A Theory of Stationary Long Waves. Part I: A Simple Theory of Blocking

K. K. Tung Center for Earth and Planetary Physics, Harvard University, Camrbdige, MA 02138

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R. S. Lindzen Center for Earth and Planetary Physics, Harvard University, Camrbdige, MA 02138

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Abstract

A theory is presented that attempts to explain the tropospheric blocking phenomenon caused by the resonant amplification of large-scale planetary waves forced by topography and surface heating. It is shown that a wave becomes resonant with the stationary forcings when the wind condition in the lower atmosphere is such that the phase speed of the wave is reduced to zero. The resonant behavior of the wave in the presence of Ekman pumping and other damping mechanisms is used to account for the time amplification of the pressure ridges that is an essential part of the blocking phenomenon. This same time behavior also allows the waves to interact with the mean flow in the stratosphere, possibly initiating major sudden warmings. Such a situation was, in fact, assumed by Matsuno (1971) in the lower boundary of his stratospheric model of sudden warming.

The basis for reviving the classical normal-mode theory (when faced with the difficulties associated with the zero-wind line) is presented in Part II. The present Part I serves as an introduction to the three-part series and discusses, with the aid of a simple mathematical model, the relevant physical mechanisms involved. Though the theory of resonant Rossby waves is a classical one, the contribution of the present papers is in pointing out that the theory offers, despite the difficulties and controversies associated with it, a viable mechanism that may be the cause of some prominent physical phenomena in the atmosphere.

Abstract

A theory is presented that attempts to explain the tropospheric blocking phenomenon caused by the resonant amplification of large-scale planetary waves forced by topography and surface heating. It is shown that a wave becomes resonant with the stationary forcings when the wind condition in the lower atmosphere is such that the phase speed of the wave is reduced to zero. The resonant behavior of the wave in the presence of Ekman pumping and other damping mechanisms is used to account for the time amplification of the pressure ridges that is an essential part of the blocking phenomenon. This same time behavior also allows the waves to interact with the mean flow in the stratosphere, possibly initiating major sudden warmings. Such a situation was, in fact, assumed by Matsuno (1971) in the lower boundary of his stratospheric model of sudden warming.

The basis for reviving the classical normal-mode theory (when faced with the difficulties associated with the zero-wind line) is presented in Part II. The present Part I serves as an introduction to the three-part series and discusses, with the aid of a simple mathematical model, the relevant physical mechanisms involved. Though the theory of resonant Rossby waves is a classical one, the contribution of the present papers is in pointing out that the theory offers, despite the difficulties and controversies associated with it, a viable mechanism that may be the cause of some prominent physical phenomena in the atmosphere.

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