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Particles moving pole-ward experience an increase in velocity because of the conservation of angular momentum. In Figure 2, there is a strip of air with velocity u and radius r. If this strip of air were to move upward, the radius would decrease and, in order to maintain angular momentum, the velocity would have to increase.
When air moving pole-ward gets to about 30°, the speed of particles gets to be too fast, and the strip of air becomes unstable, leading to a wavering strip of air as shown in Figure 1. Wind beyond this point to about 60° is very chaotic and unpredictable. The overturning circulation from the equator to around 30° is Hadley circulation, and the chaotic motion is eddy circulation. From this point on, the focus is on Hadley circulation.
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A key characteristic of Hadley circulation is that it is only maintained when velocity is slow. As velocity of air becomes too fast, eddies start to form. In order to simulate Hadley circulation, the rotation rate of a tank of water must be very slow (about 1 revolution per minute); the precise speed was 62 seconds per rotation. The tank was 44 cm in diameter and was filled with 29°C water to a depth of 9 cm. At the center of the tank was a canister, 13 cm in diameter, filled with ice, which was meant to represent one of the Earth’s poles. More specifically, the canister was filled with 415.7 grams of ice, and enough melted ice so that the water level in the canister was also at 9 cm. There were eight temperature sensors total (two sets of four sensors, at 90° apart): 2 on the side of the canister, 2 on the base of the tank at about 2 cm from the edge of the canister, 2 on the base of the tank at 10 cm from the edge of the canister, and 2 on the outer rim of the tank.
Before starting the experiment, the tank of warm water was rotated at about 1 rpm until reaching solid body rotation, which took about 20 minutes. Upon reaching solid body rotation, the ice was placed into the canister, at which point Hadley-like circulation began.
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There was sinking of water around the cold canister, outward motion at the base of the tank, rising motion at the rim, and a return flow in shallow water. Figure 12 shows the movement of permanganate, which is a substance that sinks in water. As can be seen, the permanganate moves away from the tank, thus revealing the outward movement of water at the base of the tank.
The overturning circulation described was not the only type of movement observed. In fact overturning circulation such as this would happen in a completely stationary tank. The more interesting observation, from the experiment, shown in Figure 13, was that a dome of cold air formed around the central canister.
Two simultaneous processes happened to cause this cone to form. There was clockwise sinking of cold water, that moved outward as it descended. Additionally, there was anticlockwise inward rising of warm water. The anticlockwise motion of warm water was in the same direction as the tank’s rotation. In Hadley circulation, westerlies are in the same direction as Earth’s rotation; hence, the anticlockwise motion represents the westerlies. The clockwise motion associated with sinking cold water is similar to the atmospheric easteries.
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In Figure 13, the temperatures of the different sensors are plotted.
The coldest temperatures were seen at the base of the tank close to the canister. Water sinks near the center and then flows across the bottom of the tank. As such, the sensors at this location will record very cold temperatures. The water along the base but closer to the edge of the tank will be slightly warmer as the cold water interacts with surrounding water, and warms. As water reaches the edge of the tank, it is warmer than the water closer to the tank, and it gets pushed upward. As such the sensors at the outer edge of the tank record the warmest temperatures. Lastly, water will move toward the center of the tank and then sink again, repeating the cycle. As it reaches the ice, the water will sink and cool. The sensors along the canister do not record temperatures as cold as along the base because the water cools significantly before reaching the base of the tank.
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Below (Figure 15) is the trajectory of paper dots that were placed into the rotating tank. The bottom right side of the figure lacks tracks because the sensors were there preventing the particle tracker from seeing the paper dots.
Although none of the tracks made a full circle, it is clear by comparing the radii in each track that the majority of the particles are spiraling inward. Figure 16 shows the angular velocities (in centimeters/second) associated with the inward particle tracks in Figure 15.
The figure reveals a general trend of increasing angular velocity with decreasing radius. Some negative velocities can be seen for the particles that are toward the edge of the tank, and this is because of the slow speed with which they were traveling. When there is little motion of particles, the tracker may locate the particle a pixel or two off in the wrong direction, thus leading to negative velocities. If this experiment were performed in a bigger tank, or if there was a more accurate way to track the particles, negative velocities as observed in this experiment would likely be less common.
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