Numerical Study Of The Long Range Sound Propagation

Long range sound propagation is an important propagation pattern of acoustic waves in the atmosphere. The purpose of this dissertation is to study the long range sound propagation by the method of numerical modeling. With the help of ray tracing model, the trajectories of long range propagation at high frequency and infrasonic frequency are calculated. On the basis of the FDTD method, the effects of dissipation on the propagation and the behavior of acoustic waves in the ducts of long range sound propagation is studied. The research content is summarized as follows:(1) An acoustic ray tracing model considering the real atmospheric acoustic attenuation is developed in this paper base on the local acoustic dispersion relation in the stratified atmosphere. The acoustic attenuation coefficient and growth factor in the moving atmosphere are calculated from the imaginary part of the dispersion relation, and the acoustic attenuation coefficient is corrected by the theory of attenuation in real atmosphere. The ray equations in the lossy atmosphere are then obtained through Hamilton equations. The numerical results of this ray tracing model indicate that the atmospheric absorption could play a considerable influence on the acoustic trajectory. This influence, though maybe obscure for near field propagation, cannot be neglected under the circumstance of far field propagation.(2) By using a finite-difference time-domain method consist of a 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.(3) An acoustic ray tracing model is developed to take into account the impacts of gravitational field and realistic atmospheric attenuation. Ray tracing equations are deduced from the real part of the dissipative dispersion relation, while the acoustic attenuation coefficient and growth rate in a stratified moving atmosphere are deduced from the imaginary part of the dispersion relation. To account for the non-isothermal effect and realistic attenuation, the buoyancy frequency and the cut-off frequency are substituted by the values in the slowly varying atmosphere, and the attenuation coefficient is corrected by the realistic absorption. In the validation by numerical experiment, the ray trajectory obtained by this ray tracing model agrees well with the result calculated by the FDTD method. It is shown that the acoustic trajectory can be accurately predicted by this ray tracing model. The numerical results for5Hz acoustic waves show that in the stratospheric ducting the gravitational effect plays a leading role while the attenuation effect could be neglected. But for the thermospheric ducting, the contribution of the absorption becomes more important.(4) By using a finite-difference time-domain method consist of a dispersion relation preserving scheme in space and a Runge-Kutta scheme in time, the stratospheric ducted propagation of infrasound in a dissipative, gravitational stratified atmosphere is studied. It is shown that the caustic phenomenon occurs in the reflecting region at the height of the stratosphere; the sound pressure of the infrasound is decreased while its energy is focused. This caustic phenomenon becomes weaker as the frequency of the infrasound gets higher. The energy loss of the infrasound in stratospheric duct is mainly caused by the geometric spreading. The total transmission loss increases along with the growth of the frequency. The gravitational effects not only modify the poly relation of the infrasound but also bring in the dispersion. Due to the gravitational dispersion, the velocity of the infrasound becomes higher when the frequency increases. In the reflecting region, since the ray theory becomes invalid, to make a precise prediction of the trajectory, the full wave solution should be employed.