Acoustic Field Modeling And Analysis Based On Coupled-Mode In Range-Development Waveguide

With the development of sonar techniques,the ranging performance of sonar systems have been improved a lot.Then the cumulative effect of the environment parameters'variation with range can not be ignored,and the sound propagation models based on the horizontally layered ocean waveguide are not applicable for long range sonar performance prediction any more.The coupled mode model is the extension of the normal mode model,and it can be applied to range-dependent cases.It describes the effects of range-dependent parameters by the couplings between normal modes,which has definite and intuitional physical meanings.That means the coupled mode model is of advantage in explaining the acoustic field characteristics in complicated environments.Therefore,sound propagation modeling and analyzing based on the coupled mode theory is of great significance.Under this background,the branch line integral is analyzed,and the coupled mode model for sound propagation in the complicated environments is founded in the thesis.Methods for eliminating the effects of the branch line are obtained and proved to be effective.Meanwhile,two-dimensional models and a three-dimensional model are developed,which have feasible numerical implementations and can describe the total coupling effects.Then,based on these models,the characteristics of the acoustic field in range-dependent waveguide are analyzed,and the transform of the sound field energy is expounded in complicated environments.The researches are divided into parts as follows:(1)The branch line integral and the solution of the local eigen-equationBy the normal mode theory,the generation and the influence of the branch line integral are analyzed.It is shown that the branch line is introduced by the uncloseness of the ocean waveguide.If the lateral waves contained in the branch line integral satisfy the constructive interference,the neglect of the branch line integral will cause a certain amount of error in the calculation of the acoustic field.Meanwhile,since the leaky modes are not located in the appropriate phase intervals,the acoustic field in the seafloor is divergent when the branch line is ignored.For eliminating the effect of the lateral wave and the divergence phenomenon,the complex effective depth method and the conjoint analysis method are adopted respectively.By these methods,the energy of continuous spectrum can be entirely transferred to the discrete spectrum.The simulations show that the two methods can effectively eliminate the effects generated by the neglect of the branch line.Hence,these methods can provide a foundation for handling the couplings between the discrete spectrum and the continuous spectrum.In addition,the solving methods of the eigenvalue and the eigenfunction are studied.For different seabed environments,three different calculation methods are summarized,which are the ray-normal mode method,the reference depth method and the Galerkin variation method.Through the simulation and the comparison,it is shown that these methods can compute the eigenvalue and eigenfunction efficiently in the semi-infinite seafloor,the multilayered seafloor and the truncated seafloor respectively.(2)The two-dimensional(2D)coupled mode model and the coupling characteristic of the acoustic fieldFor the point source problem and the line source problem in the 2D range-dependent ocean waveguide,a one-way higher-order coupled mode model and a two-way coupled mode model are developed.Compared with the traditional models based on the stair step approximation,the effect of the non-horizontal boundary conditions can be fully considered by the presented coupled models for the cases of arbitray submarine topography.Through the theoretical verification,the established models satisfy the energy conservation and the principle of reciprocity.Meanwhile,the coupling equations,which are derived from the equation of motion and the equation of continuity,have the formulation of parabolic equation and thus are convenient for numerical implementation with various methods.Based on the rational approximation of the Pade series and the e-index factor in the one-way coupled model,a large horizontal marching step and a feasible numerical implementation are obtined without neglecting the higher-order couplings.Therefore,the effect of the higher-order coupling can be effectively studied.Moreover,the physical mechanism of the coupling between normal modes and the coupling characteristic of the acoustic field are studied in the 2D environment.It is shown that the coupling effect is a result of normal modes' exciting by each other which is generated by the horizontal variation of the environment parameters,and is also a measurement of the energy transform between normal modes.When the transformation between the trapped mode and the leaky mode exists,acoustic coupling and energy transferring occur remarkably.Meanwhile,the effects of the non-horizontal boundary correction,the higher-order coupling term and the incoming field are analyzed.It indicates that the three effects are proportional to the rate of the horizontal variation of the parameters,among which the most important one is the topography.Compared with the higher-order coupling term and the incoming field,the effect of the correction of the non-horizontal boundary is more obvious.The correction needs to be considered in the horizontal varying waveguide,while the considerations of the other terms are depended on the certain issues.(3)The three-dimensional(3D)coupled mode model and the 3D characteristic of the acoustic fieldFor the point source problem in the 3D horizontal varying ocean waveguide,a one-way coupled normal mode model is developed.In order to describe the ocean environment and to avoid the error resulting from the change of the horizontal grid sizes,the 3D Cartesian coordinate system is considered.The 3D coupling equations and the coupling coefficients are derived by the equation of motion and the equation of continuity in the coordinate system.Through treating the non-horizontal boundary condition of arbitrary submarine topography strictly,this model can account the coupling effects in the entire horizontal plane.It is proved this model satisfies the energy conservation and the principle of reciprocity.By employing the rational approximation of the Pade series and the split-step method,a straightforward numerical calculation form is established,in which the matrix is a block tridiagonal matrix.Compared with the existing 3D models,the presented model can be numerical solved without ignoring any coupling effect.It means that this model can resolve the conflict between considering the couplings along all the horizontal directions and obtaining an efficient numerical implementation effectively.Meanwhile,based on the Fourier transform and the 2D coupled model in this paper,a wedge coupled mode model is developed.The numerical calculation form of the wedge model is realiable and the theory is undoubtedly strict.Thus it can be used to provide an effective reference for the one-way coupled normal mode model.With numerical simulations,the reliability and the accuracy of the 3D coupled models are illustrated.From the perspective of the coupling between modes,the 3D acoustic field characteristics and the regulations of how the acoustic energy propagates in the waveguide with seamounts are analyzed by the presented 3D coupled model.It is shown that the coupling effects exist obviously and are not neglectable in the all horizontal directions.The coupling effects along different direction also influence on each other.Meanwhile,due to the cut-off of trapped modes and the change of the propagating direction,the radial decay area for sound energy,the complicated interference structure and the sound diffraction phenomenon are shaped in the horizontal plane.The shape and the intensity of these phenomena are proportional to the size of the seamount,and are associated with the mountain peak position in the horizontal plane.