A quasi-geostrophic barotropic model is used to examine the role of non-linearities in limiting the growth of forced waves. Using a simple mechanism based on wave interference strong transient eddy growth can be produced. As a starting point we use an analytical linear solution for the flow evolution. Given that a rigid upper bound on wave growth is set by the potential enstrophy conservation principle, the linear solution is bound to break down at high forcing amplitudes. We form an analytical quasi-linear solution guaranteeing potential enstrophy conservation and check its domain of validity with a numerical non-linear model. The results of the numerical integrations confirm that wave-mean flow interaction is sufficient to limit eddy growth. As full non-linearities involving wave-wave interactions prove not to be important in limiting wave growth in this problem, it is interesting to consider the relation of the above results to the question about the role of wave breaking in affecting the vertical propagation of Rossby waves and in limiting their growth.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics