Coriolis Force
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Coriolis Force
I was wondering if anyone could tell me why the Coriolis Force increases in strength so it balances the Pressure Gradient Force for the Geostrophic wind?
I know that it will increase with wind speed and that wind speed increases with latitude (or at least I hope it does from what I've managed to peace together so far), but what if the high pressure was at a higher latitude than the Low pressure then the air flow and speed would decrease with latitude and so the Coriolis Force would decrease as well. Does that mean that you can only get a Geostrophic wind if the high pressure is closer to the equator than the low pressure?
please help
I know that it will increase with wind speed and that wind speed increases with latitude (or at least I hope it does from what I've managed to peace together so far), but what if the high pressure was at a higher latitude than the Low pressure then the air flow and speed would decrease with latitude and so the Coriolis Force would decrease as well. Does that mean that you can only get a Geostrophic wind if the high pressure is closer to the equator than the low pressure?
please help
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avoid cross thinking
The trick to all the more complex area of the meteorology is - Think simple
One thing at the time, in real life all factors come together and complicates the issues so much that not even the most modern supercomputers can keep track of it for more than a very limited period.
For the first question - it is very hard to answer any question with why because the whole theory is just a model to explain what is happening (how). The theory was built on observations of real life and therefore it makes sense that the theory somehow results in something close to reality. The calculations were so to say made up based on the answer. The answer is that if the forces would not equalise, the wind wouldnt follow this pattern (which we know it does) and this theory would not be good enough to appear in the books.
One thing at the time, in real life all factors come together and complicates the issues so much that not even the most modern supercomputers can keep track of it for more than a very limited period.
For the first question - it is very hard to answer any question with why because the whole theory is just a model to explain what is happening (how). The theory was built on observations of real life and therefore it makes sense that the theory somehow results in something close to reality. The calculations were so to say made up based on the answer. The answer is that if the forces would not equalise, the wind wouldnt follow this pattern (which we know it does) and this theory would not be good enough to appear in the books.
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Some more theory
To get from philosophy into something more useful...
The Coriolis force is always proportional to the speed of movement - faster - more coreolis (see it as a reversed g-force when making a turn of same radius in different speeds). A faster wind "turning" to align with a pressure gradient will theoretically need a stronger force than a slow wind to keep "on track". (Remember the force was invented to explain how the wind stays aligned with the isobars.)
It might get stronger in your book because sometimes the explanation of the wind theory starts from stillstand - when the air speeds up the coriolis increases - with the speed. The more important issue is that it also changes direction to aways keep at right angles with the movement - why - because thats how the force is defined. This causes a spiralformed "start" of the wind until it is aligned with the isobars.
With regard to the rest im not completely sure what you mean but i will give it a try.
To get geostrophic wind you need a straight airflow/isobars (otherwise there becomes more forces involved) where the Press Grad F and Coreolis F can equalise. So no friction and no curves otherwise the theory doesnt hold (In either case the wind doesnt follow those rules.)
The speed of the geostrophic wind is dependent on the latitude with stronger winds at low latitude. (Compare two similar pressure gradients on different latitude without any other change. ) Not at the equator though because there doesnt exist geostrophic wind there (how - technically the earth doesnt rotate there it only moves sideways = no coreolis) There still exists wind there but it needs another explanation so it is conveniently named into something else.
In the geostrophic case there is really neither a Low or a High only lower and higher pressure which decides the direction of flow (together with earth rotation)
If you speak about the difference of wind around circular high and low pressure centers we need a more complex solution which includes the forces induced by the turn or to keep circulating around a center. This is not completely geostrophic wind anymore.
To explain this we need one more force or just change the value of any of the other two, for example add a centrifugal force and depending on the direction of turn this force will either add too or subtract from the pressure gradient force. If it is additional this means higher windspeed in the end and vice versa. In the case of air circulating around a high we have an addition (both hemispheres since both the direction of the wind and the direction of earth rotation reverses) this means in practise that around a high pressure center the wind will be stronger compared to a low pressure center with the same pressure gradient and shape. (remember to keep all the other factors constant)
Or more commonly - when the wind turns to the right it increases in speed(northern hemisphere) and to the left decreases.
If you want to combine many factors you need to start calculating but that is not really needed at this stage ;-)
So concentrate on how not why and keep it simple and you will nail the exam.
Have fun
The Coriolis force is always proportional to the speed of movement - faster - more coreolis (see it as a reversed g-force when making a turn of same radius in different speeds). A faster wind "turning" to align with a pressure gradient will theoretically need a stronger force than a slow wind to keep "on track". (Remember the force was invented to explain how the wind stays aligned with the isobars.)
It might get stronger in your book because sometimes the explanation of the wind theory starts from stillstand - when the air speeds up the coriolis increases - with the speed. The more important issue is that it also changes direction to aways keep at right angles with the movement - why - because thats how the force is defined. This causes a spiralformed "start" of the wind until it is aligned with the isobars.
With regard to the rest im not completely sure what you mean but i will give it a try.
To get geostrophic wind you need a straight airflow/isobars (otherwise there becomes more forces involved) where the Press Grad F and Coreolis F can equalise. So no friction and no curves otherwise the theory doesnt hold (In either case the wind doesnt follow those rules.)
The speed of the geostrophic wind is dependent on the latitude with stronger winds at low latitude. (Compare two similar pressure gradients on different latitude without any other change. ) Not at the equator though because there doesnt exist geostrophic wind there (how - technically the earth doesnt rotate there it only moves sideways = no coreolis) There still exists wind there but it needs another explanation so it is conveniently named into something else.
In the geostrophic case there is really neither a Low or a High only lower and higher pressure which decides the direction of flow (together with earth rotation)
If you speak about the difference of wind around circular high and low pressure centers we need a more complex solution which includes the forces induced by the turn or to keep circulating around a center. This is not completely geostrophic wind anymore.
To explain this we need one more force or just change the value of any of the other two, for example add a centrifugal force and depending on the direction of turn this force will either add too or subtract from the pressure gradient force. If it is additional this means higher windspeed in the end and vice versa. In the case of air circulating around a high we have an addition (both hemispheres since both the direction of the wind and the direction of earth rotation reverses) this means in practise that around a high pressure center the wind will be stronger compared to a low pressure center with the same pressure gradient and shape. (remember to keep all the other factors constant)
Or more commonly - when the wind turns to the right it increases in speed(northern hemisphere) and to the left decreases.
If you want to combine many factors you need to start calculating but that is not really needed at this stage ;-)
So concentrate on how not why and keep it simple and you will nail the exam.
Have fun
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Hope this helps:
Under normal circumstances (i.e. if the Earth were not spinning) air would just move from high to low pressure, across the isobars (due to the Pressure Gradient Force, or PGF). The PGF acts at right angles to the isobars, from high to low pressure. Its size depends on the spacing of the isobars and air density.
However, this is only true around the Equator. In the Northern Hemisphere, air actually moves clockwise round a high pressure area and anticlockwise round a low, because the Earth is spinning, and deflects normal air movement (over the ground), until eventually the wind blows along the isobars (instead of across) at around 2,000 feet. Thus, an imaginary force appears to act at right angles to the rotating Earth, causing a moving body to follow a curved path opposite to the direction of the Earth’s rotation.
Not only that, the Earth moves faster at the equator than it does at the Poles (based on a cosine relationship), so, if you fire an artillery shell from the North Pole to the Equator, progressively more of the Earth's surface would pass under its track, giving the illusion of the object curving to the right (or West of A) as it lags behind - the Earth is moving slower towards the North. If you threw whatever it was the other way, it would “move” to the East of B, because you are adding the Earth’s movement at both latitudes. That is, B will be moving slower relative to A. In other words, a bullet might fly in a straight line, but its target will move to the right.
This apparent movement (East or West) is like extra centrifugal force, which is called in some places the Coriolis Effect, but actually is Geostrophic Force when it refers to air movement, although no “force” is involved, hence the use of the word “effect”. That is, the wind at 2,000 feet is assigned a geostrophic property, which is only true when the isobars are straight and parallel. They are actually mostly curved, so the geostrophic wind becomes the gradient wind. The extra energy to keep the air curving comes from the cyclostrophic force, which is similar to centripetal force, as it operates inward, at 90° to the instantaneous motion, to the right in the Northern Hemisphere and the left in the Southern Hemisphere, until it balances the PGF and the wind follows the isobars. Around a low, it is the difference between PGF and GF - around a high, between GF and PGF.
The GF increases with the speed of the air, and it is dependent on the sine of the latitude, being maximum at the Poles (sin 90° = 1) and zero at the Equator.
So, the geostrophic wind is the imaginary wind that would result if the Coriolis and Pressure Gradient forces are balanced. When the air starts to move faster, the geostrophic force is increased and deflection starts again. Coriolis force is directly proportional to wind speed, in that it is zero when the wind is still and at its maximum when the wind is at maximum speed. It is also zero at the Equator and at its maximum at the Poles (meaning that the above relationships break down near the Equator, and isobars cannot be used to represent weather patterns. Streamlines are used instead).
As always, there is a mathematical solution:
GF = 2wrVsinq
where w = the Earth’s rotational velocity, r is density, V is the wind speed and q is the latitude. You can see that, as latitude increases, so will the geostrophic force, or that the wind speed will decrease. To get windspeed, at 2,000 feet, the wind is parallel to the isobars (when they are straight and parallel), meaning that the PGF must be balanced by another force, which we shall call GF. Now all you need to do is swap GF for PGF and play with the formula:
V = PGF
2wrsinq
It also shows that the windspeed increases with height as density reduces, but it all breaks down within about 15° of the Equator, or you would have an infinite windspeed. Given the same pressure gradient at 40°N, 50°N and 60°N, the geostrophic wind speed will be greatest at 40°N.
As you descend, friction with trees, rocks, etc. will slow the wind down by just over 50%, which lessens the geostrophic effect and gives you an effective change of wind direction to the left, so there are two forces acting on air moving from high to low pressure - Coriolis effect which deflects it to the right and frictional effect which brings it back to the left slightly. Over the sea, the geostrophic effect will be less, giving about 10° difference in direction, as opposed to the 30° you can expect over land (the speed reduces to about 70% over water, and 50% over land). If the winds are high, you could get into a stall on landing as you encounter windshear, described later.
The Coriolis effect depends directly on latitude and wind speed. It is greater for stronger winds, ranging from zero at the Equator to a maximum at the Poles.
In any case, wind in a low would be lower than the equivalent geostrophic wind, and higher round a high. In the case of a low in the Northern Hemisphere, the centrifugal force goes in the same direction as the Coriolis force. Since the forces must remain in balance, the Coriolis force weakens to compensate and reduce the overall wind speed (the PGF doesn’t change), so the wind will back, tend to go inwards and contribute towards the lifting effect, since it is forced up, to cause adiabatic cooling, and precipitation.
Inside a high, air movement (winds), will tend to increase with the help of centrifugal force, other things being equal, contributing towards the subsidence and adiabatic warming from compression. However, this is offset by the pressure gradient in a low being much steeper, creating stronger winds anyway. This is known as the isallobaric effect, since lines joining places with an equal rate of change of pressure are isallobars. Centrifugal force helps a low by preventing it being filled, and causes a high to decay by removing mass from it.
According to Professor Buys Ballot's Law (a Dutch meteorologist), if you stand with your back to the wind in the Northern hemisphere, the low pressure will be on your left (on the right in the Southern hemisphere). The implication of this is that, if you fly towards lower pressure, you will drift to starboard as the wind is coming from the left (a common exam question). It's the opposite way round in an anticyclone. Buys Ballot’s Law, by the way, had already been deduced by US meteorologists William Ferrel and James Coffin, but they didn’t get to be famous. Note that it does not always apply to winds that are deflected by local terrain, or local winds such as sea breezes or those that flow down mountains.
Phil
Under normal circumstances (i.e. if the Earth were not spinning) air would just move from high to low pressure, across the isobars (due to the Pressure Gradient Force, or PGF). The PGF acts at right angles to the isobars, from high to low pressure. Its size depends on the spacing of the isobars and air density.
However, this is only true around the Equator. In the Northern Hemisphere, air actually moves clockwise round a high pressure area and anticlockwise round a low, because the Earth is spinning, and deflects normal air movement (over the ground), until eventually the wind blows along the isobars (instead of across) at around 2,000 feet. Thus, an imaginary force appears to act at right angles to the rotating Earth, causing a moving body to follow a curved path opposite to the direction of the Earth’s rotation.
Not only that, the Earth moves faster at the equator than it does at the Poles (based on a cosine relationship), so, if you fire an artillery shell from the North Pole to the Equator, progressively more of the Earth's surface would pass under its track, giving the illusion of the object curving to the right (or West of A) as it lags behind - the Earth is moving slower towards the North. If you threw whatever it was the other way, it would “move” to the East of B, because you are adding the Earth’s movement at both latitudes. That is, B will be moving slower relative to A. In other words, a bullet might fly in a straight line, but its target will move to the right.
This apparent movement (East or West) is like extra centrifugal force, which is called in some places the Coriolis Effect, but actually is Geostrophic Force when it refers to air movement, although no “force” is involved, hence the use of the word “effect”. That is, the wind at 2,000 feet is assigned a geostrophic property, which is only true when the isobars are straight and parallel. They are actually mostly curved, so the geostrophic wind becomes the gradient wind. The extra energy to keep the air curving comes from the cyclostrophic force, which is similar to centripetal force, as it operates inward, at 90° to the instantaneous motion, to the right in the Northern Hemisphere and the left in the Southern Hemisphere, until it balances the PGF and the wind follows the isobars. Around a low, it is the difference between PGF and GF - around a high, between GF and PGF.
The GF increases with the speed of the air, and it is dependent on the sine of the latitude, being maximum at the Poles (sin 90° = 1) and zero at the Equator.
So, the geostrophic wind is the imaginary wind that would result if the Coriolis and Pressure Gradient forces are balanced. When the air starts to move faster, the geostrophic force is increased and deflection starts again. Coriolis force is directly proportional to wind speed, in that it is zero when the wind is still and at its maximum when the wind is at maximum speed. It is also zero at the Equator and at its maximum at the Poles (meaning that the above relationships break down near the Equator, and isobars cannot be used to represent weather patterns. Streamlines are used instead).
As always, there is a mathematical solution:
GF = 2wrVsinq
where w = the Earth’s rotational velocity, r is density, V is the wind speed and q is the latitude. You can see that, as latitude increases, so will the geostrophic force, or that the wind speed will decrease. To get windspeed, at 2,000 feet, the wind is parallel to the isobars (when they are straight and parallel), meaning that the PGF must be balanced by another force, which we shall call GF. Now all you need to do is swap GF for PGF and play with the formula:
V = PGF
2wrsinq
It also shows that the windspeed increases with height as density reduces, but it all breaks down within about 15° of the Equator, or you would have an infinite windspeed. Given the same pressure gradient at 40°N, 50°N and 60°N, the geostrophic wind speed will be greatest at 40°N.
As you descend, friction with trees, rocks, etc. will slow the wind down by just over 50%, which lessens the geostrophic effect and gives you an effective change of wind direction to the left, so there are two forces acting on air moving from high to low pressure - Coriolis effect which deflects it to the right and frictional effect which brings it back to the left slightly. Over the sea, the geostrophic effect will be less, giving about 10° difference in direction, as opposed to the 30° you can expect over land (the speed reduces to about 70% over water, and 50% over land). If the winds are high, you could get into a stall on landing as you encounter windshear, described later.
The Coriolis effect depends directly on latitude and wind speed. It is greater for stronger winds, ranging from zero at the Equator to a maximum at the Poles.
In any case, wind in a low would be lower than the equivalent geostrophic wind, and higher round a high. In the case of a low in the Northern Hemisphere, the centrifugal force goes in the same direction as the Coriolis force. Since the forces must remain in balance, the Coriolis force weakens to compensate and reduce the overall wind speed (the PGF doesn’t change), so the wind will back, tend to go inwards and contribute towards the lifting effect, since it is forced up, to cause adiabatic cooling, and precipitation.
Inside a high, air movement (winds), will tend to increase with the help of centrifugal force, other things being equal, contributing towards the subsidence and adiabatic warming from compression. However, this is offset by the pressure gradient in a low being much steeper, creating stronger winds anyway. This is known as the isallobaric effect, since lines joining places with an equal rate of change of pressure are isallobars. Centrifugal force helps a low by preventing it being filled, and causes a high to decay by removing mass from it.
According to Professor Buys Ballot's Law (a Dutch meteorologist), if you stand with your back to the wind in the Northern hemisphere, the low pressure will be on your left (on the right in the Southern hemisphere). The implication of this is that, if you fly towards lower pressure, you will drift to starboard as the wind is coming from the left (a common exam question). It's the opposite way round in an anticyclone. Buys Ballot’s Law, by the way, had already been deduced by US meteorologists William Ferrel and James Coffin, but they didn’t get to be famous. Note that it does not always apply to winds that are deflected by local terrain, or local winds such as sea breezes or those that flow down mountains.
Phil
