...
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.
Atmospheric Data
To find the zonally and vertically integrated transient energy flux, we first started by plotting the transient heat flux in January and July at specific pressure levels. The transient heat flux in January and July at 850mb near the surface are shown below:
Image AddedWe next plotted the vertically averaged transient heat flux as shown below.
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We can notice a couple interesting things from these plots. In the January when the Northern Hemisphere is experiencing winter, we see two clear maximums of Northward heat flux. These could be because the temperature gradient is strongest during the winter. The maximums are located on coasts where there are strong land-sea interactions. The combination of the stronger gradient and land-sea interaction could result in more synoptic scale storms and more eddies, resulting in stronger heat flux in those regions. In July when the Northern Hemisphere is experiencing summer, we observe that the northward heat flux is stronger overall in the Northern Hemisphere as well as more uniform. In both January and July, we see strong southward heat flux in the Southern Hemisphere.
We next plotted the zonally averaged transient heat flux, averaged over the longitudes following:
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These two plots again show poleward heat flux in both hemispheres. Both plots also show two maximums of heat flux, one at a higher and one at a lower altitude. Maximums in heat flux can be caused by either differences in velocity or in temperature. Higher in the atmosphere, the heat flux maximum could be driven by the strong velocity difference around the fast polar jet. Lower in the atmosphere, the heat flux maximum could be caused by the difference in temperature between the land and ocean.
Finally, we vertically integrate the zonally averaged transient heat flux and multiply by some constants to find the zonally and vertically integrated transient sensible energy flux using:
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The maximum energy flux away is approximately 1PW and found around 40ºN and 40ºS because the eddy heat transport carries heat from the midlatitudes to the poles. The maximum energy flux from the atmosphere is actually about 4 PW in both North and South directions from around 40ºN and 40ºS. There is a discrepancy because we only calculated the sensible heat energy flux, neglecting the contributions from latent heat energy and potential energy that contribute to the 4PW plot.
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:
Image Modified 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 . Unfortunately, we had difficulties calculating v', so we used .6 mm/s, the value cited on the PAOC website in our calculations (http://paoc.mit.edu.ezproxyberklee.flo.org/labguide/circ_exp_fast.html). 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
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Image AddedThe two Both sides of the equation are two orders of magnitude offoff by a factor of three, which is a somewhat surprising result. This discrepancy is for close enough agreement to confirm that the relation holds. The discrepancy may be due to a couple of reasonsfactors. 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 variancevelocity variance value was taken from a different experiment, so it's likely somewhat off from the value we would expect in our experiment.
