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The temperature data from the thermometers revealed that an overall trend of decreasing temperature in the tank, as a result of the melting of the ice. The sensors at the bottom of the tank maintained a near-constant radial temperature over time, of about 4ºC. The temperatures higher up in the tank evolved differently however. The sensor on the edge of the tank measured a high temperature of about 21.2 ºC throughout the experiment, and the one on the ice bucket, gave a reading higher than all but the furthest sensor from the ice bucket at the bottom. These high temperatures are a result of the overturning circulation seen in the non-rotating case as well. Cold water near the ice bucket sinks and spreads along the bottom, leaving the surface water much warmer than that below.
Discretizing the equation for thermal wind and solving for u gives
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(Marshall & Plumb, 2008)
Tank Experiment
The second experiment was, in contrast, performed at the faster rotation speed of 10 rpm in order to replicate the regime in 30N – 60N and 30S – 60S.
Similarly, to the first tank experiment, the particle tracker and thermometers were used to monitor the circulation and temperature in the tank.
For the temperature profiles of each sensor, we found a periodic trend of temperature, which corresponds to the observed circulation pattern: circulating from the inner part to the outer part and vice versa
To verify the assumption that Eddy circulation plays role in transferring heat, we expect the calculated heat flux from the melt ice to be in the same magnitude as the heat flux from Eddy circulation.
We filled out parameters to the following equation.
Red dye dropped near the edges and blue dye dropped near the ice bucket eventually swirled together, creating the beautiful image below. The dye helps illustrate the transport of heat through the bucket. Warm water from the outside is moved radially inwards and cold water at the center is moved radially outwards, in non-axisymmetric vortices around the tank.
Similarly, to the first tank experiment, the particle tracker and thermometers were used to monitor the circulation and temperature in the tank. Below are plotted several particle tracks. The particles clearly do not follow the same regular, axi-symmetric motion as in the Hadley experiment.
For the temperature profiles of each sensor, we found a periodic trend of temperature, which corresponds to the observed circulation pattern: circulating from the inner part to the outer part and vice versa
To verify the assumption that Eddy circulation plays role in transferring heat, we expect the calculated heat flux from the melt ice to be in the same magnitude as the heat flux from Eddy circulation.
We filled out parameters to the following equation.
z = 0.15 z = 0.15 m
T’ = 1 K
ρ = 1000 kg/ m^3
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From the comparison of ice heat flux and calculated Eddy heat transport, we found that they were in almost the same magnitude—suggesting the relationship among them.
Atmospheric Data
While atmospheric mean data could be used to study the Hadley circulation, eddies are shorter timescale phenomena and are calculated through deviations from the mean.
Eddies are apparent in atmospheric potential temperature fields. The image below shows the potential temperature of the 850 mbar surface over the North Pole for a day in the winter. The swirls of the eddies between red and blue regions are particularly visible over the Pacific Ocean.
("Potential Temperature Loop", n.d.)
While atmospheric mean data could be used to study the Hadley circulation, eddies are shorter timescale phenomena and are calculated through deviations from the mean.
We were given data of We were given data of v’t’ - the heat flux from the mean deviations for all latitudes, longitudes, and heights up to 100 mbar in the atmosphere. Looking at the vertical average of the deviations in January, we see particularly strong northward flux in regions 40ºN, over the Pacific and Atlantic Oceans. As the mean data revealed, the Hadley cell descends near 30º, with little There are also similar, though not nearly as strong, negative deviations around 40ºS as well. The values here are negative because they imply transport to the South Pole from the equator, and are not quite as large as those in the Northern Hemisphere due at least in part to the fact that the temperature gradient is larger in the northern hemisphere January, when it is winter there.
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Finally, averaging both vertically and zonally gives the total northward flux at each latitude. Again, peaks occur just past 40 N and S. The peak in the Southern Hemisphere is very regular, while that in the northern hemisphere drops off less quickly at high latitudes. This lack of symmetry is likely a result of the fact that the majority of the continental land mass is located in the northern hemisphere, and the uneven surface leads to further atmospheric instabilities and eddies.
It is also useful to change the units of heat flux to Watts in order to compare our findings to the total energy flux of the earth. To do so, we vertically integrate our v’T’ zonal average and insert it into the following equation for energy flux:
where a is the radius of the earth, ɸ is the latitude, Cp is the specific heat of air, g is gravitational acceleration. For a latitude of 40ºN, the equation gives a maximum energy flux of 1.1 PW (10^15 Watts).
