The General Circulation of the Atmosphere
Introduction
The circulation of the atmosphere across the globe is chaotic; as a result, long-term weather prediction is theoretically impossible. However, large-scale structures in atmospheric circulation are stable over time and can be described by basic ideas about energy balance in the Earth system.
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where
is pressure,
is is density,
is is the acceleration due to gravity,
is the height of the free surface, and
is is height.
Geostrophic balance is between the Coriolis force and the pressure gradient force, and dominates when centrifugal force is small.
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2 \Omega v_\theta = g \frac{\partial h}{\partial r} |
where
is the component of the Earth's rotation parallel to the force of gravity, is the azimuthal velocity, is height and is radius from the tank center.Cyclostrophic balance is between centrifugal force and the pressure gradient force, and dominates when the Coriolis force is small.
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R_O = \frac{|V_\theta|}{2 \Omega r} |
Thermal Wind
The Fronts experiment introduces temperature gradients as an important factor leading to pressure gradients. As a consequence of hydrostatic and geostrophic balance, temperature gradients cause vertical shear according to the relation
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\frac{\partial \mathbf{u}_g}{\partial z} = -\frac{\alpha g}{f} \hat{\mathbf{z}} \times \nabla T |
where
is the speed vector, is the thermal expansivity of the fluid, is the Coriolis parameter, and is temperature. This expression holds only for incompressible fluids, so is valid for the tank experiment: for compressible fluids like the atmosphere, the equation can be written in pressure coordinates instead of height.Convection
The Convection experiment introduces convection as a method of heat transport that helps balance the earth's radiative budget. Since the earth's temperature is roughly constant over time, outgoing thermal radiation must equal incoming solar radiation. The level at which radiation balances turns out to be in the upper atmosphere: below that level, convection acts to transport heat more efficiently than radiation.
Two Regimes in the Atmosphere
The three experiments develop the framework for a model of atmospheric circulation on Earth. The equator-to-pole temperature gradient creates an energy imbalance which is equalized when air moves along pressure gradients and is affected by conservation of angular momentum as it travels meridionally. These constraints produce two structural regimes visible in the atmosphere: the Hadley Cell and mid-latitude eddies.
Hadley Cell
The Hadley cell is a region of convective overturning from about 0° to 30° N and S: the northern and southern extent shifts seasonally. Warm air rises at the equator, moves towards the poles, sinks in the subtropics, and returns along the surface towards the equator. Zonal winds are generated due to conservation of angular momentum. In the upper atmosphere, the westerly subtropical jet forms at the poleward boundary of the cell. Towards the equator, the easterly trade winds can be observed, although their speed is reduced by surface friction.
Poleward of 30° N and S, the Hadley cell breaks down. In a non-rotating Earth, the cell might extend all the way to the pole, but we observe that Coriolis deflection turns wind parallel to the equator at 30° where it sinks and returns to the equator. Temperature gradients poleward that cannot be equalized by convection lead to baroclinic instability.
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Mid-latitude Eddies
Baroclinic instability leads to eddy formation. While there is a mid-latitude convective cell, its importance to heat transport is dwarfed by these eddies, which stir heat from the equator towards the pole. Eddy heat transport is horizontal, in contrast to the convective overturning at lower latitudes, and so varies less with height. The mid-latitude region dominated by weather systems extends from 30° to 60° N and S, where it gives way to the polar convective cell.
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The seasonal variation and heat transport capacity of the Hadley and mid-latitude regimes can be demonstrated by examining data from the atmosphere.
General Circulation in the Atmosphere
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The meridional heat flux consists of two parts: the mean circulation and eddies. The mean circulation is most prominent in the tropics and called Hadley cell circulation, transporting heat from the equator to the sub-tropics. Eddies are the transient heat flux prominent in the mid-latitudes, transferring heat poleward. Together, they transport the heat from the equator to the pole.
Hadley Cell
We can plot climatological fields showing the meridional mean features of the atmosphere to observe the Hadley cell circulation. There are two phenomena that can be observed in the Hadley cell: the overturning circulation and thermal wind.
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The rotating table was spun up to 0.1
and allowed to spin until a paper dot placed on the surface of the water appeared motionless to the overhead corotating camera, which was physically attached to the rotating table. The canister was filled with ice until full and then
topped up with water.
The surface speed of the water was measured by tracking black paper dots in the Particle Tracker application. The speed on the tank floor was measured by tracking the purple pigment trails from granules of potassium permanganate using timecoded screenshots in the Particle Tracker. Water speed shear between the top and bottom of the tank was measured with drops of blue food dye.
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A metal canister of radius 18
was placed in the center of a tank of radius 31
. Again s
ix HOBO temperature sensors were taped to the tank in the arrangement shown in the figure below. This arrangement differs from the first experiment: thermometers 1 through 5 were placed in a line radially from the tank center; thermometer 6 was placed between 3 and 4, on the bottom of the tank but 10
further in the clockwise direction. This arrangement was devised to capture thermal signatures of the eddies that were hypothesized to form. Thermometer 1 was placed at a height of 11
and thermometer 5 at a height of 9
. The tank was filled with still water to a height of 14
with water .The rotating table was spun up to 1 and allowed to spin until a paper dot placed on the surface of the water appeared motionless to the overhead corotating camera. In this setup, the speed of the corotating camera was synced electronically with the table rotation speed through a computer interface. The canister was filled with 521.6 of ice and then topped up with water.
Surface speed, bottom speed and shear were measured as in the previous experiment: paper dots, permanganate granules and food dye, respectively. Two colors of food dye were used to illustrate eddy formation: blue dropped in the colder water near the canister and red in the warmer water near the outside edge.
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Slow Rotation Experiment
Fast Rotation Experiment
Bibliography
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