Monday Nov. 5, 2012

Some surf guitar from Dick Dale ("Peter Gunn", "Esperanza", and "Misirlou") to celebrate the beautiful fall weather.

The 1S1P 1983 Flood reports have been graded and were returned in class today.  The Tucson Fog reports are due on Wednesday.

The revised Experiment #1 reports have been graded and can be picked up.

The In-class Optional Assignment from last Friday has been graded and was also returned today.  Here are answers to the questions.

We were trying to understand why upper level winds blow the way they do around high and low pressure in the northern and southern hemispheres.  We got as far as low pressure in the northern hemisphere in class last Friday. 

Here's what happens with low pressure in the southern hemisphere
The PGF will start stationary air at Point 1 moving toward the center of the picture.  Once the air starts to move the CF will turn it to the right (northern hemisphere) or left (southern hemisphere).  Since this is the southern hemisphere the air will turn to the left.  The air will end up spinning in a clockwise direction around the L in the southern hemisphere.  Note the inward pointing PGF needs to be a little stronger than the outward pointing CF so that there is a net inward force. 

Here initially stationary air at Point 1 begins to move outward in response to an outward pointing pressure gradient force (PGF).  Once the air starts to move, the Coriolis force (CF) will cause the wind to turn to the right.  The wind ends up blowing in a clockwise direction around the high.  The inward pointing CF is a little stronger than the PGF so there is a net inward force here just as there was with the two previous examples involving low pressure.  An inward force is needed to keep anything moving in a circular path.

This is a southern hemisphere upper level center of high pressure.  You should be able to figure out how the winds will blow in this case. 
You'll find the answer at the end of today's notes.

Upper level winds blow parallel to the contour lines.  Now we'll try to understand why friction causes surface winds to blow across the contour lines (always toward low pressure).

The top figure shows upper level winds blowing parallel to straight contours.  The PGF and CF point in opposite directions and have the same strength.  The total force, the net force, is zero.  The winds would blow in a straight line at constant speed.  Since the CF is perpendicular and to the right of the wind, this is a northern hemisphere chart. 

We add friction in the second picture.  It points in a direction opposite the wind and can only slow the wind down.  The strength of the frictional force depends on wind speed (no frictional force if the wind is calm) and the type of surface the wind is blowing over (less friction when wind blows over the ocean, more frictional force when the wind is blowing over land).

Slowing the wind weakens the CF and it can no longer balance the PGF (3rd figure).  The stronger PGF causes the wind to turn and start to blow across the contours toward Low.  This is shown in the 4th figure.  Eventually the CF and Frictional force, working together, can balance out the PGF.
  The net force would again equal zero and the wind would blow in a straight line at constant speed acrosss the contours toward low pressure.

What we've learned from the straight contour example, namely that the winds will blow across the contours toward low pressure can be applied to a curved contour pattern.  The figure below wasn't shown in class.

If you take a small little piece of a curved pattern and magnify it, it will look straight. 

Now our last step, surface  winds blowing around H and L in the NH and SH.

It is easy to figure out which of the figures are centers of low pressure (the wind blows inward toward the center of the picture)  The winds are spiralling inward in the top and bottom examples (1 and 3).  These must be surface centers of low pressure.  The winds are spiraling outward from the centers of high pressure (2 and 4).

Now you probably don't want to figure out which of these are northern and which are southern hemisphere pictures.  It is probably best to remember one of the pictures.  Remember in 1, for example, that surface winds spin counterclockwise and spiral inward around centers of low pressure in the northern hemisphere (something we learned early in the semester).  Then remember that winds spin in the other direction and blow outward around high pressure in the northern hemisphere (2).  The spinning directions of the winds reverse when you move from the northern to the southern hemisphere.  Thus you find clockwise spinning winds and inward motion around low pressure (3) and counterclockwise and outward spiraling winds around high pressure in the southern hemisphere.

Converging winds cause air to rise.  Rising air expands and cools and can cause clouds to form.  Clouds and stormy weather are associated with surface low pressure in both hemispheres.  Diverging winds created sinking wind motions and result in clear skies.

Next we had a short look at the cause of the Coriolis force.  The pictures that follow aren't in the ClassNotes.

Imagine something flies over Tucson.  It travels straight from west to east at constant speed.  You would, more or less subconciously,  plot its path relative to the ground.  The next figure shows the path that the object followed as it passed over the city. 

Here's the path the moving object would appear to follow relative to the ground.  Based on this straight line, constant speed trajectory you'd conclude there was no net force acting on the object (and again no net force doesn't mean there aren't any forces, just that they all cancel each other out so the total force is zero).

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).  What would you say happened when viewing the flyby from the ground?

The path, relative to the ground, would look something like this.  It would no longer appear to be moving from W to E but rather from the NW toward the SE.  It's still straight line motion at constant speed, though, so you conclude there was no net force acting on the object.

Now the ground is moving and also spinning.

The path of the object plotted on the ground appears to be curved.  But remember that's relative to the ground and the ground is spinning.  We could take the ground's motion into account or just ignore it.  In the latter case you'd conclude that there was a net force perpendicular and to the right of the moving object.  This net force would be needed to explain the curved path that the object appears to be following. 

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 or forget about the fact that the ground on which we are standing is rotating.  We do still 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.

And that's the reason for another 1S1P Bonus Assignment.  Foucault's Pendulum was the first demonstration that proved that the ground we're standing on (at most locations on earth) is spinning.  Here's a photograph of a Foucault Pendulum at the Pantheon in Paris (Foucault conducted his demonstration apparently at the Paris Observatory).

Here's the answer to the question embedded in today's notes.  The figure below shows the upper level winds that blow around H pressure in the SH hemisphere.

Winds start to move outward and away from high pressure.  The CF then turns the wind to the left.  Winds end up spinning in a counterclockwise direction around high pressure in the southern hemisphere.