Averaging over fast gravity waves for geophysical flows with unbalanced initial data

Various facets of recent mathematical theories for averaging over fast gravity waves on advective time scales for geophysical flows with unbalanced initial data are presented here including nonlinear Rossby adjustment and simplified reduced dynamics. This work is presented within the context of simplified geophysical models involving the rotating shallow-water equations and the rotating stably stratified Boussinesq equations. Novel mechanisms for enhanced gravity wave dissipation through the catalytic interaction with potential vortical modes are also developed here within the context of the rotating shallow-water equations.