一种可稳定计算负跃层浅海环境下声场的波数积分方法

提出了一种可以稳定计算负跃层浅海环境中声场的波数积分方法，通过对艾里(Airy)函数的归一化，得到了声源位于水体不同层中的系数矩阵，该系数矩阵是无条件稳定的。结合仿真实例，将该方法的计算结果与Airy函数未作归一化得到的计算结果进行比较，结果显示，当Airy函数未作归一化时，在某些情况下不能保证深度格林函数的足够收敛性，而该方法可以很好地解决该问题。同时将该方法的计算结果与简正波模型KRAKENC的计算结果进行对比，结果表明，文中提出的数值计算模型可以作为负跃层浅海环境中声场计算的有效补充。

A stable wavenumber-integration-based solution of acoustic field in the shallow-water with a negative thermocline

In this paper, a stable wavenumber-integration method for sound field calculation in the shallow-water environment with a negative thermocline is proposed. The coefficient matrix of sound source in different water layers is obtained by normalizing Airy function. The coefficient matrix is unconditionally stable and can provide an accurate numerical solution of sound field in the shallow-water environment with a negative thermocline. Combined with a simulation instance, the calculation results of this method are compared with those of un-normalized Airy function, and the results show that the acoustic field calculation by the latter method is not accurate under some circumstances, however, the method proposed in this paper offers a good solution for this problem. Meanwhile, the comparison of the calculation results of this method with those of KRAKENC normal-mode indicates that the numerical model proposed in this paper can be used as a standard model for sound propagation in the shallow-water with a negative thermocline.