复等效深度耦合简正波模型

为了考虑海底地形随距离变化的非水平分层介质中割线积分对声场的贡献,提出了复等效深度耦合简正波模型。该耦合简正波模型由介质运动方程和连续性方程推导得到了耦合微分方程组,此方程组满足海底地形随距离变化情况下的边界条件且仅包含一个耦合矩阵,并通过引入复等效深度理论处理连续谱和离散谱之间的相互耦合。仿真计算表明,复等效深度耦合简正波模型提高了波导简正波本征值位于割线枝点附近情况下声传播损失的计算精度,充分考虑了波导简正波、非波导简正波和割线积分对声场的贡献,可快速而准确地计算非水平分层介质中的声场。      

On the acoustic field in a Pekeris waveguide with attenuation in the bottom half-space

The acoustic field in a Pekeris channel with an attenuating basement is critically examined, based on contour integrations of the wave number integrals for the two domains. In both regions, the field consists of a finite sum of proper (square integrable) normal modes plus a branch line integral around a hyperbolic cut. For low bottom attenuation, only "trapped" modes exist but as the loss increases additional "dissipation" modes contribute to the mode sum. A Newton-Raphson iterative procedure is introduced for finding the complex eigenvalues of the modes and a new expression is derived which shows that the total number of proper (trapped plus dissipation) modes supported by the waveguide increases essentially linearly with rising bottom attenuation. Approximations for the complex shape functions of the modes in the water column and the basement are developed and compared with the exact shape functions determined from the Newton-Raphson procedure. An expression derived for the modal attenuation coefficient scales in proportion to the square of the mode number and inversely with the square of the frequency. Stationary-phase approximations for the branch line integrals for both domains are developed, which serve to illustrate the asymptotic range dependence of the lateral wave but otherwise have little utility.     

一种可稳定计算Pekeris波导中声场的波数积分方法

提出一种可稳定计算Pekeris波导中声场的波数积分方法,并在此基础上开发出一个数值模型,可用于提供Pekeris波导中声场的精确、稳定的数值解。在这个方法中,由于与深度有关的波动方程齐次解中所有的上行波与下行波均采用了合理的归一化表示,从而得到的系统方程是无条件稳定的。在简正波方法中,割线积分一般只对近场有显著影响。因此,传统的简正波模型一般都忽略割线积分对声场的贡献。但是,如果某号简正波离割线非常近,则割线积分对非常远距离的声场仍可能有显著影响。在这种情况下,传统的简正波模型由于忽略割线积分的贡献,从而得到的声场结果是不准确的。本文通过数值算例比较本文提出的波数积分模型与传统的简正波模型。数值结果表明,本文提出的模型可以提供精确、稳定的Pekeris波导中声场的数值解,而在某些情况下传统的简正波模型得到的声场结果是不准确的。因此,本文提出的模型可以作为Pekeris波导中声传播问题的标准模型使用。      

Low frequency coupled mode sound propagation over a continental shelf

A two-way integral equation coupled mode method is applied to a continental shelf ocean waveguide proposed for a special session devoted to range-dependent acoustic modeling at the 141st meeting of the Acoustical Society of America. The coupled mode solution includes both sediment trapped and continuum modes. The continuum is approximated by a finite number of leaky modes but neglects the branch cut contribution. Mode coupling matrix elements and the range evolution of the modal amplitudes show the nature of the mode coupling. Transmission loss versus range at 100 Hz predicted by the integral equation approach is compared to the transmission loss predicted by a wide angle parabolic equation method. While there is very good agreement, one observes small differences that can be interpreted as backscattering predicted by the integral equation solution.     

Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.     

浅海低频声场中目标深度分类方法研究

分析了浅海甚低频声场中的垂直双水听器的互谱特性,尤其关注了声场中只存在两阶简正波时声压互谱的有功分量.数值计算表明：当两个水听器的深度布放合理时,声压互谱有功分量的正负号分布与水平距离无关,选择合适的水听器深度布放组合,可以用于水面目标、水下目标的双择判决;声速分布对该方法的使用影响不大,海底存在吸收将影响算法的作用距离,但在有效作用距离内,该算法仍有较好的稳健性.运用Pekeris波导有效深度的概念建立了声压互谱有功分量正负号分布特性的近似理论分析并可预报双水听器合理的布放深度.理论分析揭示了双水听器布放深度之和应等于波导有效深度,并且在有效深度限制的波导范围内,整个声场的声压互谱有功分量的正负号分布被分为三个水平区域.理论分析加深了对浅海低频声场特性的理解,对该算法的实际使用有指导意义. 关键词： 目标深度分类 浅海低频声场 声压互谱 有功分量     

