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

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.