Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis

Horizontal refraction notably influences propagation characteristics with the variation of the waveguide environment. In this study, the horizontal refraction phenomenon at low frequencies was investigated in a sloping sea region with an incomplete vertical sound speed profile. Using the mode coupling theory, this research explores the relationship between horizontal refraction and energy exchange among modes, examining the impact of environmental conditions on the horizontal refraction angle. Theoretical derivations and numerical simulations reveal the mechanisms by which the source depth and modal order influence the horizontal refraction. The analysis indicates that the horizontal refraction angle increases with the modal order when the real part of the horizontal wavenumber $k_m$ at the source position is less than the wavenumber $k_s$. In this situation, the horizontal refraction angle corresponding to the same modal order does not vary with the source depth. However, if the real part of $k_m$ is larger than $k_s$, then the horizontal refraction angle decreases as the source depth increases. This condition is due to the extremely small eigenfunction value at source depth of the low-order mode, thereby enhancing the mode coupling effect. The mode coupling is intimately associated with the mode excited by the source. Therefore, the source depth exerts a substantial influence on the horizontal refraction. Under these conditions, the modal order has a negligible effect on the horizontal refraction angle.