Scattering of sound by an elastic spherical shell immersed in a waveguide with a fluid bottom

The paper is devoted to modeling an acoustic field scattered by an elastic spherical shell. The shell is immersed in a waveguide with a fluid attenuating bottom. Modal analysis is applied to calculations of both the point source field in a free waveguide and the scattering coefficients of the shell. The occurring integrals along a branch cut are expressed via the probability integral. Cases are analyzed when the source frequency differs from the critical frequencies of normal waves and when it coincides with one of them. The method is applied to estimate the effect of the field scattered by a thin elastic shell filled with air with transmission loss of the total acoustic field with distance and its depth distribution.     

Coupling coefficients of synchronous modes on two arbitrarily-shaped weakly-guiding optical waveguides

Usually, coupling coefficients of parallel weakly-guiding waveguides of arbitrary crosssectional shape with uniform infinite cladding are calculated via two-dimensional overlap integrals of the refractive-index distribution of the concerned waveguide core and the field distributions of the two coupling isolated-core modes. In this paper it is shown that, in the case of synchronous coupled modes, the calculation can be reduced to the evaluation of a line integral involving only the field functions. Convenient formulations are obtained for typical forms of the field representation.     

Pekeris波导中简正波的复声强及其应用

在Pekeris波导模型下,关注了简正波的矢量场,讨论了简正波水平复声强和垂直复声强的表述,并分析了其特征.单阶简正波在水平方向是行波,相应的水平复声强仅为有功的;在垂直方向为驻波,相应的垂直复声强仅为无功的.而多阶简正波相互干涉,因此总声场的复声强既有有功分量,也有无功分量,其中只有有功分量参与声能的输运,但无功分量是反映声场信息的重要组成部分.通过对垂直(交互)复声强无功分量和水平交互复声强有功分量的数值分析,对于甚低频率的点源声场,发现当声源深度变化时,上述声场分量的正负号呈有规变化,当接收传感器置 关键词： 目标深度分类 复声强 矢量场 Pekeris波导     

Modelling of finite-size grating waveguide filters on the basis of a free-space diffraction approach

The field reflection coefficient R of a high strength and short length waveguide grating section is obtained by resorting to a free-space diffraction approach whereby the waveguide grating is excited by means of a virtual high index prism. The effective index of the guided mode, the coupling coefficient between contradirectionally propagating modes of the grating waveguide as well as the modal field are first obtained in the case of an infinite grating by interpreting the results given by an exact diffraction solution by means of a three-wave coupled mode formalism. These results are then introduced in the coupled wave analysis of the structure of finite extent to provide the field at the entrance of the waveguide grating section where the usual overlap integral with the incident field delivers the reflection coefficient. We neglect only the result of radiation mode propagation. This assumption can be made when the grating section is longer than the propagating length of all the leaky modes.     

Modelling of finite-size grating waveguide filters on the basis of a free-space diffraction approach

The field reflection coefficientR of a high strength and short length waveguide grating section is obtained by resorting to a free-space diffraction approach whereby the waveguide grating is excited by means of a virtual high index prism. The effective index of the guided mode, the coupling coefficient between contradirectionally propagating modes of the grating waveguide as well as the modal field are first obtained in the case of an infinite grating by interpreting the results given by an exact diffraction solution by means of a three-wave coupled mode formalism. These results are then introduced in the coupled wave analysis of the structure of finite extent to provide the field at the entrance of the waveguide grating section where the usual overlap integral with the incident field delivers the reflection coefficient. We neglect only the result of radiation mode propagation. This assumption can be made when the grating section is longer than the propagating length of all the leaky modes.     

