Multiple Flow Equilibria in the Atmosphere and Blocking

A barotropic channel model is used to study the planetary-scale motions of an atmosphere whose zonal flow is externally driven. Perturbations are induced by topography and by d barotropic analogue of thermal driving. The use of highly truncated spectral expansions shows that there may exist a multiplicity of equilibrium states for a given driving, of which two or more may be stable. In the case of topographical forcing, two stable equilibrium states of very different character may be produced by the same forcing: one is a “low-index” flow with a strong wave component and a relatively weaker zonal component which is locked close to linear resonance; the other is a “high-index” flow with a weak wave component and a relatively stronger zonal component which is much farther from linear resonance. It is suggested that the phenomenon of blocking is a metastable equilibrium state of the low-index near-resonant character. The existence of the two types of equilibria has been confirmed by numerical integration of a grid-point model with many more degrees of freedom than the spectral model. It has also been found spectrally and for a grid-point model that oscillations may occur when one of the equilibrium states is stable for the lowest order spectral components but unstable for the next higher order components. The oscillation apparently is due to a barotropic instability of the topographic wave of the kind discussed by Lorenz and Gill. Thermal forcing also produces multiple, stable equilibria in a spectral model but confirmation with a grid-point model has so far not been obtained.