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 a barotropic analog 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 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 that is locked close to linear resonance; the other is a high index flow with a weak wave component and a relatively stronger zonal component that is 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 a numerical integration of a grid point model with many more degrees of freedom than the spectral model. It was 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 caused by 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 not been obtained so far.