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The general circulation of the atmosphere
By S. Tibaldi* and R
Mureau
* Current address: University of Bologna,
Department of Physics, Via Imerio 46, 40126 Bologna, Italy
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3. A conceptual model: The annulus experiment
Annulus experiments can provide a (partial) conceptual model of the General Circulation which can be very useful in understanding some of the basic and fundamental processes which are at the basis, e.g. the behaviour of the atmosphere as a heat engine transporting heat from the poles to the equator in a rotating frame of reference.
The experimental apparatus is composed of two coaxial cylinders resting on a base and rotating around their common axis. The gap between the two cylinders is filled with fluid which, if the system is isothermal, rotates at the same angular speed as its container. If, however, the outer cylinder is heated and the inner one is cooled (and they, in turn, heat and cool the adjacent fluid) density gradients are created in the rotating fluid requiring motion to balance them. Such motions will, initially, be in the radial direction (`north-south'). But as soon as fluid parcels start moving in a rotating frame of reference, the Coriolis force takes action, deflecting their motion at right angles to the velocity vector (and to the right, for anticlockwise rotation), until an approximately geostrophic balance is attained, with low-level easterlies (and a weaker southward meridional flow) and upper-level westerlies (and a corresponding northward meridional flow). This Hadley-type circulation is very similar to the observed Hadley cell in the earth's NH tropical regions.
Figure 4 . Time exposures showing the motion of surface tracer particles in a rotating annulus. The four photographs illustrate various stages of a five-wave tilted trough vacillation cycle. The period of the vacillation cycle is
revolutions and the photographs are at intervals
of 4 revolutions. (Photographs by Dave Fultz).
Figure 5 . Basic isentropes at an angle
and a displacement at an angle 
.If the latitudinal thermal gradients are progressively increased, this simple and symmetric zonal regime becomes baroclinically unstable, and waves of progressively smaller and smaller wavelength start appearing (see Fig. 4 ). These waves grow at the expense of the available potential energy of the zonal mean flow and are possible because potentially warmer (and, therefore, lighter) parcels of fluid are transported upward and poleward and potentially colder (and, therefore, heavier) parcels are transported equatorward and downward, thereby lowering the centre of gravity of the entire system (see Fig. 5 ). Their main purpose is to increase the efficiency of the N-S transport of beat, to make it compatible with the increased temperature gradient, since the symmetric Hadley circulation is inefficient in transporting heat N-S.
The large-scale waves so produced in the annulus resemble closely the large-scale waves that dominate the mid-latitude tropospheric circulation of the real atmosphere, but this resemblance can be partially misleading. We will, in fact, see in a later lecture how the planetary-scale atmospheric waves could well exist in a purely barotropic atmosphere, solely due to the latitudinal variation of the Coriolis parameter, while we have just seen that in the annulus such waves are purely baroclinic. In reality, planetary waves are ruled by a mixed barotropic-baroclinic dynamics, in which both conversion between available potential energy and kinetic energy of the zonal flow and kinetic energy of the waves are important.
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07.06.2002 |
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