n , the wave number vector of volumetric scattered field K n is calculated, and this used to compute the volumetric wave spectrum and the joint surface roughness/volumetric wave spectrum. The obtained spectra are then used to compute scattering strengths. Comparison of the obtained results against the results of experimental Critical Sea Tests shows good agreement. Finally, a parametric study is conducted to examine the effects of wind speeds, grazing angles, and frequencies on the scattering strengths. Keywords: Small Perturbation Method; Sound Scattering; Helmholtz-KirchhoffFresnel Integral; Bubble Plumes INTRODUCTIONEffects of sea surface on the incident sound have been examined by different acousticians due to its important role on sound propagation and reverberation and wide variety of sound applications in underwater environment. Underwater acoustic communication channels [1][2][3][4][5], sound emission from the submerged and floating objects [6,7], sound scattering of underwater sources from the sea surface [8] are among the most important subjects in underwater acoustics related to sea surface effects. In most of these subjects, it is necessary to provide an appropriate acoustic model in order to entail sea surface effects on the entry sound. Active control and acoustic response of structure and fluid interaction [9,10], attenuation and absorption [11], bubble plumes [12][13][14][15], sound transmission [16][17][18], sound propagation in shallow water [19][20][21] and surface waves [22][23] can be considered as important phenomena in the sea.There are different approaches adopted by investigators in order to examine sound scattering from the sea surface. These approaches can be categorized as experimental, theoretical, and numerical studies [24]. Several experimental studies

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