Form-Drag Instability, Multiple Equilibria and Propagating Planetary Waves in Baroclinic, Orographically Forced, Planetary Wave Systems

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  • 1 Massachusetts Institute of Technology, Cambridge 02139
  • | 2 National Research Council, Washington, DC, and Laboratory for Atmospheric Sciences, NASA Goddard Space Flight Center, Greenbelt, MD 20771
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Abstract

A two-layer baroclinic model is used to study the planetary-scale motions of a thermally driven atmosphere in the presence of topography, and in doing so to extend previous results obtained with a barotropic model. Highly truncated spectral equations are used to obtain multiple wavelike stationary equilibrium states, to examine the instabilities that produce them, and to study the instabilities that feed on them and give rise to traveling planetary waves. Although the equilibria cannot exist without orography, their energy comes from the potential energy of the mean flow, not from kinetic energy transfer via the mountain torque. Low-index (blocking) equilibria as well as high-index equilibria require a large thermal driving and are associated with both orographic and baroclinic instability of the Hadley circulation. The blocking state is stable to the gravest y mode but unstable to the next highest y mode: the high-index states are unstable to both modes. The instabilities of the equilibria lead to vacillation cycles in which the wave field with the gravest y mode propagates westward with periods of ∼5–15 days, interacting with a fluctuating zonal flow.

It is suggested that blocking in nature is a quasi-stable circulation arising from orographic instability with strong thermal driving; and that observed low-frequency, propagating planetary waves are due to instabilities of the quasi-stationary, topographically forced equilibria.

Abstract

A two-layer baroclinic model is used to study the planetary-scale motions of a thermally driven atmosphere in the presence of topography, and in doing so to extend previous results obtained with a barotropic model. Highly truncated spectral equations are used to obtain multiple wavelike stationary equilibrium states, to examine the instabilities that produce them, and to study the instabilities that feed on them and give rise to traveling planetary waves. Although the equilibria cannot exist without orography, their energy comes from the potential energy of the mean flow, not from kinetic energy transfer via the mountain torque. Low-index (blocking) equilibria as well as high-index equilibria require a large thermal driving and are associated with both orographic and baroclinic instability of the Hadley circulation. The blocking state is stable to the gravest y mode but unstable to the next highest y mode: the high-index states are unstable to both modes. The instabilities of the equilibria lead to vacillation cycles in which the wave field with the gravest y mode propagates westward with periods of ∼5–15 days, interacting with a fluctuating zonal flow.

It is suggested that blocking in nature is a quasi-stable circulation arising from orographic instability with strong thermal driving; and that observed low-frequency, propagating planetary waves are due to instabilities of the quasi-stationary, topographically forced equilibria.

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