运动粘滞大气中的耦合方程组解析解的新方法

A new method for analytical solution of the coupled equations set through a windy, viscous atmosphere

摘要:

由于声波在大气中传播特性处理的数学复杂性，求耦合方程组解析解的工作已很少见。本文首次将NMA(Normal Mode Analysis)和同伦分析方法(HAM, Homotopy Analysis Method )相结合对考虑风和粘滞因素的耦合方程组进行解析解的求解。首先由基本控制方程推导了运动粘滞大气中的耦合方程组，通过匀质无风的耦合方程组，对声波在大气中衰减特性和相速度进行了分析，之后利用NMA对其进行了解析解求解，并将其作为初始近似，利用同伦分析方法对有风、粘滞分层大气中的耦合方程组进行了三阶近似解析解的求解，最后进行了数值模拟。结果表明，由于多种大气要素的影响，随着传播距离的增加，声压峰值越小，且频率越大衰减越快，因此风和粘滞特性是影响近地面声波传播特性的重要因素。

Abstract:

Due to mathematical complexity to process acoustic wave propagation in the atmospheric, the work of the analytic solutions for coupled equations set was very rare. Normal mode analysis and the homotopy analysis method were firstly combined to solve analytic solutions of the coupled equations set in a viscous, windy atmosphere. Firstly, the coupled equations set were deduced from the government equations, the attenuation characteristics and phase velocity were analyzed by the coupled equations set in the uniform and no wind atmosphere, and the analytical solutions of the equations set were solved by normal mode analysis，meanwhile the analytical solutions were used to initial approximations, the 3rd-order approximation analytical solutions of the coupled equations set in a windy and viscous atmosphere were obtained by homotopy analysis method. The numerical simulation indicates that due to the influence of the variety of atmospheric elements, the sound pressure peak value is smaller and bigger frequencies have faster attenuation with the increase of propagation distance, so the wind and viscous properties are the important factors that affect near surface acoustic wave propagation characteristics.