Abstract
In this study, an f-plane dynamical model for incompressible flows is presented to examine the mechanisms underlying the structure and stability of large-scale zonally symmetric circulations. Analyses based on the Principle of Exchange of Stabilities reveal that this zonally symmetric model possesses a single-cell structure in the absence of the Coriolis force, similar to the single-cell general atmospheric circulation in the absence of the Earth’s rotation as previously hypothesized. The circulation, however, bifurcates into a triple-cell structure in the presence of the Coriolis force if the vertical temperature gradient, the rotational rate, and the momentum eddy coefficients satisfy a certain constraint. Further analyses of this triple-cell structure as a result of the Coriolis force show that this structure is topologically stable, thus offering new insight into the highly resilient structure of the Earth’s atmospheric global circulations.
Highlights
The atmosphere is a complex dynamical system
The fundamental questions that we wish to address here are 1) whether the zonally symmetric circulations (ZSC) possesses a triple-cell structure similar to the Hadley, Ferrel, and Polar cells in the Earth’s global atmospheric circulations, 2) does the ZSC accept a single-cell structure in the absence of the Coriolis force as previously hypothesized?, and 3) what is the condition for the triple-cell structure to emerge as a consequence of the Earth’s rotation? In addition to these questions, it is of importance to examine the stability of these single-cell and triple-cell structures such that these structures can represent a real configuration of the atmospheric circulations
Using the dynamical transition framework developed by Ma and Wang, it was found that the incompressible NavierStokes equations under the zonally symmetric configuration could naturally support intricate structures of the ZSC
Summary
The atmosphere is a complex dynamical system. Due to uneven distribution of solar radiation on the Earth’s surface that generally decreases with increasing latitudes, the existence of global atmospheric circulations in response to the uneven absorption of the solar radiation at the surface is necessary, which play an important role in maintaining the energy balance between the equator and the poles. At the deepest essence, the global circulations can be considered as a direct response of the atmosphere to the warmer temperature at the Earth’s surface due to solar heating. Held and Hou proposed a steadystate axially symmetric model that could demonstrate the factors that most control the variability of the global circulations in a dry stably stratified atmosphere Their results suggested that the vertical eddy viscosity plays an important role in maintaining the steady structure for the global circulations. By improving the steady-state model in Ref. 12, Farrell speculated that the Hadley cell could extend all the way from the equator to the poles in the limit of an inviscid fluid with a sufficiently high Rossby number such that the Coriolis force can be neglected This single-cell hypothesis of the global circulations in the limit of no Earth’s rotation is somewhat similar to the early concept of a general circulation suggested by Hadley..
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