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From Figure 1.7 the horizontal distance traveled by the fluid as a function of height may be obtained, allowing one to deduce the translational velocity at different levels throughout the fluid. Figure 1.8 shows this analysis:
Figure 1.8:
Throughout figure 1.8 the height and the velocity (fourth column) can be seen, and graphed in figure1.9:
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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 1.9192, 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 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:
this is where the flux is the least.
Using the above plots, we can confirm the thermal wind relationship using the Margulis equation; though solving as displayed in figure 1.91 yields a somewhat unbalanced equation, in the absence of thermistor errors, etc., the fact that the results share the same order of magnitude is enough to lend confidence that the thermal wind balance applies.
Figure 1.91:
Hadley Cells in the Atmosphere
Figure 1.92:
(Please do note that the Transient Heat Flux in Petawatts should not feature a 10^-21 factor; that should be omitted).
Using NCDC's and NCEP's data, the Transient Energy Flux
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. This is shown in figure 1.92.
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.
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