Hurricane Physics
Here are some random notes on Hurricane physics – Don’t ask me why I did this, I just did, OK? (hey, if I want to drive my readership to zero, that’s my business).
1. How might a Hurricane develop? Here is a possible scenario
Ok, let's say a group of thunderstorms develops in the south Atlantic at a latitude high enough for significant ‘spinning’ to occur (caused by the Coriolis force: I attempt to explain this below) , yet low enough to be over nice warm water. The lower airmasses there would be humid and hot, and therefore they rise easily when given a little extra heat. As they rise, they cool, and become saturated with liquid water. When water goes from gas to liquid in the rising air, it releases ‘latent heat’, and the air rises further. Eventually, at very high altitudes, the air cools, loses its water, and becomes dense, and circulates back down, to do it all again - however, all the time, the growing monster is sucking in more and more warm, moist air.
This has to happen over the water, not land, because a large reservoir of warm water is necessary to supply the enormous quantites of heat and moisture. Also, there are other subtle effects of the ocean: its surface provides a low friction plate overwhich high winds can develop, and some atmospheric physicists think that small droplets of seaspray break up turbulent eddies in the air, allowing faster moving winds to develop. These storms weaken considerably when the move over land, and are relieved of their source of heat and moisture.
2. Individ, sounds like an ‘engine’…Yes, this cyclic process acts like an engine (all engines run in cycles), with energy first being input from the heat and gaseous moisture of the ocean, and then transferred to the upper atmosphere. An engine takes in heat, and converts some of that heat into work. Now, the work in this case is pushing the wind around (in your car, the engine's work is pushing the wheels around).
3. Yeah, OK, but why does it SPIN??? As the warm, moist air rises because of its low density, more surface air rushes into the engine at the sides, near the water level. That's when the spinning starts. Why? If you were to view this process from a bird’s eye directly over the North Pole, the entire northern hemisphere would look like a revolving disk, turning from west to east. Points on the disk closer to the equator have higher speeds (in say, miles per hour) than points closer to the pole. So, a wind that blows to the north from the equator starts out with a higher tangential velocity (the red arrow in this pic is “tangential”), than the "land speed" where it ends up. This produces an apparent drift of the wind to its right. For a wind blowing out from the pole toward the developing storm, it’s tangential speed is slower than that of the ground surface farther along its path, so it winds up also deflected to its right. That is, winds that blow into a storm are deflected to the right, or counterclockwise. This induces a circular flow, or vortex. So the spinning of the storm is really a manifestation of the spinning of the Earth on its axis.
4. So, what controls the wind speed? First, let me point out that winds blow from high pressure to low pressure (but the direction s and speed are modified by the spinning of the earth or the storm itself). The updraft, the rising hot, moist air, (similar to the draft in a chimney) creates a low pressure at the center of the storm near its base that draws in air from the sides. As the storm develops into an organized tropical depression, the chimney effect, or draft, becomes stronger, that is, the pressure in the center, or “eye”, continues to drop. As it drops, the wind speed increases. I have my own favorite oversimplified version of the equation that governs wind speed in these situations (yes, that’s right, MATH IS REAL). I am sure the meteorologists will not like this, but here goes. Note: the high wind speeds and rising air masses are in the wall of the eye, not the eye itself, due to centrifugal and other forces that are acting).
5. The force (per unit mass) that causes the wind to accelerate is (1/d)(dP/dx)sinA, which translates to ‘one over’ the density of the air, d, (which is about 1Kg/cubic meter), times the gradient in pressure (that’s calculus, but you can think about the old “rise over run”), times the sine of the Angle, A between the wind direction and the pressure contours.
If that was it, any wind would accelerate to supersonic levels, and we would all die at the slightest hint of a breeze, because an unbalanced force would not produce a contant speed, but a contant acceleration: luckily, wind is opposed by friction; a constant speed, even a high constant speed, implies a balance of forces.
There are lots of ways to formulate this force balance. I will use an old, over-simplied equation that says that the opposing frictional force (per mass) that slows down the wind is given by 0.000002 times the wind speed squared (this accounts for the friction between the water surface and the wind). Solving the two equations by adding them together and setting their sum to zero (i.e., there is a balance of forces, so the net force, or acceleration, is zero), we get for the wind speed, v:
v ~ 2.23 times square root of (156 *sinA* pressure difference/ storm radius).
This equation will give you the speed in mph if you express the pressure difference in millibars and the radius of the storm in miles. For example, if they say the pressure in the eye is 913 millibars, subtract that from standard atmospheric pressure (1013 millibars), and the pressure difference is 100 millibars. Then, I'll use the radius of a big hurricane, 200 miles. If the average angle of the winds is 20 degrees off the isobars (a middle of the road number) , then sinA is about 1/3: so, multiply 100 times 0.33, divide this by 200, take the square root, multiply by 2.23, and you get a wind speed of 145 mph (if you examine the calculation before you multiply by 2.23, the answer you see is v in meters per second: 65). -----this is a very approximate number, because I had to oversimply the equation. (As it is, I am sure that I am being erased from blogrolls by the dozen as you, the three readers I still have left, are reading this). So, take this number with a BIG grain of sea salt. It is meant to show the relationships involved, rather than yield very accurate numbers. I could expand on this, but I will leave it here!
Individ
The lowest pressure recorded in an eye was 888 millibars for Gilbert in 1988, I believe.
technorati: hurricane rita hurricanes
rita
(– Disclaimer – I ain’t a weathaman – Um jus’ a stoopid RedStater who can’t tie his own shoes without a Leftist helpin ‘im - but don’t worry, as with everything I write here, I just copied it off the NRA website, and got a sound bite from Karl Rove - gotta reassure the prejudices and biases of my leftist readership! Otherwise, their narrow minds ex-plode!) "Oh, I - do - NOT - approoove" "where is my NY Times? My Move-on.org...Op-rah?
1. How might a Hurricane develop? Here is a possible scenario
Ok, let's say a group of thunderstorms develops in the south Atlantic at a latitude high enough for significant ‘spinning’ to occur (caused by the Coriolis force: I attempt to explain this below) , yet low enough to be over nice warm water. The lower airmasses there would be humid and hot, and therefore they rise easily when given a little extra heat. As they rise, they cool, and become saturated with liquid water. When water goes from gas to liquid in the rising air, it releases ‘latent heat’, and the air rises further. Eventually, at very high altitudes, the air cools, loses its water, and becomes dense, and circulates back down, to do it all again - however, all the time, the growing monster is sucking in more and more warm, moist air.
This has to happen over the water, not land, because a large reservoir of warm water is necessary to supply the enormous quantites of heat and moisture. Also, there are other subtle effects of the ocean: its surface provides a low friction plate overwhich high winds can develop, and some atmospheric physicists think that small droplets of seaspray break up turbulent eddies in the air, allowing faster moving winds to develop. These storms weaken considerably when the move over land, and are relieved of their source of heat and moisture.
2. Individ, sounds like an ‘engine’…Yes, this cyclic process acts like an engine (all engines run in cycles), with energy first being input from the heat and gaseous moisture of the ocean, and then transferred to the upper atmosphere. An engine takes in heat, and converts some of that heat into work. Now, the work in this case is pushing the wind around (in your car, the engine's work is pushing the wheels around).
3. Yeah, OK, but why does it SPIN??? As the warm, moist air rises because of its low density, more surface air rushes into the engine at the sides, near the water level. That's when the spinning starts. Why? If you were to view this process from a bird’s eye directly over the North Pole, the entire northern hemisphere would look like a revolving disk, turning from west to east. Points on the disk closer to the equator have higher speeds (in say, miles per hour) than points closer to the pole. So, a wind that blows to the north from the equator starts out with a higher tangential velocity (the red arrow in this pic is “tangential”), than the "land speed" where it ends up. This produces an apparent drift of the wind to its right. For a wind blowing out from the pole toward the developing storm, it’s tangential speed is slower than that of the ground surface farther along its path, so it winds up also deflected to its right. That is, winds that blow into a storm are deflected to the right, or counterclockwise. This induces a circular flow, or vortex. So the spinning of the storm is really a manifestation of the spinning of the Earth on its axis.
4. So, what controls the wind speed? First, let me point out that winds blow from high pressure to low pressure (but the direction s and speed are modified by the spinning of the earth or the storm itself). The updraft, the rising hot, moist air, (similar to the draft in a chimney) creates a low pressure at the center of the storm near its base that draws in air from the sides. As the storm develops into an organized tropical depression, the chimney effect, or draft, becomes stronger, that is, the pressure in the center, or “eye”, continues to drop. As it drops, the wind speed increases. I have my own favorite oversimplified version of the equation that governs wind speed in these situations (yes, that’s right, MATH IS REAL). I am sure the meteorologists will not like this, but here goes. Note: the high wind speeds and rising air masses are in the wall of the eye, not the eye itself, due to centrifugal and other forces that are acting).
5. The force (per unit mass) that causes the wind to accelerate is (1/d)(dP/dx)sinA, which translates to ‘one over’ the density of the air, d, (which is about 1Kg/cubic meter), times the gradient in pressure (that’s calculus, but you can think about the old “rise over run”), times the sine of the Angle, A between the wind direction and the pressure contours.
If that was it, any wind would accelerate to supersonic levels, and we would all die at the slightest hint of a breeze, because an unbalanced force would not produce a contant speed, but a contant acceleration: luckily, wind is opposed by friction; a constant speed, even a high constant speed, implies a balance of forces.
There are lots of ways to formulate this force balance. I will use an old, over-simplied equation that says that the opposing frictional force (per mass) that slows down the wind is given by 0.000002 times the wind speed squared (this accounts for the friction between the water surface and the wind). Solving the two equations by adding them together and setting their sum to zero (i.e., there is a balance of forces, so the net force, or acceleration, is zero), we get for the wind speed, v:
v ~ 2.23 times square root of (156 *sinA* pressure difference/ storm radius).
This equation will give you the speed in mph if you express the pressure difference in millibars and the radius of the storm in miles. For example, if they say the pressure in the eye is 913 millibars, subtract that from standard atmospheric pressure (1013 millibars), and the pressure difference is 100 millibars. Then, I'll use the radius of a big hurricane, 200 miles. If the average angle of the winds is 20 degrees off the isobars (a middle of the road number) , then sinA is about 1/3: so, multiply 100 times 0.33, divide this by 200, take the square root, multiply by 2.23, and you get a wind speed of 145 mph (if you examine the calculation before you multiply by 2.23, the answer you see is v in meters per second: 65). -----this is a very approximate number, because I had to oversimply the equation. (As it is, I am sure that I am being erased from blogrolls by the dozen as you, the three readers I still have left, are reading this). So, take this number with a BIG grain of sea salt. It is meant to show the relationships involved, rather than yield very accurate numbers. I could expand on this, but I will leave it here!
Individ
The lowest pressure recorded in an eye was 888 millibars for Gilbert in 1988, I believe.
technorati: hurricane rita hurricanes
rita
(– Disclaimer – I ain’t a weathaman – Um jus’ a stoopid RedStater who can’t tie his own shoes without a Leftist helpin ‘im - but don’t worry, as with everything I write here, I just copied it off the NRA website, and got a sound bite from Karl Rove - gotta reassure the prejudices and biases of my leftist readership! Otherwise, their narrow minds ex-plode!) "Oh, I - do - NOT - approoove" "where is my NY Times? My Move-on.org...Op-rah?
posted by individ at 10:06 AM
<< Home