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Coherent Structures in a Baroclinic Atmosphere. Part III: Block Formation and Eddy Forcing

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  • 1 Department of Earth, Atmospheric, and Planetary Sciences, Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, Cambridge, MA 02139
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Abstract

In this paper we exploit a nonlinear baroclinic theory of atmospheric Rossby waves superimposed on westerly winds with meridional and vertical shear which was proposed in two earlier studies, Parts I and II. In Part I, nonlinear, stationary Rossby wave solutions were found consisting of a localized vortex pair and having an equivalent barotropic structure. These solutions, found in the context of an asymptotic theory for the quasi-geostrophic baroclinic potential vorticity equation, were proposed as a model for atmospheric blocking. In Part II, the theory was extended to the time-dependent, highly nonlinear case, removing the weak-amplitude limitations of the asymptotic theory of Part I. The localized highly nonlinear dipole solution of Part II was found to be remarkably robust to different energetic perturbations, even with a baroclinically unstable mean zonal wind. A typical persistence (predictability) time for the solution of Part II was of the order 10 to 15 days, consistent with observations of blocking patterns.

In this paper we investigate two further aspects of the high-amplitude solution of Part II. First, we study the formation of the coherent dipole starting from rather different initial conditions. We establish a necessary and sufficient criterion for the formation of the coherent structure. This criterion involves the preexistence of a zonal low wavenumber component (wavenumber one) in an antisymmetric meridional mode having a large enough amplitude. If this condition is satisfied, the evolution into the block configuration is assured by the model internal dynamics that is of the Korteweg-deVries type.

Second, we study the effect of short-scale, transient eddies upon the blocking dipole. We include dissipative effects and find that the eddy forcing is such to maintain the coherent structure against both mean advection and dissipation. The eddy forcing pattern resulting from the numerical experiments compares well with the observational evidence, given the high truncation of the model used.

Abstract

In this paper we exploit a nonlinear baroclinic theory of atmospheric Rossby waves superimposed on westerly winds with meridional and vertical shear which was proposed in two earlier studies, Parts I and II. In Part I, nonlinear, stationary Rossby wave solutions were found consisting of a localized vortex pair and having an equivalent barotropic structure. These solutions, found in the context of an asymptotic theory for the quasi-geostrophic baroclinic potential vorticity equation, were proposed as a model for atmospheric blocking. In Part II, the theory was extended to the time-dependent, highly nonlinear case, removing the weak-amplitude limitations of the asymptotic theory of Part I. The localized highly nonlinear dipole solution of Part II was found to be remarkably robust to different energetic perturbations, even with a baroclinically unstable mean zonal wind. A typical persistence (predictability) time for the solution of Part II was of the order 10 to 15 days, consistent with observations of blocking patterns.

In this paper we investigate two further aspects of the high-amplitude solution of Part II. First, we study the formation of the coherent dipole starting from rather different initial conditions. We establish a necessary and sufficient criterion for the formation of the coherent structure. This criterion involves the preexistence of a zonal low wavenumber component (wavenumber one) in an antisymmetric meridional mode having a large enough amplitude. If this condition is satisfied, the evolution into the block configuration is assured by the model internal dynamics that is of the Korteweg-deVries type.

Second, we study the effect of short-scale, transient eddies upon the blocking dipole. We include dissipative effects and find that the eddy forcing is such to maintain the coherent structure against both mean advection and dissipation. The eddy forcing pattern resulting from the numerical experiments compares well with the observational evidence, given the high truncation of the model used.

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