Hi! We're Elizabeth, Elizabeth and Katrina, and here's our write-up of the midlatitude eddy circulation portion of our general circulation project.
Introduction
Source: http://visibleearth.nasa.gov/view.php?id=56236
The midlatitude eddy circulation, which we can observe surrounding the pole in the satellite image above, is important for heat transport in the atmosphere. Eddies occur at higher latitudes than the Hadley Cells and as estimates in the plot below show, are responsible for most of the heat transport required by the differential heating of the Earth. Once again we used a tank experiment and atmospheric data to study these eddies. Eddies occur in the midlatitudes, where Earth's rotation is more significant. Thus, to mimic eddies in our tank experiment, we used a high rotation rate and temperature gradient. To study eddies in the atmosphere, we used atmospheric data to study the heat transport involved in the midlatitude eddies.
Source: "Atmosphere, Ocean, and Climate Dynamics: An Introductory Text" by John Marshall & Alan Plumb (2007).
From the figure above, detailing heat transport by latitude, heat transport is at a maximum near 40ºN and S, where eddies occur. We integrate the zonally averaged heat flux due to eddies, to find the net poleward heat flux using the following equation,
where a is the Earth’s radius, is the latitude, cp is the specific heat, g is gravity, and 
is the zonal average of 
, with v referring to meridional wind and T referring to temperature. Here, 
is the total heat flux and 
is the monthly mean transport. Thus, is the meridional heat flux due to transient eddies; using this equation we will compare its result to what the figure above predicts.
Tank Experiment
Using a high rotation rate (10 rotations per minute) to simulate the much higher Coriolis parameters at near-polar latitudes, we set up a tank experiment to observe eddy heat transport. As in the Hadley experiment, a metal bucket of ice was placed at the center of a rotating circular tank. However, due to the high rotation rate, dots placed on the surface of the water were observed to follow the shape of smaller-scale eddy currents, rather than rotating around the tank. Similarly, red and green dye placed in the tank highlighted small disturbances and rotating cells.
Again, thermometers were placed around the tank to measure the temperature gradient generated. Two sets of four sensors each were placed at similar heights 50 degrees apart, to ideally record both sides of a single eddy. See the schematic below.
As in the Hadley cell experiment, a temperature gradient was observed to have developed much more strongly at the bottom of the tank, due to the denser, colder water sinking downwards.
The 988.7 grams of ice were not replenished over the course of the experiment and took thirty minutes to fully melt. Assuming that the power outputted by the ice was equal to the heat transported by the eddies, the system could be described by the following equation:
where L is the latent heat of fusion, m is the starting mass of the ice, t is the time it took to melt, ρ is the density of water, cp is heat capacity, and v’ and T’ are the variance in velocity and temperature, respectively. While inaccuracies in the measurements and the fact that we could not place thermometers over the entire tank led to some imprecision, we would still expect the right and left sides of the equation to agree within approximately an order of magnitude. Calculations can be found below:
RHS
LHS
Both sides of the equation are two orders of magnitude off, which is a somewhat surprising result. This discrepancy is for a couple of reasons. We had some delays starting the experiment,which meant that the ice started to melt and the starting mass may have been much less than 988.7 grams. Additionally, the particle tracks show a wobbling effect, most likely due to the table being uneven. In order to determine an average velocity value, we may have overcompensated for this effect, and linearized the curve enough to drastically reduce the variance.
