In order to understand how powerful and potentially damaging a vortex in earth’s atmosphere may be, we must understand the mechanisms that the drive the damaging wind speeds. In 12.307, we learned how movement of fluid on a rotating frame is different than movement of that fluid on a non rotating frame.
First we look at how hurricanes are created and sustained. Hurricanes unfold over low pressure regions of water with warm temperatures. The moisture formed from the evaporation of this warm water is what continues to fuel this cyclcone. Studies suggest that there is a minimum requirement of water temperature to be 26 degrees Celcius for devlopment of a cyclone. Once a cyclone has been formed, the sea surface temperature can account for a portion of the fluctuation that is correlated with the intensification of the storm. In Sarah's portion of our project, we see that hurricanes are weakened upon approaching land due to the lack of supply of moisture and the terrian's friction. In theory, dampening of the cyclone's wrath can occur when it reaches areas of colder waters and strong winds opposing it's path.
Experiment
In this lab experiment, we analyzed a supply of heat can drive the motion of vortices.The materials we used for this experiment were a tank of fluid, heating pad and a camera (from above in the rotating frame and on the side). We used a camera on the side to track the height at which these plumes (that we hoped to see!) reached to the surface of the water.
We set up a rectangular tank of water with a heating pad at the bottom delivering a constant source of 1620 W over the area of 6148 m2. We filled the tank so that the depth of the fluid is .46m. The rotation rate of the tank was 2 radians per second.
If there are plumes present, we would like to see if there have their own spriraling motion. By analyzing the upward velocity of these plumes and the rotation rate of the tank, we can calculate a local Rossby Number that will meaningful information about how strong vortices form on the rotating earth.
Figure 1: Above shows an image of the tank when the potassium permangenate was initially dropped in.
Figure 2: Above shows an image of the tank when the potassium permanganate had reached the top surface. We can see the coloring at the top has a pinkish tint. We observe that the potassium permangante has spread into seperate plumes throughout the tank.
Theory
The buoyancy of a fluid is equal to :
Here the represents the difference in density between that of the “plume” and that of the ambient fluid. In our tank experiment, both the plume and the fluid are pure water.
Here the heating from the bottom we expect to cause mini regions of low pressure sections, that would lead to the creations of plumes. If the parcel is positively buoyant, it is "light" compared to it's surroundings and will rise.
In order to calculate how much heat is being transported vertically from these plumes, we must find it's heat flux.
The heat content of a fluid is defined as:
Here, cp is the specific heat of water. In our tank, we know the heat flux because we can read it on the heating pad. If we did not know it we would calcualte this by using a reference density and the change in temperature the tank before and after the experiment had been done.
Below, we will use the buoyancy flux which is proportional to the heat flux to get an understanding of the nature of these convecting plumes.
Results
We dropped potassium permangante into the tank at 1 minute and 28 seconds and watched the evolution of the plume. It took roughly 144 seconds for the potassium permangenate to reach the top of the tank. Since the height of the tank was .46 meters, the vertical velocity of the plumes was .00319m/s.
Figure 3: Above are the constants and values that we are using in order to solve for relationships between the Buoyancy Flux, radius of a rotational plume and then local Rossby Number.
Figure 4: Above show the following calculations: (1) the buoyany flux - 5.3x10^-6 m^2/s^2 (2) rotational radius of a plume 2.8x10 -4 m (3) local Rossby number - 6.29x10^-4
The first relationship proves that the buoyancy flux, B, is proportional to the heat flux, H. Thus, as the heat flux increases, holding the density of the fluid constant, the bouyancy flux also increases.
The next equation solves for Lrot, which is the a length scale. We can see from the equation, that in theory the radius should increase as the heat flux, H, increases and would decrease as the rotational rate decreases. The derivtive of this value is the velocity of a particle that is moving in circles with a radius of Lrot. This is in theory makes sense when applied to our atmosphere. Near the equator and tropics, rotational rates are lower, thus the Coriolis parameter, f, is smaller. We observe many more strong hurricanes in the tropics where there is a lower rotational rate and higher temperatures of water.
We also calculated a very small Rossby number, thus implying that the rotational rate of the tank (or relative rotational rate of earth) is important on the trajectory. In our observations, we saw that the vertical velocity of the plumes seemed unneffected by the rotation rate. Perhaps, a pressure drag force can cause a change in the acceleration of a plume due to the buoyancy force. It is interesting that all of the external parameters, (ex: rotational rate and heat flux), lead to a description of plumes which has an intensity very dependent on the constant rotation rate.
In our tank we only used one fluid, water. In the atmsophere, the interaction between the air and the amount of water it holds and interacts with is impertative to understanding the mechanisms of a cyclone.
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Hurricane Tank Experiment
Background
In order to understand how powerful and potentially damaging a vortex in earth’s atmosphere may be, we must understand the mechanisms that the drive the damaging wind speeds. In 12.307, we learned how movement of fluid on a rotating frame is different than movement of that fluid on a non rotating frame.