三维浅海下弹性结构声辐射预报的有限元-抛物方程法

利用多物理场耦合有限元法对结构和流体适应性强、抛物方程声场计算高效准确的特点,提出了三维浅海波导下弹性结构声振特性研究的有限元-抛物方程法.该方法采用多物理场耦合有限元理论建立浅海下结构近场声辐射模型,计算局域波导下结构声振信息,并提取深度方向上复声压值作为抛物方程初始值;然后采用隐式差分法求解抛物方程以步进计算结构辐射声场.重点介绍了该方法对浅海下结构声辐射计算的准确性、高效性以及快速收敛性后,对Pekeris波导中有限长弹性圆柱壳的声振特性进行了分析.研究得出,当圆柱壳靠近海面(海底)时,其耦合频率比自由场下的要高(低),当潜深达到一定范围时,与自由场耦合频率基本趋于一致;在低频远场,结构辐射场与同强度点源声场具有一定的等效性,且等效距离随着频率增加而增加;由于辐射声场受结构振动模态、几何尺寸和简正波模式影响,结构辐射场传播的衰减规律按近场声影响区、球面波衰减区、介于球面波和柱面波衰减区、柱面波衰减区四个扩展区依次进行.     

用耦合波理论求解渐变折射率光纤的传播常数和模式场

本文应用耦合波理论来计算任意渐变折射李光纤的传播常数和模场分布.将无限伸展的抛物型折射率分布光纤作为一个理想波导,任意径向不均匀折射率分布光纤便可以视作该理想波导的微扰,其模场可以展开成一组完备的理想波导模的叠加.然后,模场和传播常数可以通过耦合波方程求得.进一步将一阶微分方程组形式的耦合波方程变换成线性方程组,使计算过程大大简化.文中给出了数值计算结果,并将其与准确值进行了比较.     

SiO2波导布拉格器件中声表面波及声光相互作用分析

针对SiO2光波导声光布拉格器件,计算了SiO2非对称平板波导TE模式的横向场分布;给出了SiO2/ZnO/Air层状介质结构的性能方程、运动方程和麦克斯韦方程,推导出这种层状结构的特征方程,并结合所满足的边界条件,得到了各层介质的位移及电磁场分布;计算了声表面波所引起的光学相对介质隔离率张量的变化,最后讨论了声光衍射效率和光场与声场的重叠积分、声功率、声频率、声孔径和光波导参数之间的关系。结果表明,在低频范围内光场与声表面波场重叠良好;低阶模的重叠积分始终大于高阶模重叠积分,最低阶模与声表面波相互作用最强,所需声功率最小;当声功率一定时,增加声孔径可以提高衍射效率。     

浅海不确定声场的随机多项式展开法研究

为获得求解浅海不确定声场的普适模型,建立了随机多项式展开法与Helmholtz方程的非嵌入式耦合模型,其间运用概率配点法求解多项式系数。针对仅当海水深度不确定时的Pekeris波导、声速剖面和海深均不确定时的Pekeris波导以及下限深度不确定温跃层等几种情形,计算了传播损失概率密度分布。结果表明所建模型对声场计算模型普适性强,计算精度和计算效率高,可用于研究含多个不确定环境参数、声速剖面复杂的浅海环境中声传播的不确定性。      

浅海波导中目标散射的边界元方法

提出了一种计算三维散射体在声速剖面随深度变化、距离无关浅海波导中散射声场的数值方法波导边界元方法。当散射体不十分靠近波导界面因而边界多次散射可以忽略时,在边界元计算中可以用自由场格林函数近似波导格林函数。应用镜像法和球波函数加法定理推导了理想波导中球体散射声场的解析解,用来验证波导边界元方法的计算精度,证明该数值方法是准确的。对浅海波导中水下潜器散射声场数值模拟的结果表明,浅海波导海面、海底界面反射、声速剖面等对目标散射声场的幅值和方向性都有很大的影响。      

理想浅海波导中声场奇异点与声源深度的关系

为了有效利用声场奇异点蕴含的声源参数信息,研究了在理想浅海波导中,远场不同邻阶模态组的声场奇异点与声源深度之间的关系。推导计算了典型浅海声源声场的邻阶模态组奇异点位置,并通过仿真对奇异点的分布进行分析,结果显示邻阶模态组的阶数和阶差越大,奇异点分布越复杂。进一步研究发现,邻阶模态组第一组奇异点的深度和声源深度之间存在联系,并且基于奇异点与声压场的对应关系,在获得准确模态分布的前提下,可以通过两个邻阶模态组的第一组奇异点深度逆运算获得对应声源深度信息,也可以通过第一组奇异点深度反演获得声源深度信息。该文为获取浅海声源深度提供了思路。     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

Theory of an SAW filter operating in weakly coupled resonance modes

Modified coupled-mode equations are employed to develop a theory of filters that use waveguide modes of two surface acoustic wave (SAW) resonators weakly coupled in the transverse direction. Results of simulation based on this theory are compared with the earlier experiment.