Local Multiple equilibria and Regional Atmospheric Blocking

Stationary flow of a barotropic fluid in a β channel has been shown by Charney and De Vore (1979) to possess multiple-equilibrium solutions when sinusoidal topographic forcing is exerted within the region of resonance near the wavenumber of stationary Rossby waves, and nonlinear effects are taken into account. Charney and De Vore associate the different solutions with zonal and blocking states of global circulation. However, real topography is non-sinusoidal and, most of the time, observed blocking configurations display a pronounced regional character. On the other hand, the problem of superimposing different harmonics is made difficult here by the essential role played by nonlinearity in the theory of multiple equilibria. In this paper, the mathematical problem of determining the stationary states of flow of barotropic fluid in a β plane when topography is nonsinusoidal is analyzed with the help of the perturbative assumptions that the latitudinal scale of the flow is very large and topography has the form of a slowly modulated sinusoid. The multiple states of stationary flow described by Charney and De Vore are found to exist simultaneously in different regions of the β plane. Theoretical solutions corresponding to different kinds of resonant forcing are analyzed. The theoretical solutions are discussed in relationship to the problem of blocking as a “regional” phenomenon and are shown to have several different features in common with observed persistent blocking patterns.