The role of nonlinear self-interaction in the dynamics of planetary-scale atmospheric fluctuations

A central role in the general circulation of the atmosphere is played by planetary-scale inertial fluctuations with zonal wavenumber in the range k = 1-4. Geopotential variance in this range is markedly non-gaussian and a great fraction of it is non-propagating, in contrast with the normal distribution of amplitudes and the basically propagating character of fluctuations in the baroclinic range (3 > k > 15). While a wave dispersion relationship can be identified in the baroclinic range, no clear relationship between time and space scales emerges in the ultra-long regime (k < 5, period > 10 days). We investigate the hypothesis that nonlinear self-interaction of planetary waves influences the mobility (and, therefore, the dispersion) of ultra-long planetary fluctuations. By means of a perturbation expansion of the barotropic vorticity equation we derive a minimal analytic description of the impact of self-nonlinearity on mobility and we show that this is responsible for a correction term to phase speed, with the prevalent effect of slowing down the propagation of waves. The intensity of nonlinear self-interaction is shown to increase with the complexity of the flow, depending on both its zonal and meridional modulations. Reanalysis data of geopotential height and zonal wind are analysed in order to test the effect of self-nonlinearity on observed planetary flows.