Nonlinear balance and gravity-inertial wave saturation in a simple atmospheric model

Numerical experiments with a highly truncated, forced-dissipative version of the shallow water equations suggest that for realistic atmospheric parameters, high-frequency inertial-gravity waves are almost always present in the solution, even in the limit of small Rossby numbers and long times. The waves are intermittent in character and appear to be generated naturally by the nonlinear interactions of the system. This behaviour is at variance with the notion that under normal atmospheric scaling, there is an attracting invariant manifold embedded in the full phase space which is completely free of fast oscillations (i.e., corresponding to “super quasigeostrophic” motion). The high-frequency component leads to systematic differences between actual flow and high-order balanced states, suggesting that there is an inherent limitation to the amount of information about the divergent part of the flow that can be gleaned from the rotational motion. The information is expected to be a rapidly decreasing function of Rossby number.