Tuesday Nov. 9, 2010
click here to download today's notes in a more printer friendly format

A couple of songs from Dire Straits before class today ("Sultans of Swing" and "Walk of Life").  I hope I haven't already played this earlier this semester. 

Quiz #3 has been graded and was returned in class.  Grades are often lower than normal on this quiz (midsemester burn out or something like that) but this class went against that trend this time.

The Experiment #3 reports (and a few book reports) have been graded.  You have two weeks to revise your report is you want to.  Revised reports are due on Tue., Nov. 23 (the Tuesday before Thanksgiving).  Please return your original report with your revised report.

The 1S1P Assignment #2a reports were collected today.  The Bonus Assignment reports ("Write Your Own Story") are due by Friday this week.  Since we don't have class on Thursday you can either drop them off in my office or email them to me.  The  Assignment #2b reports are due by Tuesday next week.

In the next couple of classes we will be looking at how and why surface and upper level winds blow the way they do.

Some real world examples of where this occurs are shown in the figure below.



The two largest types of storm systems, middle latitude storms and hurricanes, develop around surface centers of low pressure.  Winds spin counterclockwise around low in the northern hemisphere then reverse direction and spin clockwise in the southern hemisphere. Winds spin clockwise around "anticyclones" (high pressure) in the northern hemisphere and counterclockwise in the southern hemisphere.
 

Some things change direction in the southern hemisphere, others remain the same.
Storm systems in the tropics (0 to 30 degrees latitude) generally move from east to west.  This is true in both hemispheres.  At middle latitudes (30 to 60 degrees), storms move in the other direction, from west to east.  To understand why this is true we need to learn something about the earth's global scale pressure and wind patterns.  This is a topic we will be getting into next week.



I've borrowed the more carefully drawn figures below from the Spring 2009 online notes.  Steps 1-8 below were on a 4 page handout distributed in class.  An In-class Optional Assignment was distributed in class today.  If you weren't in class but are reading through these notes you can download the assignment & turn it in at the beginning of class next Tuesday and receive at least partial credit.




Upper level winds spinning around high and low pressure in the northern and southern hemispheres are shown in the first set of four pictures.  The first thing to notice is that upper level winds blow parallel to the contours.  We will see that 2 forces, the pressure gradient force (PGF) and the Coriolis force (CF), cause the winds to blow this way.  Eventually you will be able to draw the directions of the forces for each of the four upper level winds examples.  Here is an example of what you will be able to do. 

The four drawings at the bottom of the page show surface winds blowing around high and low pressure in the southern hemisphere.  These winds blow across the contour lines slightly, always toward low pressure.  The frictional force is what causes this to occur.  He is an example of what you will be able to say about surface winds blowing around low pressure in the southern hemisphere.

The main point to take from Step #2 is that a net inward force is needed anytime an object is moving in a circular path.  It doesn't matter what direction the object is moving.  The net force is inward anytime something moves in a circular path.

Quite a few people would say there is an outward force being exerted in the bottom picture below, but the force is inward in all 3 cases.

It's just not the same amount of inward force.  The amount of force is just right in the top figure, a little "too strong" in the middle figure, and "not quite strong enough" in the bottom figure.


Now we'll start to look at the forces that cause the wind to blow.



Here's the rule for the direction of the pressure gradient force: the PGF is perpendicular to the contours and always points toward low pressure.  Each of the forces that we will discuss has a unique property.  In the case of the PGF, it can cause stationary air to begin to move (the initial motion will always be toward low pressure).



The Coriolis force is caused by the rotation of the earth and points in a direction that is perpendicular to the wind (direction rule).  It can only change the wind's direction, it can't cause the wind to speed up or slow down (it's unique property).  The direction of the CF depends on whether you're in the northern or southern hemisphere.  There is a short section at the end of today's notes that tries to explain the cause or origin of the Coriolis force.





Now we start to put everything together.  The PGF at Point 1 starts stationary air moving toward the center of low pressure (just like a rock would start to roll downhill).  Once the air starts to move, the CF causes it to turn to the right (because this is a northern hemisphere chart).  The wind eventually ends up blowing parallel to the contour lines and spinning in a counterclockwise direction.  Note that the inward PGF is stronger than the outward CF.  This results in a net inward force, something that is needed anytime wind blows in a circular path.






Start with some stationary air at Point 1 in this figure and see if you can figure out how the winds will develop and end up blowing.  When you think you have the answer click here.




