Tue., Feb. 6 notes

Tuesday Feb. 6, 2007

The 1S1P Assignment #1 and the Experiment #1 reports were collected today. The Experiment #2 materials should be available on Thursday.

We need to finish up trying to understand why warm air rises and cold air sinks. We covered the first two of three steps last Thursday before the Practice Quiz. That is summarized below.

The last of the three steps is to look at the upward and downward pointing forces that act on a balloon and try to figure out what might cause one of the forces to become stronger than the other. That is covered on p. 53 in the photocopied Class Notes.

Air has mass and weight When an air parcel has the same temperature, pressure, and density as the air around it, the parcel will just sit still and remain in one place. With gravity pulling downward on the air, there must be another force pointing upward of equal strength. The upward force is caused by pressure differences between the bottom (higher pressure pushing up) and top of the balloon (slightly lower pressure pushing down on the balloon).

If the balloon is filled with warm, low density air the gravity force will weaken (there is less air, less mass, in the balloon so it weighs less). The upward pressure difference force (which depends on the surrounding air) does not change. The upward force will be stronger than the downward force and the balloon will rise.

Conversely if a balloon is filled with cold low density air, gravity will strengthen and the balloon will sink.

When air inside a balloon is less dense than the air outside, the balloon will rise. When the air inside the balloon is denser than the air outside the balloon will sink. We can see this happen in a simple demonstration. It is similar to the Charles Law demonstration that we did last week before the Practice Quiz. That demonstration is summarized below.

Charles Law was demonstrated by dipping a balloon in liquid nitrogen. When we pulled the balloon out of the liquid nitrogen it was very small; it was filled with cold high density air. As the balloon warmed the balloon expanded and the density of the air inside the balloon decreased. Air temperature and air density (or volume) inside the balloon changed in a way that kept the pressure constant.

We modified the earlier demonstration somewhat (see bottom of p. 54 in the photocopied class notes). We used a balloon filled with hydrogen instead of air. Hydrogen is less dense than air even when the hydrogen has the same temperature as the surrounding air. A hydrogen filled balloon doesn't need to warmed up in order to rise.

We dunked the hydrogen filled balloon in some liquid nitrogen to cool it and to cause the density of the hydrogen to increase. When removed from the liquid nitrogen the balloon can't rise, the gas inside is denser than the surrounding air (the purple and blue balloons in the figure above). As the balloon warms and expands its density decreases. The balloon at some point has the same density as the air around it (green above) and is neutrally bouyant. Eventually the balloon becomes less dense that the surrounding air (yellow) and floats up to the ceiling.

You might have a look at the material on Archimedes' Law on pps 53a and 53b in the photocopied Class Notes. That explains this same material in a slightly different way, a way that you might be better able to relate to.

Air can rise or sink freely in the atmosphere. This is called "free convection." One of the ways of causing air to rise is shown below.

Sunlight passes through the mostly transparent atmosphere and is absorbed by the ground. The ground gets hot and air in contact with the ground warms. Volumes of air that become warmer and have lower density than the air around them. The warm low density air begins to rise. And you know what happens when air rises: it expands and cools. If the air is moist and is cooled enough clouds can form. Free convection is what initiates many of our summer thunderstorms.

Note this is a second way of causing air to rise.

Now back to surface weather maps. We learned about the winds that blow around surface centers of high and low pressure a week ago. Differences in pressure cause the wind to blow. The pressure pattern can give you an idea of where you might expect fast and where you might find slow winds.

In the left figure pressure changes 4 mb over some horizontal distance. In the figure at right there is a 12 mb pressure change over the same distance. The pressure is changing slowly with distance in the figure at left, this is a weak pressure gradient. A stronger pressure gradient is shown in the figure at right.

The overall orientation of the isobars is the same in the two figures, it is just the contour spacing that is different. The winds blow in the same direction in both figures (from SW toward the NE), but the speeds are different. The winds in the figure at right with the strong pressure gradient are three times faster than the winds at left.

In some respects weather maps are like topographic maps. The map above at top right represents the hill at top left. Closely spaced contours on the topographic map correspond to a steep slope on the hill. Widely spaced contours depict the gradual slope on the right side of the hill. If you were to trip and roll downhill, you would roll faster on the steep slope than on the gradual slope.

Here's a fairly complex but more realistic weather map example (found at the bottom of p. 40c in the photocopied class notes). The arrows indicate the directions of the winds (clockwise and outward around the high, counterclockwise and inward around the low). Fast 30 knot winds are found in the strong pressure gradient region shaded orange (#2). Slower 10 knot winds are shown in the weak pressure gradient region colored blue (#3). The green shaded region (#1) has a moderate pressure gradient and 20 knot winds.

Once the pressure pattern gets the wind blowing, the winds can affect and change the temperature pattern. The figure below shows the temperature pattern you would expect to see if the wind wasn't blowing at all or if the wind was blowing straight from west to east. The bands of different temperature air are aligned parallel to the lines of constant latitude.

This isn't a very interesting picture. If you were to travel from west to east you wouldn't experience much of a temperature change. It gets a little more interesting if you put centers of high or low pressure in the middle.

The clockwise spinning winds move warm air to the north of the western side of the HIGH. Cold air moves toward the south on the eastern side of the high.

Counterclockwise winds move cold air toward the south on the west side of the LOW. Warm air advances toward the north on the eastern side of the low.

The converging winds in the case of low pressure will move the air masses of different temperature in toward the center of low pressure and cause them to collide with each other. The boundaries between these colliding air masses are called fronts.

Cold air is moving from north toward the south on the western side of the low. The leading edge of the advancing cold air mass is a cold front. Cold fronts are drawn in blue on weather maps. The small triangular symbols on the side of the front identify it as a cold front and show what direction it is moving. The fronts are like spokes on a wheel. The "spokes" will spin counterclockwise around the low pressure center.

A warm front (drawn in red with half circle symbols) is shown on the right hand side of the map at the advancing edge of warm air.

Clouds can form along fronts (often in a fairly narrow band along a cold front and over a larger area ahead of a warm front). We need to look at the crossectional structure of warm and cold fronts to understand better why this is the case.

Crossectional view of a cold front

At the top of the figure, cold dense air on the left is advancing into warmer lower density air on the right. We are looking at the front edge of the cold air mass. The warm low density air is lifted out of the way by the cold air.

The lower figure shows an analogous situation, a big heavy Cadillac plowing into a bunch of Volkswagens. The VWs are thrown up into the air by the Cadillac.

Crossectional view of a warm front

In the case of a warm front we are looking at the back, trailing edge of cold air (moving slowly to the right). Note the ramp like shape of the cold air mass. Warm air overtakes the cold air. The warm air is still less dense than the cold air, it can't wedge its way underneath the cold air. Rather the warm air overruns the cold air. The warm air rises again (more gradually) and clouds form. The clouds generally are spread out over a larger area than with cold fronts.

In the automobile analogy, the VWs are catching a Cadillac. What happens when they overtake the Cadillac?

The Volkswagens aren't heavy enough to lift the Cadillac. They run up and over the Cadillac.

Fronts are another way of causing air to rise. Rising air cools and if the warm air is moist, clouds and precipitation can form.