Low-frequency variability and the instability of zonally varying atmospheric flows

The instability of the barotropic vorticity equation on the sphere, linearized about a zonally varying, time-mean basic state, was examined by Simmons et al (1983). They demonstrated similarities between the most unstable eigenmodes of this problem and patterns of low frequency variability in the atmosphere. Although empirical evidence for this relation is suggestive, no satisfactory physical explanation of the mechanism involved has been proffered.; The sensitivity of this eigenvalue problem to changes in parameters of the barotropic model is studied. The sensitivity of the unstable modes with respect to changes in resolution, in the basic state, and in diffusion are presented. Results suggest that many supposedly relevant modes are disconcertingly sensitive to model parameters. If unstable modes of this problem are a viable explanation of atmospheric low frequency variability, more robust unstable modes need to be presented.; Since the observed atmospheric state does not satisfy the vorticity equation, a forcing term is assumed to balance the basic state time tendency for the eigenvalue problem. Three infinite beta plane models are used to gain insight into the validity of this assumption.; The first investigates instabilities of finite amplitude, stationary Rossby waves of arbitrary orientation. The second examines instabilities of finite amplitude, stationary baroclinic Rossby waves of arbitrary orientation in a two level model with zonal shear. Finally, a forced barotropic model, linearized about the upper level basic state from the two level model, is examined. Results suggest that the free barotropic model does a better job reproducing low frequency, approximately equivalent barotropic unstable modes of the two level model than does the forced model. This result provides an incentive for examining the instability of nearly stationary basic states.; Nearly stationary states of the barotropic vorticity equation on the sphere close to observed states of the atmosphere are produced using minimization algorithms. The unstable modes of nearly stationary states appear more robust than those of the observed January states, suggesting that nearly stationary states are superior for this instability problem. The nature and existence of nearly stationary states also has implications for the predictability of the atmosphere.