With high pressure the air starts moving outward.  In this northern hemisphere example the wind then takes a right turn and ends up blowing in a clockwise direction around the high.  Note there is a net inward force here just as there was with the two previous examples involving low pressure.




Start again with some stationary air at Point 1 and try to figure out the rest on your own.  When you think you have the answer, click here.



The last two steps deal with surface winds.  We'll start with an upper level wind blowing parallel to straight contours, add the frictional force, and see why/how that causes the surface wind to turn and blow across the contours 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 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 (direction rule) and can only slow the wind down (it's unique property).  The strength of the frictional force depends on wind speed (no frictional force if the wind is calm) and the surface the wind is blowing over (less friction over the ocean than when the wind is blowing over the 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.

As long as we're talking about friction, here's the answer to one of the questions on the In-class Optional Assignment.


If you stop pedaling a bicycle friction (due to wind resistance, the roughness of the road surface, and the wheel bearings) will slow you down and eventually bring you to a stop.

What we've learned from the straight contour example above, namely that the winds will blow across the contours toward low pressure, can be applied to a curved contour pattern.


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



It is easy to figure out which of the figures are centers of low pressure.  The winds are spiraling 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.



It seemed appropriate at this point to look at a common misconception involving the Coriolis force.  You might already have heard that water spins in a different direction when it drains from a sink or a toilet bowl in the southern hemisphere than it does in the northern hemisphere.  You might also have heard that this is due to the Coriolis force or the Coriolis effect. 

The Coriolis force does cause winds to spin in opposite directions around high and low pressure centers in the northern and southern hemisphere. 
The PGF starts the air moving (in toward low, out and away from high pressure) then the Coriolis force bends the wind to the right (N. hemisphere) or to the left (S. hemisphere).
Here's what you end up with in the case of low pressure (you'll find these figures on p. 130 in the photocopied ClassNotes):




Air starts to move inward toward low pressure.  Then the Coriolis force causes it to turn to the right or left depending on which hemisphere you're in.  You should be able to figure out which of the pictures above is the northern hemisphere and which is the southern hemisphere picture.




The same kind of idea applies to high pressure except that the air starts moving outward.  The Coriolis force then turns it to the right or left.  The CF is very important in this case because it supplies the net inward force needed to keep wind blowing in a circle.

There are situations where the PGF is much stronger than the CF and the CF can be ignored.  A tornado is an example.  Winds can blow around Low pressure because the PGF points inward.




The wind can spin in either direction in either hemisphere.


Without the CF winds can't spin around High pressure because there is nothing to provide the needed inward force.


What about water draining from sinks, buckets, toilets etc.



There's just an inward pointing PGF that is stronger than the CF (you'll just have to trust me on that).  Water can spin in either direction in either hemisphere.


Now we watched a short video segment that seemed to show otherwise.  In the video a young man living at the Equator in Kenya was making a living demonstrating the Coriolis effect to tourists.  He showed water draining from a bucket and spinning in opposite directions depending on whether he was north or south of the equator.  The water seemed to drain without spinning at all right at the equator.

Don't believe everything you see on video.  The gentleman in the video was just very good at getting the draining water to spin one direction or another as he moved on opposite sides of the equator.  Probably the most difficult part would be to get the water draining without spinning, which is what he was able to do when standing right on the equator.


But this something we should probably checkout for ourselves, so here is one of my favorite optional assignments of the semester. 



Now here is a self guided explanation of the cause or origin of the Coriolis force.  We didn't have time to cover this in class on Tuesday.

Next we had a short look at the cause of the Coriolis force.  Most of what follows can be found on p. 122c in the photocopied ClassNotes.

Imagine something flies over Tucson.  It travels straight from west to east at constant speed.  The next figure shows the path that the object followed as it passed over the city. 




It would appear (relative to the ground) to be moving in a straight line at constant speed.  You would conclude there was zero net force acting on the moving object (Newton's first law of motion).




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.  Because the object's perceived motion (relative to the ground) is still in a straight line at constant speed, you would conclude the net force acting on the object was zero.



In this last figure the object flies just as it did in the 2 previous pictures.  In this case however the ground is rotating.


Now the path of the object plotted on the ground appears to be curved.  Maybe you're not aware of the fact that the ground is spinning or you choose to ignore it.  In that case and based on the path relative to the ground you'd conclude that there was a net force perpendicular and to the right of the moving object.  This net force would explain the curved path that the object appears to be following. 

At most locations on the earth the ground IS rotating (we're just not aware of it).  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.