Seasonal Climate Fluctuations as Steady and Periodic Flow States of a Barotropic Model of Planetary Waves.

The variability of the seasonal climate may be due, not only to variations in the atmospheric forcing fields, but to internal variability due to the nonlinear nature of the governing equations. In this work, we develop this concept by considering the interactions between planetary waves at different planetary wave numbers, using a spectral form of the barotropic vorticity equation on the sphere, driven by the effects of large scale orography, friction, and momentum forcing. The model is truncated to the minimum number (three) of planetary waves permitting mutual interactions. Zonal flow is also included. The steady state properties of the model are identical to those of a simpler model with wave-zonal flow interactions, due to Charney and De Vore. Only one planetary wave mode (the "middle wave") has nonzero amplitude, with three possible values; giving rise to subresonant, low superresonant and high superresonant flow states according to the zonal flow value. The other two wave modes ("outer waves") have zero amplitude. However, we show that when the forcing exceeds a critical value, the subresonant state becomes unstable and the system undergoes a Hopf bifurcation into a periodic orbit. Periodic orbits are found for various planetary wave modes. The middle wave mode and the zonal flow remain stationary, while the outer waves travel in a periodic orbit with slow period (about ten days) so that a fixed pattern travels slowly through a stationary one. The period, amplitudes, and phases of the periodic orbit are all functions of forcing. As forcing is increased still further, the periodic orbit ceases to exist. In this case the system falls into the high superresonant (zonal flow) state, which remains stable. The above results extend the concept of long-wave dynamics as transitions between metastable stationary states. In the model we find internal variability not only due to multiple equilibria, but because small changes in forcing can produce very different responses in the qualitative behavior of the system. The pattern of slowly moving waves traveling through a stationary pattern generated by topography and momentum forcing suggests an explanation for the transition into and out of a blocking episode. The model permits intermittent periodic behavior as forcing changes. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI.