A nonlinear model of the break-up of internal gravity waves due to their exponential growth with height

A nonlinear finite-difference model has been used to investigate the creation of unstable regions in the atmosphere by internal gravity waves. These waves grow exponentially with height, so that an upward-propagating wave that is not reflected or absorbed will eventually cause nonlinear interactions or regions of instability or both. In this model the unstable regions are produced at roughly the height predicted from the linear theory if the transients produced by the source are considered. Simultaneously with the development of the instability, a jet develops in the originally at-rest atmosphere. Very shortly after the first instabilities appear, this jet becomes large enough to possess a critical level, so the problem of turbulence generation in the stratosphere by internal gravity waves is complicated by the nonturbulent wave interaction in a sheared region containing a critical level and by the nonlinear interaction of the wave with the turbulence it is generating.