全局矩阵耦合简正波方法与现有模型的比较

水平变化波导中的全局矩阵耦合简正波方法具有数值稳定、计算精度高、计算效率高、适用范围广等优点。骆文于等人开发了全局矩阵耦合简正波模型DGMCM (Luo et al, "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci.China-Phys.Mech.Astron.55,572(2012))。与现有耦合简正波模型COUPLE相比,DGMCM模型主要有如下改进:无条件稳定;适用范围更广;计算效率更高。DGMCM模型具有与COUPLE模型同等的计算精度,均能提供声场的完全双向解,两者在计算精度方面均优于基于抛物方程理论的单向声传播模型RAM。本文从理论上分析DGMCM模型与现有模型COUPLE和RAM的差异,并利用数值算例加以验证。      

基于BDRM理论的深海声场快速预报研究

深海存在深海声道和双轴声道两种典型环境，WKBZ简正波方法已实现了深海声道中声场的快速准确预报，而对于双轴海洋声道则存在一定的误差。本文在WKBZ本征函数的基础上，推导出了参考界面相位修正的一致表达式，并将浅海声传播的波束位移射线简正波（BDRM）理论应用于计算双轴海洋声道中的声场，进行了数值模拟并与传统简正波方法进行比较，结果表明应用BDRM理论计算的传播损失具有很高的精度和速度。     

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。      

水平变化波导中的全局矩阵耦合简正波方法

提出了一种新的水平变化波导中声场的耦合简正波求解方法,该方法能够处理二维点源和线源问题,提供声场的双向解。该方法利用全局矩阵(DGM)一次性求解耦合模式的系数,消除了传播矩阵递推求解中存在的误差累积问题;此外,改善了现有模型中对距离函数的归一化方法,从而避免了泄露模式指数增长导致的数值溢出问题。本文还给出了绝对软海底理想波导中耦合矩阵的闭合表达式,并分析了单个阶梯下简正波耦合现象。此外,本文还计算了理想楔形波导中的声传播问题(ASA标准问题),并与解析解及COUPLE07计算结果进行了比较,结果表明该方法是一种稳定、精确的水平变化波导中的声场计算方法。      

水平缓变声道中的WKBZ绝热简正波理论

本文利用具有海面相移修正的本征函数的ＷＫＢＺ近似，并同时考虑波导简正波和海底反射简正波的贡献，提出了适合于水平缓变水下声道的ＷＫＢＺ绝热简正波理论。数值结果表明，会聚区声场主要由波导简正波决定，而影区声场主要由海底反射简正波决定。在菲律宾海中，频率范围在１０９ＨＺ至８６０ＨＺ，距离至２５０ｋｍ范围时，用ＷＫＢＺ绝热简正波理论计算的结果与实验数据符合得很好。     

运动声源简正波模型稳相点的射线多普勒近似算法

从航空声源水下声场建模出发,提出了运动声源稳相点的近似算法。由于Hawker给出的运动声源声场简正波模型计算方法不适用于高速运动声源,针对速度相对较大的低空运动声源辐射噪声激发的水下声场建模,采用虚源概念,基于射线声学理论得到近似多普勒频率,结合简正波理论求解稳相点,较好地解决了高速运动声源声场的解算问题。几种波导环境下两种方法数值计算比较结果表明该算法的有效性。     

三维耦合简正波-抛物方程理论及算法研究

研究三维海洋环境下声传播的快速数值预报方法。在广义相积分(WKBZ)理论和波束位移射线简正波(BDRM)理论的基础上,将二维耦合简正波-抛物方程理论推广至三维。三维耦合简正波-抛物方程(CMPE3D))理论的级数解由垂直方向的本地简正波和水平与方位角方向的简正波幅度系数组成。为了实现该理论的快速算法,在垂直方向上采用WKBZ理论和BDRM理论进行简正波分析,在水平与方位角方向采用与抛物方程模型FOR3D[Lee D.et al.,"Numerical Ocean AcousticPropagation in Three Dimensions",World Scientific,Singapore,1995]类似的方法来求解简正波幅度系数方程。数值计算结果表明,在精度相当的情况下,计算速度比抛物方程算法提高了约100倍,具有计算精度高、速度快的优点。     

