声-重力波在两层大气模型中的频散理论和数值计算

本文根据Pekeris曾提出的大气两层模型,考虑在每一层中有风的影响,讨论了在这种条件下大气层对声-重力波的频散理论。 我们从声-重力波的波动方程出发,导出了两层模型下的合流超几何方程,给出了它的通解。在导出相应的频散方程以后,给出了相速度和群速度的解析表示式。在计算机上进行了数值计算,给出了在两层中有不同风速时的相速度和群速度的频散特性,从中可以看到风对声-重力波的传播和激发都有很大的影响。     

DISPERSIVE THEORY AND NUMERICAL COMPUTATION OF THE ACOUSTIC-GRAVITY WAVE IN TWO-LAYER MODEL

Based on the two-layer model suggested by Pekeris, a developed theory of the dispersionof the acoustic-gravity wave dealing with a constant wind speed in each layer is discussed in thispaper. From the basic wave equations of the acoustic-gravity wave,the confluent hypergeometic equa-tion for the two-layer model with a constant wind speed is derived,and its general solutions aregiven.We obtain the dispersive equation by utilizing the continuous condition of the vertical veloc-ity of air particle motion and the sound pressure on the boundary between the two layers,aswell as the stiffness condition on the ground.The analytical representations of the phase andgroup velocities are also given. The methods of the computation are given in detail.The results of numerical calculation onthe computer show that the wind speeds have a great effect on the propagation of the acoustic-gravity wave.The phase and group velocities depend on the wind speeds in two layer.Theexcited cutoff frequency of the acoustic-gravity wa