Thu., Nov. 8 notes

Thursday Nov. 8, 2007

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The Quiz #4 Study Guide has made an early appearance on the class web page. The study guide isn't complete, material will be added once it is covered in class.

We covered the pressure gradient force last Tuesday but didn't have time to give the Coriolis force (CF) the full attention it deserves. It is confusing, don't worry too much if you don't understand what causes it. You'll learn some simple rules that will allow you to determine the direction and strength of the CF.

You'll find the figure above on p. 122c in the photocopied Class Notes. Imagine an object of some kind flies over Tucson. It travels straight from west to east at constant speed. The next figure shows the path that the object followed relative to the ground as it passed over the city.

The moving object appeared to be moving in a straight line at constant speed. You would conclude that there was zero net force acting on the object.

In this second picture the object flies by overhead just as it did in the previous picture. In this picture, however, the ground is moving (don't worry about what might be causing the ground to move).

This is the path that you would see relative to the ground in this case. Even though the object flew from west to east it appears to have been traveling from the NW toward the SE because the ground was moving as the object passed overhead. Because the motion is still in a straight line at constant speed, you would conclude the net force acting on the object was zero.

At most locations on the earth the ground is not just moving but rotating or spinning. This is most easily seen at the poles.

Imagine a piece of paper glued to the top of a globe. As the globe spins the piece of paper will rotate. A piece of paper glued to the globe at the equator won't spin, it will flip over. At points in between the paper would spin and flip, the motion gets complicated.

In this last figure the object flies by again from west to east. In this case however the ground is rotating. The path that the moving object would appear to follow relative to the ground is shown below:

Now the object appears to have been turning to the right as it passed over Tucson. Because it is no longer traveling in a straight line you would conclude there was a net force acting on the object. The direction of this net force would be to the right of the motion.

The easiest thing for us to do is to ignore the fact that the ground on which we are standing is rotating (it's not something we are really aware of anyway). However, if we do that we need to account for the curved paths that moving objects will take when they move relative to the earth's surface. That is what the Coriolis force does.

Here are some rules that you can use to determine the direction and strength of the Coriolis force (whether you understand what causes it or not). It always points in a direction that is perpendicular to the wind, it can't cause the wind to speed up or slow down, it will only change the wind's direction.

Here are some examples of winds in the northern and southern hemispheres (NH and SH in the figure). The red arrows show the direction of the CF. The CF is to the right of the wind (you need to look in the direction the wind is blowing, you need to look downstream) in the northern hemisphere and to the left of the wind in the southern hemisphere.

Now we are ready to work through several examples showing how the PGF and CF determine how upper level winds blow. First a couple of things that we will use over and over again.

The strength of the Coriolis force and the Frictional force both depend on wind speed. If the wind is blowing there isn't any Coriolis or Frictional force. Thus the PGF is the only force that can cause stationary air to start to move.

We will start with upper level winds because they involve only the PGF and the CF. For surface winds you must include the frictional force.

We'll start with a simple upper level contour pattern, straight parallel contour lines. The figure below is found at the top of p. 123 in the photocopied Classnotes.

Placing a parcel of air in the pressure pattern below is analogous to placing a rock on a ramp. The rock will begin to roll downhill, the air will begin to move toward low pressure (or low height on a constant pressure chart). The wind will pick up speed as it goes.

On the upper level chart above, we start with a stationary volume of air at Point 1. The PGF (perpendicular to the contour lines and pointing toward low) will start the air moving toward low pressure. The dots show this initial motion.

At Point 2 the air is moving and the Coriolis force appears. It is perpendicular and to the right of the wind (this is a northern hemisphere map). It is weak because the wind speed is low. The CF begins to bend the wind (it is bending to the right if you look in the direction the wind is blowing).

The wind picks up speed and, in Points 3 and 4, the CF is getting stronger and the wind is continuing to bend.

At Point 5, the wind is blowing parallel to the contours, and the wind speed is high enough that the CF is able to balance the PGF. The net force is now zero. From this point on the winds will blow in a straight line at constant speed parallel to the contour lines. This is known as a geostropic wind or geostrophic flow.

Some more examples and some questions from p. 124 in the photocopied Class Notes.

The PGF force starts the stationary air (at the starting position) moving (the dots show the direction of this initial motion). Low pressure would be found at the top of both maps in this figure. Then if we watch the motion carefully we see the air beginning to turn to the right in the left figure and turning to the left in the right hand figure. This is caused by the Coriolis force. The CF is to the right of the wind in the left figure, this is a northern hemisphere (NH) chart. The CF is to the left of the wind in the right figure, this is a southern hemisphere (SH) chart.

The CF and PGF again balance by the time you get to point where the winds are blowing parallel to the contour lines.

