Tue., Nov. 7 notes

Tuesday Nov. 7

Dr. Weidman is out of town because of a family emergency. The quizzes will be returned when he returns.

An optional assignment handed out in class today will be due at the end of the period on Thursday. It is referred to as an in class assignment because you should be able to answer most of the questions while in class.

Now back to Chapter 6 where we left off working before the quiz. I've moved some of what we covered on Tuesday here to today's notes. I've also added some additional material that wasn't covered in class on Tuesday.

We'll learn why winds spin counterclockwise (CCW) around Low pressure and clockwise (CW) around High pressure in the northern hemisphere. We'll see why the spinning winds reverse direction in the southern hemisphere. You may already have been to the southern hemisphere or you may go there one day (see Question #11 on the In-class Optional Assignment). You'll probably hear about how the Coriolis force or the Coriolis effect causes water draining out of sinks and toilet bowls to spin in the opposite direction in the southern hemisphere (it's not true). That's another reason for covering the Coriolis effect in NATS 101.

This figure shows the winds spinning around middle latitude storms (extratropical cyclones) and hurricanes (tropical cyclones) in both the northern and southern hemispheres. The term cyclone refers to winds blowing around low pressure. Note how the directions of the spinning winds change as you move from one hemisphere to the other.

Note how middle latitude storms tend to move from west to east in both hemispheres. Hurricanes, which are found in the subtropics, move from east to west in both hemispheres. We will learn more about why this occurs in the next week or so.

Now back to Newton's 1st and 2nd laws of motion (this is review, we covered this material last Tuesday)

The 1st law really has two parts: one that deals with stationary objects and another part that treats moving objects.

A stationary object is shown in all three figures above. In the left example there aren't any forces at all being exerted on the object, there is no reason for it to suddenly start to move. In the middle and right examples there are two forces present but they are of equal strength and point in opposite directions. They cancel each other out and the net or total force is zero. Again the stationary object won't suddenly begin to move.

In the first example above there aren't any forces at all. In Examples #2 & #3 and #4 & #5 below (on p. 121 in the photocopied notes) the next force is zero (the two forces present cancel each other out). The object will continue to move in a straight line at constant speed (the thin arrows show the direction of motion, the length of the arrow provides an idea of speed.

We are used to seeing falling objects pick up speed as they fall. But if an upward drag or friction force becomes strong enough to balance the downward pull of gravity and the net force is zero, the object will fall at constant speed. Parachutists take advantage of this.

By now you should be able to answer questions 1-6 and 11 on the in-class optional assignment.

Next we will look at the motion that occurs when a net force is present. You should be able to look at the motion and determine whether a net force is needed.

If there were no net force at the point indicated, Newton's 1st law of motion would say the object would travel in a straight line at constant speed (the blue arrows). But the object turns to the right. A force acting perpendiculary and to the right of the object's direction of motion are needed. A net inward force is needed to keep an object moving in a circular path.

An example would be a satellite orbiting the earth

Gravity supplies the net inward force needed to keep the satellite in a circular orbit.

In the case of the rapid winds in a tornado, a very strong inward force is needed (it turns out to be the pressure gradient force (PGF) or pressure difference force).

What we will be most interested in are the upper level winds which, if you remember from earlier in the semester, blow parallel to the contour lines on an upper level chart from west to east.

Note that the net force is sometimes to the right of the wind and sometimes to the left of the wind.

Now Newton's 2nd law of motion. This is still review from last Tuesday

The 2nd law of motion really just says that if you exert a net force on an object it will accelerate. Acceleration can mean start moving, speed up or slow down, start moving in a different direction.

In the first example unequal forces (2 and 5) are applied to equal masses (5 and 5), don't worry about the units. You can calculate the acceleration by dividing force by mass. This gives you the acceleration, the lower object will speed up five times faster than the top object which has a weak force exerted on it.

In the bottom example equal forces (5 and 5) are applied to two different masses (2 and 10). Mass can be thought as being inertia, or resistance to change. An object with a large mass is resistant to a change of direction or speed. A large object is harder to start moving than a small object (imagine pushing a stalled Volkswagen and a stalled Cadillac out of an intersection). The large mass accelerates 5 times more slowly than the smaller mass. Once the large mass gets up to speed however, is is hard to slow it down (a decrease in speed with time is a form of acceleration, we usually call it deceleration)

Note that a change in direction, with or without a change in speed, is also a form of acceleration.

The first two forces above determine upper level winds; we'll study them first. For surface winds you must include the frictional force.

That's about where we finished up before the quiz.

Next we will try to understand what causes these forces. That's pretty easy with the pressure gradient and frictional force, not so easy with the Coriolis force. In each case we will learn rules that determine the direction and the strength of these forces.

Pressure at any level in the atmosphere is determined by the weight of the air overhead. If you stack up a bunch of bricks as shown at upper left it is easy to understand that the pressure at the bottom center of the picture would be higher than an the edges.