浅海中运动声源径向速度与距离的无源估计

针对浅海波导中声源距离的无源估计问题,提出了一种环境参数和声场模型无关的、不依赖于引导声源的运动声源径向速度以及距离估计方法。该方法首先通过双水听器低频声场强度距离波数谱变换(R-K)的相位差获得干涉简正波水平波数,对水平波数轴定标来估计运动声源的径向速度。进一步地,对接收信号自相关函数进行WARPING变换得到运动声源距离的无源估计。对于反射类简正波为主的声场,在某一假定距离下根据某两时刻接收信号WARPING变换后干涉简正波谱峰频率与假定距离的关系估计距离;对于反射类或折射类简正波为主的声场,根据两个时刻接收信号的β-WARPING变换后干涉简正波的脉冲时延估计距离的值。数值仿真分析了等声速、负梯度以及温跃层3种水文环境下的噪声以及环境宽容性,结果表明径向速度与距离的估计不依赖于环境参数。利用2005年北黄海实验数据验证了方法的可行性,径向速度与距离的估计值与实际值符合良好。      

指向性辐射器的简正波声场

本文讨论比较一般的指向性辐射器在分层介质中的声场,并将指向性概念应用于简正波计算。结果表明,对无方向性点源的简正波表示式补充以指向性激发函数,就可得到指向性辐射器的简正波声场,而指向性激发函数与辐射器的位置及指向特性有关。文中还分别计算了具有垂直对称性、反对称性、单边指向性以及尖锐指向性的辐射器的简正波声场。对于均匀水层中的垂直线阵,若源的分布函数正比于某一简正波的本征函数,则指向性激发函数的零点正好对应于其他简正波的本征射线的方向。 关键词：     

一种水平变化可穿透波导中声传播问题的耦合简正波方法

通过利用标准简正波程序KRAKEN计算本地简正波解及耦合矩阵, 进一步发展了求解水平变化波导中声场的全局矩阵耦合简正波方法(Luo et al., "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci. China-Phys. Mech. Astron. 55, 572 (2012)), 使得该方法可以处理具有可穿透海底及随深度变化声速剖面等实际问题, 并提供声场的完全双向解. 本文还给出了双层波导中耦合矩阵的解析表达式, 并利用其验证了本方法中耦合矩阵数值算法的精度. 最后, 利用改善后的全局矩阵耦合简正波模型(DGMCM)计算了美国声学学会(ASA)提出的可穿透楔形波导标准问题, 将所得数值解与参考解比较, 结果表明DGMCM方法可以精确处理水平变化波导中声传播实际问题. 关键词： 耦合简正波理论 全局矩阵方法 可穿透楔形波导     

Coupled perturbed modes and internal solitary waves

Coupled perturbed mode theory combines conventional coupled modes and perturbation theory. The theory is used to directly calculate mode coupling in a range-dependent shallow water problem involving propagation through continental shelf internal solitary waves. The solitary waves considered are thermocline depressions, separating well-mixed upper and lower layers. The method is fast and accurate. Results highlight mode coupling associated with internal solitary waves, and mode capture or loss to and from the discrete mode spectrum.     

单阶简正波宽带干涉特性与孤立子内波定位

为了分析孤立子内波(SIW)对声场干涉特性的影响以及由此监测SIW,我们采用抛物方程模型,分析了孤立子内波影响下简正波耦合带来的单阶简正波宽带脉冲序列的干涉特性;仿真了宽带脉冲信号穿过SIW时,单阶简正波接收脉冲序列随内波位置的变化情况,分析了它们的时空干涉特性和机理;基于耦合简正波理论,推导得到了内波位置和干涉条纹斜率之间的关系。仿真表明,这一关系式可以精确估计SIW距离,估计精度和稳定性比以往方法大大提升。此外,还根据单阶简正波干涉图样在频率上的周期性,推导了另一种估计SIW距离的方法,该方法具有更好的实时性。SIW-简正波干涉关系可用于改善声场定位,对于海洋学、海洋工程和海洋军事等方面具有重要价值。此外,该关系还可以拓展到其他的局部特性变化的探测,如金属探伤和海底地形突变定位等。      

孤子内波导致海洋环境噪声垂直指向性异常分析

依据近场波数积分、远场耦合简正波相结合的二维噪声场模型,侧重理论研究孤子内波所在扇区,环境噪声垂直阵响应的变化,分析了某些孤子内波情形下垂直阵环境噪声水平凹槽变深这一异常现象的原因:孤子内波离垂直阵较近时,远离内波的海面噪声源多,其激发的简正波能量由低号耦合到高号,在垂直阵处高号简正波能量对环境噪声场贡献增大,导致环境噪声水平凹槽加深;对于大尺度、多波包孤子内波,其范围相对较大,内波所在区的局部简正波本征值和本征函数产生的变化影响显著,使低号简正波衰减变快,而高号衰减慢,导致接收阵处高号简正波能量增加,低号简正波变弱,这样,无论孤子内波群靠近或离接收阵远,都将使垂直阵环境噪声水平凹槽加深。      

