The Effect of Weak Non-Linearity on Vertically Propagating Internal Gravity Waves in the Atmosphere.
The linear and weakly non-linear limits of two -dimensional gravity waves in an incompressible, inviscid and stably stratified atmosphere are studied. The linear results indicate the growth of waves propagating upward leading to the breakdown of the linear theory. The three -wave resonant interaction theory indicates an energy cascade from a vertically propagating wave (primary wave) to waves having smaller absolute values of Doppler shifted frequency ((OMEGA)). When the non-dimensional parameter. (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI). is in the range "1 to about 0.8" (N being the Brunt-Vaisala frequency), the energy of the primary wave is transferred to bands of small amplitude waves. The triads in these bands include a member with the same vertical group velocity as the primary wave while other triads contain a member with larger vertical group velocity. The band widths approach zero as the primary wave amplitude is reduced. The analysis suggests that the three-wave resonant interactions should be replaced by a higher order approximation in this limit.
- Pub Date:
- Physics: Atmospheric Science