Now imagine carrying a bucket of water to the center of a swimming pool and pouring it out on the water that is already there. You wouldn't be able to pile up water at the center of the pool. As soon as you tried the higher pressure at the bottom of the pool would cause water to flow. The same kind of thing happens with air. The pressure difference force pushes air from high to low pressure.

The rules used to determine the direction and strength of the PGF are given in the center of the picture.

Some examples of PGF force directions and relative strengths are shown at the bottom of the figure. Note the analogy between weather maps and geographical features like hills and valleys.

You have enough information now to answer Question #7

The PGF can cause stationary air to begin to move. In the top example a stationary volume of air is placed in a center of low pressure. The PGF will cause the air to begin to move toward low pressure in the center of the picture. The dotted line shows the direction of initial motion. This like placing a ball on the side wall of a valley. The ball will roll downhill.

In the second example, a center of high pressure, the PGF causes a stationary volume of air to again begin to move toward low pressure which is outward and away from high pressure. In the analogy a ball placed on the side of a hill will roll downhill and away from the summit.

So given a pressure pattern you should be able to determine the direction of initial motion (see Question #8). Or as in Question #10 you should be able to determine whether the motion is being caused by a center of high or low pressure.

The figure above is from p. 122c in the photocopied notes. Imagine that a flying saucer flies over Tucson. It travels straight from west to east. The next figure shows the path that the saucer followed as it passed over the city.

The flying saucer appeared (relative to the ground) to be moving in a straight line at constant speed. You would conclude that there was zero net force acting on the flying saucer.

In this second picture the flying saucer 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 flying saucer flew from west to east it appears to have been traveling from the NW toward the SE because the ground was moving as the flying saucer passed overhead. Because the motion is still in a straight line at constant speed, you would conclude the net force acting on the flying saucer was zero.

In this last figure the flying saucer flies by again from west to east. In this case however the ground is rotating.

Now the flying saucer 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 flying saucer. The direction of this net force would be to the right of the motion.

At most locations on the earth the ground is rotating. 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.

The easiest thing for us to do is to ignore the fact that the ground on which we are standing is rotating. 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. 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.

The red arrows show the direction of the CF in the northern and southern hemispheres. 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're ready to do lots of examples.

Start with the analogous situation at upper left. If you put a rock on a ramp and let it go, it will roll downhill. If you put some air in a pressure gradient as shown at upper right. The pressure gradient force (PGF) will start the air blowing toward low pressure. The wind will speed up as it goes.

On the larger weather chart at the bottom of the page, 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.

At Point 2 the air is moving and the Coriolis force makes an appearance. It is perpendicular and to the right of the wind. It is weak because the wind speed is low. The CF begins to cause the wind to bend (it is bending to the right if you look in the direction the wind is blowing).

The wind picks up speed in Points 3 and 4 and continues to bend.

At Point 5, 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 similar examples with just the essential details included.

We start with the top left figure. Some air is placed at Point 1. The dots show the direction of the initial motion. The PGF force starts stationary air moving, so we can identify the force at Point 2 as the pressure gradient force (low pressure would be found at the top of this figure. Then if we watch the motion carefully we see the air beginning to turn to the right at Point 3. This is caused by the Coriolis force. We know now that this is a northern hemisphere map. Points 1 and 2 are similar in the top right figure. But at Point 3 the wind turns to the left. The top right map is in the southern hemisphere.

The two middle figures 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 needed to balance the strong PGF. The slow winds at right produce a weaker CF.

In the bottom 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 bottom right the wind takes a left turn once it begins to blow (remember you must be looking in the direction the wind is blowing). That identifies this as a southern hemisphere chart.

Next we'll look at upper level charts with circular contour patterns.

The rock rolling down a hill vs air moving in a pressure gradient analogy is shown again at the top of the figure.

By now you should be understanding what is shown in Points 1 in the figure lower figures. 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 at Point 2. This is a northern hemisphere (NH) chart. The wind turns to the left at Point 2 in the bottom figure, this is a southern hemisphere chart.

Note at Point 3 in both charts that the PGF and the CF point in opposite directions but they are no longer equal in strength. The inward point PGF is stronger than the outward CF. The difference provides the net inward force 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.

These figures show the wind motions around high pressure centers. The initial motion is ouward. The CF then bends the wind right or left depending on hemisphere. A net inward force is present again in both cases. Winds blow clockwise around high in the NH and counterclockwise around high in the SH.

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.

If you look closely at the figure you will notice that the CF force is sometimes stronger (left side) and sometimes weaker (right side) than the PGF. This changing imbalance is 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 (left side), weakest when the winds are close to the equator (right side).

If you ever go to the southern hemisphere one of the first things you might do, once you land, is to rush into the airport bathroom and flush the toilet or drain a sink. You would do this because you might remember having heard that as the water drains it spins in the opposite directions in the northern and southern hemispheres. It is an interesting story but unfortunately it isn't true (don't worry there are still plenty of other interesting things to do in the southern hemisphere).

Spinning motions do change directions when the Coriolis force is involved.

In some cases such as water draining from a sink or winds in a tornado, the PGF is much stronger than the CF and the CF can be ignored. In this case the winds or water can spin in either direction in either hemisphere.