南海北部海域内波环境下声传播损失起伏统计特性

浅海内波会引起声传播能量随时间的起伏变化,进而影响水声设备的工作性能.本文利用2015年南海北部一次浅海声场起伏实验数据,对比分析了浅海线性内波和孤立子内波条件下的声传播损失统计特性.在孤立子内波条件下,声传播损失起伏明显加剧,可达11 dB,且分布明显展宽,相对于线性内波的环境,声传播损失起伏可增加5 dB.从简正波...     

Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates

We have theoretically investigated Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates. Counterrotating perturbation induces an elliptical instability to the initially straight vortex line, driven by a parametric resonance between a quadrupole mode and a pair of Kelvin modes of opposite momenta. Subsequently, Kelvin waves rapidly decay to longer wavelengths emitting sound waves in the process. We present a modified Kelvin wave dispersion relation for trapped superfluids and propose a simple method to excite Kelvin waves of specific wave number.     

Mode perturbation method for optimal guided wave mode and frequency selection

With a thorough understanding of guided wave mechanics, researchers can predict which guided wave modes will have a high probability of success in a particular nondestructive evaluation application. However, work continues to find optimal mode and frequency selection for a given application. This “optimal” mode could give the highest sensitivity to defects or the greatest penetration power, increasing inspection efficiency. Since material properties used for modeling work may be estimates, in many cases guided wave mode and frequency selection can be adjusted for increased inspection efficiency in the field. In this paper, a novel mode and frequency perturbation method is described and used to identify optimal mode points based on quantifiable wave characteristics. The technique uses an ultrasonic phased array comb transducer to sweep in phase velocity and frequency space. It is demonstrated using guided interface waves for bond evaluation. After searching nearby mode points, an optimal mode and frequency can be selected which has the highest sensitivity to a defect, or gives the greatest penetration power. The optimal mode choice for a given application depends on the requirements of the inspection.     

Acoustic-gravity waves in atmospheric and oceanic waveguides

A theory of guided propagation of sound in layered, moving fluids is extended to include acoustic-gravity waves (AGWs) in waveguides with piecewise continuous parameters. The orthogonality of AGW normal modes is established in moving and motionless media. A perturbation theory is developed to quantify the relative significance of the gravity and fluid compressibility as well as sensitivity of the normal modes to variations in sound speed, flow velocity, and density profiles and in boundary conditions. Phase and group speeds of the normal modes are found to have certain universal properties which are valid for waveguides with arbitrary stratification. The Lamb wave is shown to be the only AGW normal mode that can propagate without dispersion in a layered medium.     

Frequency shifts of sound field maxima under the effect of intense internal waves

Numerical simulation is carried out to study frequency shifts of a low-frequency sound field maxima under the effect of solitary internal waves (solitons) propagating along an acoustic track in the presence of mode coupling. The frequency shifts are measured by the correlation method. Simulation data obtained with allowance for mode coupling and data obtained in the adiabatic approximation are compared and analyzed.     

Nonlinear propagation of ion plasma waves in dust-ion plasma including quantum-relativistic effect

In this paper we have theoretically investigated the quantum and relativistic effects on ion plasma wave in an unmagnetised dust-ion plasma. By using the method of normal mode analysis, we have obtained a linear dispersion relation. It has been analysed numerically for quantum and relativistic effects on the propagation of ion plasma wave. By using the standard reductive perturbation technique, we have derived a Korteweg–de Vries (KdV) equation which describes the nonlinear propagation of the wave. Numerically, it is shown that only compressive type of soliton can exist in the plasma under consideration. It is found that the solitary wave profile depends significantly on the quantum and relativistic parameters. The dust size, dust charge and the dust number density are also shown to have significant influences on these solitary waves. The results of this present investigation have some relevance to the nonlinear propagation of ion plasma wave in some astrophysical, space and laboratory plasma environments.     

Dissipative Nonlinear Schrödinger Equation with External Forcing in Rotational Stratified Fluids and Its Solution

The dissipative nonlinear Schrödinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency and β effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schrödinger equation and forced nonlinear Schrödinger equation are derived, respectively. With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves.