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Although classical theories of midlatitude momentum fluxes focus on the wave-mean flow interaction, wave-wave interactions may be important for generating long waves. It is shown in this study that this nonlinear generation has implications for eddy momentum fluxes in some regimes. Using a two-layer quasi-geostrophic model of a baroclinic jet on a  β -plane, statistically steady states are explored in which the vertically integrated eddy momentum flux is divergent at the center of the jet, rather than convergent as in Earth-like climates. One moves towards this less familiar climate from more Earth-like settings by reducing either  β , frictional drag, or the width of the baroclinic zone, or by increasing the upper bound of resolvable wavelengths by lengthening the zonal channel. Even in Earth-like settings, long waves diverge momentum from the jet, but they are too weak to compete with short unstable waves that converge momentum. We argue that long waves are generated by breaking of short unstable waves near their critical latitudes, where long waves converge momentum while diverging momentum at the center of the jet. Quasi-linear models with no wave-wave interaction can qualitatively capture the Earth-like regime but not the regime with momentum flux divergence at the center of the jet, because the nonlinear wave breaking and long wave generation processes are missing. Therefore, a more comprehensive theory of atmospheric eddy momentum fluxes should take into account the nonlinear dynamics of long waves.

Nonlinear generation of long waves and the reversal of eddy momentum fluxes in a two-layer quasi-geostrophic model