- Introduction
Due to differential heating and conservation of energy, as well as the Earth’s rotation and conservation of momentum, there is a general trend of energy and momentum transportation from the equator to the poles. The transport of heat from the equator to the poles is not done through just one large circulation from the equator the poles, but rather a couple smaller circulations limited in size by the effects of the rotation of the Earth. More specifically, due to the rotation of the Earth, the general circulation in the atmosphere breaks down into two main regimes:
1) the Hadley Cell transporting heat from the equator to midlatitudes
2) Eddies transporting heat from the midlatitudes to the poles
In this study, through the use of rotating tank experiments and analysis of atmospheric data, we examined the dynamics and energy transport involved in both the Hadley Cell and midlatitude eddies to study the general circulation of the atmosphere.
2. Hadley Circulation
2.1) Introduction:
Hadley circulation works to transport heat from the warm equator to midlatitudes. The Hadley Cell consists of warm air rising from the equator and moving poleward to 30ºN and 30ºS where it falls to the surface. Due to the Coriolis effect which turns winds to the right in the Northern Hemisphere and to the left in the Southern Hemisphere, this air moves westward at the equator and eastward in the midlatitudes around 30ºN and 30ºS.
2.2) Tank Experiment:
To better understand Hadley circulation, a tank experiment was set up to mimic these atmospheric conditions in a controlled environment. A metal container filled with ice was placed in the center of a slowly rotating circular tank. The low rotation rate, 1.28 RPM, and correspondingly low Rossby number (f = 2Ω) was chosen to replicate the low latitude regions where the Hadley Cell forms. Five thermometers (labelled A through E) were placed on the outside of the ice bucket and along the sides and bottom of the plastic tank, in order to measure the generated temperature gradient.
Particle tracking software was used to track the motion of paper dots on the surface of the water, in order to determine how velocity varied as a function of distance. The tracks of the five particles studied, along with the plot of their velocities (in meters per millisecond) as a function of distance from the center of the tank, are included below.
In addition to the motion of air towards and away from the equator, the Hadley circulation is also responsible for the trade winds, which travel along lines of roughly constant latitude. These trade winds are represented by the green dye, which was observed to spiral around the center of the tank. This spiral was also observed to form a sloping temperature surface, similar to the conical shape of the sloping density surface observed in the fronts experiment. While the frontal slope created in that experiment was due to the density difference between fresh and salty water, here the slope marked the colder, denser water, which had sunk to the bottom, and the warmer water on top.
Thermometers B (at the bottom of the outer wall of the ice bucket) and C (on the bottom of the tank) clearly measure much colder temperatures than sensors placed elsewhere. The maximum temperature gradient recorded between B and D, both near the bottom of the tank, is roughly 5.5K The maximum gradient found at the top of the tank is .5K. Averaging these gives an approximate temperature gradient of 3K over the 18 cm region, or 16.67 K/m.
We can recall the thermal wind equation for an incompressible fluid that we derived in our study of fronts:
This relationship relates the fluid horizontal speed in the tank to the tank’s rotation rate and temperature gradient. By plugging in the calculated value for the 
where u(z1) is the average velocity of a particle traveling on the surface of the water (8.5E-2 m/s for this experiment), u(z2) is the average velocity of a particle traveling near the bottom of the tank (assumed to be roughly 0), and Δz is the depth of water in the tank, here roughly 10cm. Plugging in these values, we find that the expected velocity of a particle traveling at the surface of the tank is:
This result is within the same order of magnitude as the observed values of roughly 8.5E-2 m/s. The slight differences are probably due to the inaccuracy of approximating the temperature gradient as the average of the difference at the top and the difference at the bottom. In reality, the temperature gradient was only observed at around the bottom fifth of the tank, but we didn’t have enough thermometers to measure this precisely.
2.2) Atmosphere:
As with the Hadley Cell tank experiment under low rotation described above, through atmospheric data analysis we will find that we can observe similar motions as observed in the tank near the equator, where Coriolis parameter is low and Earth’s rotation is felt very weakly.
For this study we analyzed zonally averaged data averaged over the years 1948-2015 to observe the general atmospheric circulation trends. NCEP reanalysis data from http://www.esrl.noaa.gov/psd/cgi-bin/data/composites/printpage.pl was plotted during both January and July to observe winters in both the Northern and Southern Hemispheres, during which the temperature gradients and the Hadley Cell circulation would be strongest.
We first plotted the zonally average temperature as shown below:
Note that the temperature gradient is stronger during winter (January in the Northern Hemisphere and July in the Southern Hemisphere). The sloping temperature surfaces shown are analogous to the sloping density surfaces we observed in the tank experiment in our study of fronts.
We next plotted the zonally averaged potential temperatures calculated using the expression we previously derived in our studies of fronts and convection:
Again we observe steeper temperature gradients in the Northern Hemisphere in January and in the Southern Hemisphere in July. Note that potential temperatures over the equatorial region are relatively constant, because there is more moisture in the air above the warmer equatorial regions, according to the Clausius-Clapeyron relation. Above the 200mb height, the shape of the isotherm curves reverses direction, because this is where the stratosphere begins.
Next, we plotted the zonally averaged zonal winds:
