Wave propagation inside and Inertia Wave. Part I: Role of time dependence and scale separation

By launching monochromatic gravity wave packets of different frequencies, wavenumbers, and amplitudes below a localized inertia "background" wave, several assumptions and issues related to gravity wave dissipation and parameterizations are investigated: The influence of the time dependence of the background wave on the wave packet propagation, whether wave breaking occurs at caustics or in their vicinities, the importance of partial back-reflection, and the performance of ray theory when the scale separation hypothesis between the background wave and the wave packets breaks down. An intermediate model is used that is two-dimensional, linear, and that models wave breaking with a mixed shear and convective adjustment scheme. It is found that the time dependence of the background wave strongly influences the gravity wave packet propagation. For example, the time variations may inhibit critical levels, which are observed when the background wave is time independent. The gravity wave activity that escapes the background wave and the wave activity that is back-reflected are quantified for gravity waves of different vertical wavenumbers and frequencies. Strong partial back-reflection associated with elastic scattering is commonly observed. Furthemore, it is found that ray theory performs remarkably well even when the scale separation between the background wave and the gravity wave breaks down completely both in the vertical and time.