Nonlinear dynamics of vertically propagating acoustic waves in a stratified atmosphere

A method is suggested for separating gas-dynamical disturbances propagating in a one-dimensional atmosphere into components of upwards propagating, downwards propagating and stationary wave components. For the linearized problem projection operators (which are obtained in explicit form) are used for describing the evolution of the initial disturbance. The wave components thus described are used as input to the nonlinear equations. The wave components are shown by numerical calculations to keep their propagation direction, even for quite large initial amplitudes. The nonlinear system is splitted into three nonlinear equations of the interacting components. Numerical simulation results of the evolution of one of the components are shown, and the effect of nonlinear terms compared. The examples demonstrate the evolution of the downwards propagating wave with account of nonlinear terms, and a small contribution to the upwards propagating wave component generated by nonlinear effects. The importance of this method for the class of wave theory problems characterized by the similar integral dispersion operator is pointed out.