Comparing this figure to the graph of total energy flux in the atmosphere (the first figure in the eddy section), we can see that it is on the same order of magnitude as the total transport of 5.5 PW at 40ºN; from our numbers, eddy transport would constitute 20% of the total at this latitude. This number seems slightly low however, considering that eddies are the predominant transport mechanism in mid-high latitudes. Our data has been filtered somewhat, to only account for the eddies that exist on timescales on the order of a week, but some eddies last only a couple days. There are also stationary eddies that remain relatively constant over several months. These are especially prominent in the Northern Hemisphere during the wintertime.
We can compare the results here to those summarized by Peixoto and Oort in their book, Physics of Climate. The figure below shows the total northward flux of sensible heat (not including latent heat), with breakdowns for transient eddies, stationary eddies, and mean meridional circulation. The units here are in K m/s the original units of our calculations, and winter (thin), summer (dashed) and yearly averages (thick) are plotted for each. The review here found a maximum transport for transient eddies of about 8 K m/s, twice as much as our calculations.
(Peixoto & Oort, 1992)
One potential contributing factor to the discrepancy is that our data has been filtered somewhat, to only account for the eddies that exist on timescales on the order of a week, but some eddies last only a couple days. There are also stationary eddies that remain relatively constant over several months, plotted in the Peixoto and Oort graph. These are especially prominent in the Northern Hemisphere during the wintertime, accounting for another 12 K m/s at 40N. Since our calculations were performed for the month of January, we can expect that the missing stationary eddy flux, if included, would improve the comparison.
The mean meridional circulation, or Hadley circulation, is also plotted, and provides a maximum of over 30 K m/s near 10ºN and S. This circulation has a much smaller effect at high latitudes however, as our mean data also showed.
It is also useful to change the units of heat flux to Watts in order to compare our findings to the total energy flux of the earth. To do so, we vertically integrate our v’T’ zonal average and insert it into the following equation for energy flux:
where a is the radius of the earth, ɸ is the latitude, Cp is the specific heat of air, g is gravitational acceleration. For a latitude of 40ºN, the equation gives a maximum energy flux of 1.1 PW (10^15 Watts).
This can be compared to the image below, of the total northward energy flux in the atmosphere. The ocean contributes an important part of the heat flux at low latitudes, but beyond 40N and S its transport becomes insignificant. The atmosphere
(Marshall & Plumb, 2008)
Comparing this graph to our results, we can see that it is on the same order of magnitude as the total transport of 5.5 PW at 40ºN; from our numbers, eddy transport would constitute 20% of the total at this latitude. Our results seem slightly low again however, considering that eddies are a predominant transport mechanism in mid-high latitudes. Factoring in the transient eddies and data filtration would bring us closer to the 5.5 PW, but not nearly there. The other significant method of energy transport is through latent heat, which is included in the total energy flux graph but not in our calculationsThe figure below shows the total northward flux of sensible heat (not including latent heat), with breakdowns for transient eddies, stationary eddies, and mean meridional circulation. The units here are in K m/s the original units of our calculations, and winter (thin), summer (dashed) and yearly averages (thick) are plotted for each. The review here found a maximum transport for transient eddies of about 8 K m/s, twice as much as our calculations. Stationary eddies account for another 12 K m/s in the winter in the northern hemisphere, but disappear in the summertime. The mean meridional circulation, or Hadley circulation, is also plotted, and provides a maximum of over 30 K m/s near 10ºN and S. This circulation has a much smaller effect at high latitudes however, as our mean data also showed. One other significant source of energy transport is through latent heat, a topic not discussed in this project, but important to mention. Water that evaporates near the equator and is lifted and transported poleward transported pole-ward condenses, releasing latent heat and further warming the higher high latitudes.
(Peixoto & Oort, 1992)
Including this term would likely account for most of the remaining discrepancy.
Bibliography:
Illari, L., & Marshall, J. (2010). 12.307 Project 4 General Circulation. Retrieved from http://paoc.mit.edu.ezproxyberklee.flo.org/12307/gencirc/climatology_lab.pdf
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Peixoto, J.P., and A.H. Oort. (1992). Physics of Climate. United States: New York, NY (United States); American Institute of Physics.
"Potential Temperature Loop." n.d. Retrieved from http://paoc.mit.edu.ezproxyberklee.flo.org/labguide/images_new/850mbPotTempLOOP.gif
