Time series analysis of normal mode energetics for Rossby wave breaking and saturation using a simple barotropic model

In this study, Rossby wave breaking and saturation are examined for an idealized situation using a simple barotropic spectral model. In the model, a Rossby wave is amplified by parameterized baroclinic instability. The increase of the wave energy stops at the level where the high and low potential vorticities (PVs) indicate overturning, which is equivalent to the fact that the meridional PV gradient becomes negative somewhere in the domain. In this study, it is shown theoretically that the criterion may be represented by the point when the wave energy exceeds a quarter of the originally proposed saturation level specified by E = (ps/g)c2 in the spectral domain, by assuming a sinusoidal curve for the wave. Rossby wave saturation under the new definition proposed in this study could be followed by wave breaking, which occurs when the energy level of the background noise becomes comparable to that of harmonic waves of the amplified unstable wave. It is found that the criterion of PV overturning is equivalent to the energy level of wave saturation, and wave breaking is a distinct phenomenon from wave saturation. In this study, the criteria for Rossby wave breaking and saturation are examined in the view of the time evolution for an idealized numerical experiments using a simple barotropic general circulation model. We found that negative PV gradient appears when the eddy energy overshoots the saturation level suggested in this study, and the excess energy is transferred to back ground noise energy by the nonlinear wave–wave interactions.