耗散作用对大气中声波传播影响的数值研究

通过结合保色散关系空间差分格式和Runge-Kutta时间格式的数值方法，研究了耗散作用对声波传播的影响.结果表明，耗散的不均匀性会同时影响声波的传播轨迹和传输损耗.不均匀的耗散会使得波包上部和下部承受不同程度的衰减，造成波包能量中心向弱耗散方向移动，使波包能量中心的传播轨迹发生偏折.与此同时，声波的传输损耗也受到了改变：与无耗散情况相比，声波的几何扩散衰减受到抑制；与均一耗散情况相比，声波的大气声吸收明显减小.由于声波衰减系数与声波频率的平方成正比，耗散作用使声波传播具有色散性质.不均匀耗散对于声波波包能量中心传播轨迹的偏折作用随频率的增加而增强.

A numerical study of the effects on acoustic propagation caused by dissipation in the atmosphere

By using a finite-difference time-domain method combining the dispersion relation preserving scheme in space and a Runge-Kutta scheme in time, the effect of dissipation on acoustic propagation is studied. It is shown that both trajectory and transmission loss of the wave packet are changed by the inhomogeneity of dissipation. Due to the inhomogeneous dissipation, the upper and lower part of the wave packet is attenuated at different levels, so that the energy center of the packet is shifted to the area where the dissipation is weaker, and the wave trajectory is refracted too. As for the transmission loss, compared to the zero absorption case, the geometric spreading loss is reduced;the atmospheric absorption is smaller than the constant absorption case. The dissipation makes acoustic propagation become dispersive because the attenuation coefficient is proportional to the square of frequency. The deflection of the acoustic wave caused by the inhomogeneous dissipation is enhanced as the frequency goes up.