Gravity Wave Turbulence Interaction in the Presence of a Critical Level

Abstract

The analysis of an earlier work on the interaction between an internal gravity wave and the wave-induced turbulence is extended here to the case where the wave is generated by vertical wind shear. The initial system is described by a background wind and a temperature distribution such that the Richardson number is less than ¼. A gravity wave is generated by such a dynamically unstable system and grows exponentially in time. The wave modifies the Richardson number and lowers it, particularly in the neighborhood of the critical level. When the generalized Richardson number falls below an assumed critical level, turbulence is assumed to develop and is described by a ?1½th order? scheme. A diffusion coefficient can then be calculated which has a mean and a fluctuating part. It is the latter which turns out to be responsible for the positive feedback between the wave and the wave-induced turbulence resulting in the wave growing at a faster rate than the one predicted by linear theory.