The two figures above (middle of p. 124) show maps with strong and weak pressure gradients. The wind in the left figure ends up blowing much faster than the wind in the right figure (much as a rock would roll quickly down a steep ramp and slowly down a more gradual slope). The fast wind in the left figure produces a strong Coriolis force that is eventually able to balance the strong PGF. The slow winds at right produce a weaker CF. The CF is to the right of the wind in both examples, so these are both in the northern hemisphere.

In the left figure the direction of the initial motion (the dots) is toward the bottom of the figure. The initial motion is caused by the PGF. The PGF points toward low pressure at the bottom of the chart.
In the right figure the wind takes a left turn once it begins to blow (turn the page upside down so you are looking in the direction the wind is blowing). That identifies this as a southern hemisphere chart.

Now we'll look at upper level circular centers of low and high pressure.

Just like a rock rolling downhill toward the center of a depression, air will begin to move inward toward a center of low pressure

The dots tell you the direction of the initial motion. They tell you the direction of the PGF, inward toward low pressure in both these figures.

In the middle figure the wind takes a right turn (identifying this as a northern hemisphere chart) and eventually ends up blowing parallel to the contour lines in a counterclockwise direction.

In the bottom figure the wind turns to the left and ends up blowing parallel to the contour lines in a clockwise direction. The CF points to the left of the wind in this figure, this is a southern hemisphere chart.

Note in both charts that the PGF and the CF point in opposite directions but they are no longer equal in strength. The inward pointing PGF is stronger than the outward CF. The difference provides the net inward force (the purple arrow) needed to keep the wind blowing in a circular path.

Because of the Coriolis force, winds blow counterclockwise around low pressure in the NH and clockwise around low in the SH.

Here's what happens with upper level high pressure centers.

The initially stationary air begins to move outward and away from the high pressure in the center (the dots show this initial motion).

In the middle figure the CF is to the right of the wind. This is a northern hemisphere map. Winds blow parallel to the contours and spin clockwise around high in the northern hemisphere.

The winds blow parallel to the contours and in a counterclockwise direction around circular centers of high pressure in the southern hemisphere.

Note the net force is inward in both cases.

Now before you get the idea that all winds change directions in the NH and SH we'll look at the next figure.

The winds are blowing from west to east in both hemispheres even though the CF changes directions in the NH and SH. How is this possible. If you look closely you will notice that the pressure pattern is also "flipped." Low pressure is found at the top of the map in the NH and at the bottom of the chart in the SH. The direction of the CF changes directions in the NH and SH hemisphere, the PGF also charnges directions and the winds blow in the same direction.

The spacing of the contour lines and the strength of the PGF stays about constant on this chart. If you look closely at the figure you will notice that the CF force is sometimes stronger and sometimes weaker than the PGF. This changing imbalance results in a net force needed for the right and left turns that the winds take as they blow through this pattern. If you remember that the strength of the CF depends on latitude (as well as wind speed) you can understand why the CF changes strength. The CF is strongest when the winds are far from the equator, weakest when the winds are close to the equator (the CF is zero at the equator).

Now we will have a brief look at surface winds. Upper level winds are determined by the pressure gradient force and the Coriolis force.

In the figure above, we drew in the pressure gradient force arrow (perpendicular to the contour lines and pointing toward low pressure). Then we can drew in an equal and oppositely directed CF so that the net force would be zero. We then saw that the CF was to the right of the wind and we could then say this was a N. hemisphere chart.

For surface winds, you must add the frictional force to the mix.

The frictional force will always point in a direction opposite the wind. Friction always try to slow moving objects (it doesn't cause you to speed up on your bicycle or to veer suddenly to the right or left). The strength of the frictional force depends on wind speed (stronger when the winds are fast and zero when the wind isn't blowing at all). Friction also depends on the type of surface the wind is blowing over (there is less friction when winds blow over the ocean than when blowing over land).

Note in the figure above that adding friction slows the wind. This in turn weakens the Coriolis force and the CF no longer balances the PGF. The PGF turns the wind slightly toward low pressure, the winds blow across the contours toward low pressure. You eventually end up with a new balance: CF together with F are able to balance the PGF and the net force becomes zero.

This figure summarizes most everything we have done. The upper level winds are shown in the figure at left. The upper level winds blow parallel to the contour lines.

At right surface winds around centers of high and low pressure are shown. You should remember from early in the semester that winds blow counterclockwise and inward around low pressure in the NH. They blow clockwise and outward around high pressure.

In the southern hemisphere the directions of spin change (clockwise around low and counterclockwise around high). Winds still blow converge into low pressure and diverge from centers of high pressure. This means that rising air (which expands and cools) and clouds will be found with centers of low pressure in both the northern and southern hemispheres.

Note the locations and directions of motion of the southern hemisphere warm and cold fronts. The winds spin clockwise around low pressure in the southern hemisphere. The coldest air is found in the south in the southern hemisphere.