Abstract
A nonlinear numerical model of the gravity wave-critical level interaction is developed in this paper. This model is used to examine and compare the effects of viscosity, time-dependence and nonlinear interactions on the development of the critical level interaction. It is found, in agreement with earlier studies, that viscosity and heat conduction strongly stabilize the interaction very near the critical level. Time-dependence and nonlinear interactions are found to be strongly stabilizing only for very transient or low viscosity flows, respectively. These two effects are very important, however, in the development of Kelvin-Helmholtz instabilities within unstable velocity shears. Once excited, these instabilities grow on the excess energy available in the unstable shears. When large unstable velocity shears are produced, the Kelvin-Helmholtz instabilities grow until they dominate the critical level interaction. It is argued that the break-down of these Kelvin-Helmholtz billows produced by the critical level interaction can explain some of the thin turbulent layers observed in the atmosphere and the oceans.
