Pseudomomentum and breaking of Rossby waves

Of the many contributions of Isaac Held's, his work on the fluid dynamics of the midlatitude atmosphere made a lasting impression on me. This includes the particularly elegant result that orthogonality of wave modes may be established even for non-normal (shear) flows using pseudomomentum and/or pseudoenergy and that this fact can be used to partition the effects of discrete modes and those of continuum on the mean flow modification (Held 1985, Held and Phillips 1987). In his work with John Fyfe, Held used pseudomomentum to predict the onset of Rossby wave breaking (Fyfe and Held 1990), which, to me, the first theory that did not require the pre-existence of critical lines for waves to break.

In this presentation I'd like to revisit some of these problems considered by Held and attempt at extending the theory to finite amplitude waves. While some advantages of the linear theory are lost (e.g., orthogonality of modes), the extended theory provides a complete budget of pseudomomentum including the effects of mixing, and it gives an insight on how to generalize the notion of critical lines for finite-amplitude waves.