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。

Numerically stable,wavenumber-integration-based solution of acoustic field in a Pekeris waveguide

A wavenumber-integration-based method is developed and implemented to provide accurate and stable acoustic field solutions in a Pekeris waveguide. In this method, all the up- and downgoing waves in the homogeneous solution of the depth-dependent wave equation are appropriately normalized, leading to an unconditionally stable system of equations for the amplitudes of the homogeneous solution. For the normal-mode method, in general the contribution from the branch line integral is significant only in the near field. For this reason, the branch line integral is generally ignored in traditional normal-mode models. However, when a mode lies very close to the branch cut, the branch line integral might still contribute to the field significantly at very long ranges. In this case, traditional normal-mode- based models provide inaccurate field solutions because of ignoring the branch line integral. Numerical examples are also provided to compare the present model and a traditional normal-mode model. Numerical results indicate that the present model is accurate and numerically stable, whereas the results by that traditional normal-mode model are inaccurate in certain cases. Hence, the present model can serve as a benchmark model for the problem of sound propagation in a Pekeris waveguide.