Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
J Acoust Soc Am. 2011 Jul;130(1):72-83. doi: 10.1121/1.3592236.
The frequency dependence of a waveguide's Green's function can be summarized by a single parameter known as the waveguide invariant, β. Although it has been shown analytically that β≈1 for ideal waveguides, numerical and experimental results have shown that β≈1 for many realistic shallow water waveguides as well. There is not much prior work explaining why the non-uniformities present in realistic sound speed profiles sometimes have such a small effect on the value of β. This paper presents a method for calculating β using a modal Wentzel-Kramers-Brillouin (WKB) description of the acoustic field, which reveals a straightforward relationship between the sound speed profile and β. That relationship is used to illustrate why non-uniformities in the sound speed profile sometimes have such a small effect on β and under what circumstances the non-uniformities will have a large effect on β. The method uses implicit differentiation and thus does not explicitly solve for the horizontal wavenumbers of the modes, making it applicable to waveguides with arbitrary sound speed profiles and fluid bottom halfspaces. Several examples are given, including an analytic estimate of β in a Pekeris waveguide.
波导 Green 函数的频率相关性可以用一个称为波导不变量β的单一参数来概括。虽然已经从理论上证明了理想波导中的β≈1，但数值和实验结果表明，许多现实中的浅层水波导中的β≈1。目前还没有太多的前期工作来解释为什么现实中声速分布中的不均匀性有时对β值的影响如此小。本文提出了一种使用声场的模态 Wentzel-Kramers-Brillouin（WKB）描述来计算β的方法，该方法揭示了声速分布与β之间的直接关系。该关系用于说明为什么声速分布中的不均匀性有时对β的影响如此小，以及在什么情况下不均匀性会对β产生较大的影响。该方法使用隐式微分，因此不会显式地求解模态的水平波数，从而使其适用于具有任意声速分布和流体底部半空间的波导。文中给出了几个例子，包括在 Pekeris 波导中β的解析估计。
