Parabolic Moment Equations and Acoustic Propagation through Internal Waves

• Published in: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1980-08, Vol.372 (1748), p.117-148
• Main Author: Uscinski, B. J.
• Format: Article
• Language: English
• Subjects: Acoustic propagation; Acoustic spectra; Audio frequencies; Autocorrelation; Internal waves; Light refraction; Mathematical moments; Oceans; Spectral index; Wave propagation
• ISSN: 1364-5021; 0080-4630; 1471-2946; 2053-9169
• DOI: 10.1098/rspa.1980.0105

Internal waves present in the ocean modulate its acoustic refractive index so that it behaves like a random weakly irregular medium with respect to an acoustic signal. The parabolic equations for the propagation of the moments of an acoustic wave are applied to this case to describe the random fluctuations of a sound wave in the ocean. A form of the GarrettMunk spectrum with a continuous range of vertical wavenumbers instead of a discrete set of mode numbers is used to describe the irregularities of refractive index due to internal waves and to obtain the transverse autocorrelation function that appears in the moment equations. This transverse autocorrelation function differs in several important aspects from that of a turbulent medium with ‘frozen’ irregularities advected with the medium. Some analytical solutions for the fourth and second moments are given. The solution of the fourth-moment equation is extended to give a new result: the temporal frequency spectrum of the intensity fluctuations This spectrum, which behaves like ω_1 in the region where the fluctuations, are large but not saturated, describes a feature common, under certain conditions, to optical and radio-wave scatter as well as to the acoustic case. The theory is compared with some experimental observations of acoustic scattering by internal waves where a frequency spectrum of this type first seems to have been observed.