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As expected, the velocity begins negative, or directed radially outwards, becoming neutral with height and eventually positive; as one moves towards the vertical extremities of the tank, the maximum positive and negative velocities are found. This is exactly what is to be expected in the Hadley cell. Towards the base of the tank, a weak easterly due to subjecting and "unwinding" fluid and associated frictional drag due to contact with the container's base. Meanwhile, a much stronger westerly developed further up in the tank as water moving towards the center gained zonal velocity due to the conservation of angular momentum.
Hadley Cells in the Atmosphere
//Under Development
One may notice here that the maximum westerly is not found at the maximum in height. Instead, the maximum westerly wind occurs just below the surface of the water. This is similar to the manner by which the atmosphere behaves; the maximum thermal flux, according to figure 1.91, is visible not at 1000 millibars, but rather at 850 millibars slightly aloft in the atmosphere. In fact, 1000 millibars is home to the least thermal flux. In fact, 1000 is the location of the least thermal flux towards the poles. This is a direct result of the behavior of Hadley cells; despite a net positive flux towards the poles, as is necessary,
Hadley Cells in the Atmosphere
Figure 1.95:
Using NCDC's and NCEP's data, the Transient Energy Flux across different levels of the atmosphere in January can be plotted with relative ease. As previously mentioned, the Coriolis parameter of the earth only supports a regime of Hadley cell occurrence between 0 and 30º on either side of the equator. As such, the remainder of the globe is dominated by eddy heat transport, which will be detailed later. However, in plotting the heat flux across different levels of the atmosphere (where positive flux describes heat carried northwards), one may confirm the existence of Hadley cells is this region.
Because January features winter in the northern hemisphere, a stronger temperature gradient leads to a more significant poleward heat transport than in the southern hemisphere. This is evident in our findings, given that the peak at northern latitudes in flux is far greater than in southern latitudes. The Hadley cell theory is also supported by the weak positive flux at the surface (1000 millibars) between 0º and 30º north. This is because there is a weak easterly with a slightly northerly component as air returns radially towards the equator; theoretically, there could be negative flux, but some "mixing" of northerly winds likely aids in some weak northerly flow near the surface. The majority of the heat transport occurs aloft, but the heat flux which measures the amount of heat transport at various levels, should be directly proportional to height (for obvious reasons described previously under the theory of Hadley cells) and pressure (as denser air can carry more heat per unit area). Therefore, the location of the "maximum" should be the "happy medium" between height and pressure, which we would estimate to be located around 700-850 millibars, as revealed by the graph. This is coincident with the jet stream, which is essentially the a narrow band of intense westerlies. In addition, the rising air characteristic of the Intertropical Convergence Zone at the equator is tempered by a weak high pressure dome aloft, which can be seen in the extremely weak flux towards the equator at the uppermost levels of the atmosphere. In addition, it was previously mentioned that friction with the surface would reduce the flux close to the ground, which is supported by the lower level of flux at the 1000 millibar level.
// Magical Theory and Stuff
//Verification of Thermal Wind Equation
Eddy Heat Transport in the Tank
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One item of note in figure 2.1 is that the temperature at each sensor, though subject to slight oscillations due to eddies, slowly decrease with time somewhat uniformly throughout the fluid. This is to be expected, as the thermal energy contained within the relatively warmer is transferred and over time reduced as it in turn warms the ice to above melting point. Thus, though the temperature of the ice/water solution remains at 32 degrees, the increased thermal energy is instead utilized in the form of latent heat, responsible for the change in phase of the liquid. As such, the amount of energy needed to fully melt the block of ice placed in the center should be equal to product of the ice's mass and the specific heat of fusion. Therefore, considering that 771.4 grams of ice were used in the experiment, one would anticipate that roughly 258,000 Joules of energy would be necessary complete this thermal transaction. Spread over a period of approximately 4,000 seconds, the result is in effect the energy required to power a 64-Watt light bulb, and may be practically thought of as a "negative light bulb" placed in the center of the tank according to Dr. John Marshall.