Modeling And Analyzing Sound Propagation In Range-Dependent Waveguides Based On The Two-Way Coupled Mode Method

The sound propagation in shallow water is one of the hot research topics in underwater acoustics.The shallow water environment is complex,such as rough sea surface,uneven seabed topography,inhomogeneous water media,as well as scatterers such as marine organisms,bubble groups and ships.The shallow water can be regarded as a range-dependent waveguide with variable physical parameters(sound velocity and density)and range-dependent interfaces(bathymetry).In a horizontally layered marine environment,the normal mode solution of the wave equation gives in principle a rigorous solution to the sound field.When there are changes in the horizontal distance or azimuth of the acoustic parameters of the marine medium or the upper and lower boundary characteristics of the waveguide,in principle,the solution of the normal mode method is no longer applicable.On the basis of the local normal mode orthogonal expansion of the sound field solution,the coupled or adiabatic mode method in the horizontally changing environment can be extended,and a set of coupling equations about the normal mode expansion coefficients need to be solved.Considering the difficulty of solving the coupled equations,most of them adopt the coupled mode solution form with one-way propagation in the horizontal distance,which is not suitable in the case of large changes in the horizontal distance,and the solution form of the backward propagation needs to be considered,namely a coupled mode solution that takes into account both forward and backward propagation.In this paper,the research on two-way acoustic propagation in ocean level changing waveguide is carried out.The multi-modal admittance method proposed by Pagneux in aeroacoustics is an effective two-way coupled mode theory.The scattering matrices are closely related to the two-way sound propagation phenomenon,but it is only suitable for varying cross section waveguides.For ocean waveguides where the media parameters are dependent on depth and distance and the interfaces are variable,the Helmholtz equation that the sound pressure satisfies is more complicated,and the existing multi-modal admittance method is not applicable.In order to effectively study the problem of two-way acoustic propagation in complex range-dependent waveguides,this paper firstly establishes a two-way coupled model based on the multi-modal admittance method.The scattering matrix in a two-dimensional horizontal arbitrarily changing waveguide is given to quantitatively describe the scattering effect and mode coupling effect produced by the horizontally changing environment,so as to analyze the influence of the characteristics of the horizontally changing medium on the sound propagation.Then for the two-dimensional waveguides with penetrable half space,an efficient truncation model is established by introducing false bottom and Gaussian acoustic absorption.The truncation model is used to analyze the influence of varying bathymetry,rough sea surface,internal solitary waves and scatterers on sound propagation.Finally,for the problem of threedimensional sound propagation in a two-dimensional range dependent waveguide,a threedimensional two-way coupled mode model based on cosine transform is established,and a method for judging the strength of the backscattering effect in a three-dimensional sound field is proposed.The specific research content of this article is as follows:1.Two-way coupled mode model for waveguides with range-dependent physical parameters and boundaries: Based on the multi-modal admittance method,a two-way coupled mode model is established.The new model uses orthogonal complete local basis functions with analytical expressions to expand the sound field,avoiding the tedious calculation of local modes and their derivatives in traditional algorithms;by introducing auxiliary quantities related to the particle velocity,the boundary value problem of the Helmholtz equation is transformed into a first-order coupled mode system;in order to solve the sound field numerically and stably,the concept of admittance matrix is introduced,and the initial value condition of the admittance matrix and the initial value condition of the sound pressure local basis function coefficients are derived;the Magnus algorithm is used to calculate the local basis function coefficients of sound pressure,and finally substituted into the sound pressure expansion equation to obtain the twoway sound field.The scattering matrix under the local modes is deduced to analyze the scattering effect and coupling effect.The simulation results show that: for range-dependent waveguides with total reflection boundary conditions,the two-way coupled mode model in this paper can realize the accurate calculation of the two-way sound field;the scattering matrix in the local mode domain can accurately describe the two-way scattering effect and coupling effect produced by the range-dependent environments;the boundary and medium characteristics related to the distance may have non-negligible backscattering effect and modal coupling effect on the sound wave,both of which affect the interference pattern of the sound field and the energy transmission;especially,when the continuously range dependent environments causes cut-off phenomena,the backscattering effect of this normal mode is strong,causing the energy carried by this normal mode to be fully or partially reflected back to the sound source direction.2.The establishment and application of the high-efficiency truncation model for waveguides with a penetrable liquid half space: The acoustic field in the liquid semi-infinite ocean bottom waveguide contains discrete and continuous spectrum components.It is difficult to directly add the continuous spectrum contribution to the coupled mode theory.Although the common sound-speed gradients method solves this problem,the sound absorption introducedby this method is very small,and the seabed thickness requires more than ten wavelengths,which affects the calculation efficiency of the sound field.In this paper,an efficient truncation model is established by introducing false bottom and Gaussian acoustic absorption in the liquid seabed.Combined with the two-way coupling mode model,the accurate calculation of the two-way sound field in the waveguide about the distance under the liquid semi-infinite seabed is realized,and the truncation model is used to study the influence of uneven seabed,rough sea surface,internal solitary waves and scatterers on sound propagation.The simulation results show that the thickness of the seabed in the truncated model only needs to be greater than three wavelengths,which improves the calculation efficiency of the sound field compared with sound-speed gradients method;the scattering matrix of the truncated model can indirectly describe the scattering effect and coupling effect of the range dependent environment on the mode in the shallow ocean waveguide;when the bathymetry changes cause the cut-off phenomenon of a certain order of trapped modes,the backscattering effect of this order of modes may not be ignored or may be approximately zero,which is related to the degree of seabed topography change and the seabed characteristic impedance;rough sea surface and internal solitary wave environment are not easy to produce strong backscattering effect,because the local mode variation is relatively small and both the trapped modes and the leaky modes can propagate energy;the liquid scatterer can have a non-negligible backscattering effect on the sound wave,which is related to the sudden change of the local modes.3.Three-dimensional two-way coupled mode model based on cosine transform method:For the three-dimensional sound propagation in a two-dimensional range-dependent waveguides,a three-dimensional two-way coupled mode model based on cosine transform is established.By comparing with the calculation results of the existing 3D model,the accuracy of the 3D model in this paper is verified.A method for judging the strength of the backscattering effect in the three-dimensional sound field is proposed,that is,the reflection matrix under different out-of-plane wave numbers.Finally,an example of a waveguide in which the threedimensional backscattering effect cannot be ignored is considered,and the influence of the backscattering effect on the three-dimensional sound propagation is analyzed.The simulation results show that when the backscattering effect produced by the range-dependent environment is strong,there is a superimposed field of the forward field and the reverse field in both the horizontal and vertical planes,and because part of the energy is reflected,the transmission loss in the transmission area is relatively large.