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.
These constraints are explored in three other tank experiments described on this wiki: Balanced Motion, Fronts and Convection. Bringing these concepts together into a general circulation model explains the existence of some persistent features of the atmosphere, including the subtropical and polar jet streams, the trade winds, and the midlatitude bands in which rotating weather systems can be observed.
Theory
Balanced Motion
The Balanced Motion experiment develops three kinds of force balance: hydrostatic balance in the vertical, and geostrophic and cyclostrophic balance in the horizontal. It also introduces the Rossby number as a tool to determine whether geostrophic or cyclostrophic balance dominates in a given system.
Hydrostatic balance relates the pressure at a given surface to the weight of fluid above it.
| p = \rho g (H - z) |
Geostrophic balance is between the Coriolis force and the pressure gradient force, and dominates when centrifugal force is small.
| 2 \Omega v_\theta = g \frac{\partial h}{\partial r} |
Cyclostrophic balance is between centrifugal force and the pressure gradient force, and dominates when the Coriolis force is small.
| \frac{v_\theta^2}{r} = g \frac{\partial h}{\partial r} |
Whether geostrophic or cyclostrophic balance is a better approximation is determined by the Rossby number, which is simply the ratio of centrifugal to Coriolis forces in a system.
| R_O = \frac{|V_\theta|}{2 \Omega r} |
General Circulation in the Atmosphere
The earth receives heat energy from incoming solar radiation. Because the earth is round and its rotating axis is slightly tilted, the amount of income radiation is different depending on the latitude and time of the year. The mean incoming solar radiation is at a maximum in the tropics, and decreases as the latitude increases to the pole. The difference in radiative budget results in atmosphere’s meridional instability. To counteract the instability, the atmosphere transports heat from the equator poleward.
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.
Overturning Circulation
Figure 1: Zonally averaged temperature in January and July from 1948 to 2016. The warmest air is always at the tropics, but the temperature gradient is strongest over the mid-latitude in the northern hemisphere in January and in the southern hemisphere is July.
The overturning circulation functions by the convection of heat in the tropics. In Figure 1, the meridional temperature plot has its maximum in the tropics, where the incoming solar radiation is more perpendicular to the surface than the pole, hence the larger effective solar radiation.
In January when it is summer in the southern hemisphere, the solar radiation comes slightly more from the south, so the temperature peak is slightly to the south. As it is winter in the northern hemisphere, the temperature gradient in the northern hemisphere is larger than in the southern hemisphere. While in July where it is summer in the northern hemisphere and winter in the southern hemisphere, the temperature peak is slightly to the north, and the temperature gradient is larger in the northern hemisphere.
Because the incoming solar radiation in January and July is not equal in southern and northern hemisphere, the Hadley cell will not be two symmetrical cells over the equator. One cell will be weaker and one stronger, where it is easier to observe the stronger cell.
Thermal Wind
Tank Experiment
Two rotating tank experiments were set up. Tank rotation speed was the important parameter varied: one tank rotated at a speed of 1 rad s^{-1} and the other at 0.1 rad s^{-1}.
Slow Rotation Experiment
A metal canister of radius 12 cm was placed in the center of a tank of radius 22 cm. Six HOBO temperature sensors were taped to the tank in the arrangement shown in the figure below. The thermometer cables were taped along the bottom and edge of the tank to minimize interference with water flow. The tank was filled with still water to a height of 12.6 cm.
The rotating table was spun up to 0.1 rad s^{-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 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.
Fast Rotation Experiment
A metal canister of radius 18 cm was placed in the center of a tank of radius 31 cm. Again six 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 cm 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 cm and thermometer 5 at a height of 9 cm. The tank was filled with still water to a height of 14 cm with water
The rotating table was spun up to 1 rad s^{-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 g of ice and then 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.
Results
Slow Rotation Experiment
Fast Rotation Experiment
Bibliography