Nonlinear Stationary Rossby Waves on Nonuniform Zonal Winds and Atmospheric Blocking. Part I: The Analytical Theory

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Abstract
Many recent theoretical and observational studies have been devoted to the understanding of atmospheric patterns that persist beyond the synoptic time scale. These patterns are known as blocking events. Properties of blocking events emerging from the observational evidence are consistent with the properties of nonlinear, i.e., coherent, localized structures characterized by locking of phases and phase speeds which are amplitude dependent. In the present paper we develop a nonlinear, analytical theory with solutions in the form of stationary, coherent structures superimposed on a mean westerly wind. The model is the inviscid, quasi-geostrophic potential vorticity conservation equation with a mean zonal wind having vertical as well as horizontal shear. The used mean wind profile is typical of the atmosphere at midlatitude. The stationary, coherent solution is an antisymmetric dipole, with the anticyclone north of the cyclone; it has an equivalent barotropic vertical structure, is meridionally as well as zonally trapped and obeys a nonlinear dynamics in the zonal wave guide. This pattern, even though idealized, exhibits a strong similarity and is consistent with observations of blocking patterns.

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