Optical Model Analysis of Gravity WaveCritical Layer Interaction
Abstract
In this paper our primary concern is to determine the degree of reflection of the original incident wave when the background wind is (1) stable, (2) unstable. To determine such reflections we use the optical model treatment, a method which is especially designed for problems involving diverse and relatively unstructured absorption mechanisms. As a first attempt, we use an analytic model for our wind profile to obtain analytic solution in order to be sure to take care of the various hydrodynamic singularities as well as to obtain a better understanding of the various complicated processes, especially for the case of over reflection. We have found that the dissipations from viscosity and heat conduction losses are very small in comparison with other absorption except very close to the actual critical level. So we model only the absorption due to nonlinearity and turbulence, leaving the reflection at the critical layer as a variable parameter. In this way, our approach takes into consideration the absorption mechanisms from (a) to (d). For (e) (the excitation and reradiation), we have found that the gravity wavecritical layer interaction in the presence of an unstable background wind is equivalent to the corresponding interaction in a stable background wind with an emission instead of an absorption mechanism. In other words, with an emission mechanism the absorbing optical model "potential" changes sign and becomes a "source" for radiating gravity waves instead of a "sink" for absorbing gravity waves. The over reflection whose occurrence depends on the phase of the reflection from the optical "potential" serves as an example for energymomentum transfer from the background winds back into the gravity waves; the opposite to the absorption into the mean flow. All this can be analytically demonstrated by incorporating the optical model into our SturmLiouville equation and derive a generalized form of the Eliassen and Palm theorem.
 Publication:

Ph.D. Thesis
 Pub Date:
 June 1992
 Bibcode:
 1992PhDT........21H
 Keywords:

 CRITICAL LAYER;
 Physics: Atmospheric Science;
 Absorptivity;
 Gravity Waves;
 Mathematical Models;
 Optical Reflection;
 Wind Profiles;
 Hydrodynamics;
 Singularity (Mathematics);
 Theorems;
 Geophysics