First we look at how hurricanes are created and sustained. Hurricanes unfold over low pressure regions of water with warm temperatures. The moisture formed from the evaporation of this warm water is what continues to fuel this cyclcone. Studies suggest that there is a minimum requirement of water temperature to be 26 degrees Celcius for devlopment of a cyclone. Once a cyclone has been formed, the sea surface temperature can account for a portion of the fluctuation that is correlated with the intensification of the storm. In Sarah's portion of our project, we see that hurricanes are weakened upon approaching land due to the lack of supply of moisture and the terrian's friction. In theory, dampening of the cyclone's wrath can occur when it reaches areas of colder waters and strong winds opposing it's path.
Experiment
In this lab experiment, we analyzed a supply of heat can drive the motion of vortices. The materials we used for this experiment were a tank of fluid, heating pad and a camera (from above in the rotating frame and on the side). We used a camera on the side to track the height at which these plumes (that we hoped to see!) reached to the surface of the water.
We set up a rectangular tank of water with a heating pad at the bottom delivering a constant source of 1620 W over the area of 6148 m2. We filled the tank so that the depth of the fluid is .46m. The rotation rate of the tank was 2 radians per second.
If there are plumes present, we would like to see if there have their own spriraling motion. By analyzing the upward velocity of these plumes and the rotation rate of the tank, we can calculate a local Rossby Number that will meaningful information about how strong vortices form on the rotating earth.
Figure 1: Above shows an image of the tank when the potassium permangenate was initially dropped in.
Figure 2: Above shows an image of the tank when the potassium permanganate had reached the top surface. We can see the coloring at the top has a pinkish tint. We observe that the potassium permangante has spread into seperate plumes throughout the tank.
Theory
The buoyancy of a fluid is equal to :
Here the represents the difference in density between that of the “plume” and that of the ambient fluid. In our tank experiment, both the plume and the fluid are pure water.
Here the heating from the bottom we expect to cause mini regions of low pressure sections, that would lead to the creations of plumes. If the parcel is positively buoyant, it is "light" compared to it's surroundings and will rise.
In order to calculate how much heat is being transported vertically from these plumes, we must find it's heat flux.
The heat content of a fluid is defined as:
Here, cp is the specific heat of water. In our tank, we know the heat flux because we can read it on the heating pad. If we did not know it we would calcualte this by using a reference density and the change in temperature the tank before and after the experiment had been done.
Below, we will use the buoyancy flux which is proportional to the heat flux to get an understanding of the nature of these convecting plumes.
Results
We dropped potassium permangante into the tank at 1 minute and 28 seconds and watched the evolution of the plume. It took roughly 144 seconds for the potassium permangenate to reach the top of the tank. Since the height of the tank was .46 meters, the vertical velocity of the plumes was .00319m/s.
Figure 3: Above are the constants and values that we are using in order to solve for relationships between the Buoyancy Flux, radius of a rotational plume and then local Rossby Number.
Figure 4: Above show the following calculations: (1) the buoyany flux - 5.3x10^-6 m^2/s^2 (2) rotational radius of a plume 2.8x10 -4 m (3) local Rossby number - 6.29x10^-4
The first relationship proves that the buoyancy flux, B, is proportional to the heat flux, H. Thus, as the heat flux increases, holding the density of the fluid constant, the bouyancy flux also increases.
The next equation solves for Lrot, which is the a length scale. We can see from the equation, that in theory the radius should increase as the heat flux, H, increases and would decrease as the rotational rate decreases. The derivtive of this value is the velocity of a particle that is moving in circles with a radius of Lrot. This is in theory makes sense when applied to our atmosphere. Near the equator and tropics, rotational rates are lower, thus the Coriolis parameter, f, is smaller. We observe many more strong hurricanes in the tropics where there is a lower rotational rate and higher temperatures of water.
We also calculated a very small Rossby number, thus implying that the rotational rate of the tank (or relative rotational rate of earth) is important on the trajectory. In our observations, we saw that the vertical velocity of the plumes seemed unneffected by the rotation rate. Perhaps, a pressure drag force can cause a change in the acceleration of a plume due to the buoyancy force. It is interesting that all of the external parameters, (ex: rotational rate and heat flux), lead to a description of plumes which has an intensity very dependent on the constant rotation rate.
In our tank we only used one fluid, water. In the atmsophere, the interaction between the air and the amount of water it holds and interacts with is impertative to understanding the mechanisms of a cyclone.
https://www.weather.gov/source/zhu/ZHU_Training_Page/tropical_stuff/hurricane_anatomy/hurricane_anatomy.html
http://www.hurricanescience.org/science/science/hurricanedecay/
http://curry.eas.gatech.edu/Courses/6140/ency/Chapter11/Ency_Atmos/Hurricanes.pdf
https://journals.ametsoc.org/doi/pdf/10.1175/1520-0485%281993%29023%3C1009%3ACWRIAN%3E2.0.CO%3B2