空气中快速运动声源水下声场的波数积分模型

本文采用二维波数积分，对空气中高速运动声源激发的水下声场进行建模。针对二维波数积分计算声场时域解计算量大的问题，提出一种快速计算方法。用本文提出的方法，对深海和浅海情况下，空气中高速运动单频点声源激发的水下声场进行了计算和仿真。计算结果表明：在深海，水下接收信号的幅度和瞬时频率随时间发生变化；接收器深度、接收器与声源运动轨迹的最小距离对接收信号的变化快慢有较大影响，而声源高度的影响较小；在浅海中，接收信号呈现快速的幅度起伏，明显的多普勒频移和大的频率展宽效应。与简正波方法相比，本文方法主要适用于近场计算，而简正波方法适用于远场。另外，当声源频率较高时，二维波数积分方法的计算量将迅速增大。

Modeling the underwater sound field by wavenumber integration for a rapidly moving source in air

In this paper, a two-dimensional wavenumber integration model is developed to calculate the underwater received temporal signal for a rapidly moving acoustic source above the water. Both shallow water and deep water cases are considered. When receiver is in deep water, the calculated results show that its amplitude and instantaneous frequency change with time. Receiver depth and the closest horizontal distance between receiver and source affect the change rate. Yet, the source height has little influence. When receiver is in shallow water, the results show that the amplitude of the received signal fluctuates quickly, the Doppler shift is evident, and the spectrum broadening due to the Doppler effect is significant. Comparing with the normal mode method, the approach presented in this paper could be used in the near field, while normal mode method is used in far field. Furthermore, the computation cost becomes large for the high frequency source.