Friday Apr. 6, 2018

Los Lobos "Chuco's Cumbia" (at Austin City Limits 2006) (3:45), "One Time One Night" (Munich, Germany, 1987) (4:31), "Cumbia Raza" (8:18),
"Que Nadie Sepa Mi Sufrir" (2:55), "Someday Love Song for Bobby Long" (3:44), "Luz de Mi Vida" (Sydney, Australia, 2011) (5:21),
"Don't Worry Baby" (3:55), "Maricela" (4:10), "Yo Canto" (4:34)

We'll be learning what causes surface and upper level winds to blow the way they do in both the northern and southern hemispheres today and next Monday.

Step #1 - Upper level and surface winds in the N. and S. hemisphere - summary

I've included Step #1 even though we went through this briefly at the end of class on Monday.



Upper level winds are shown in the first set of four pictures above.  All the possibilities (H and L pressure in both the northern and southern hemispheres) are here.  The first thing to notice is that upper level winds blow parallel to the contours.  Just 2 forces, the pressure gradient force (PGF) and the Coriolis force (CF), cause the winds to blow this way.  Eventually you should be able to draw the directions of the forces for each of the four upper level winds examples.  Here is an upper level wind example showing what you should 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.  Surface winds blow across the contour lines slightly, always toward low pressure.  A third force, the frictional force is what causes this to occur.  He is an example of what you will be able to say about surface winds.


Step #2 - Newton's 1st law of motion


If there's no net force being exerted on an object it will either be stationary or moving in a straight line at constant speed.



Anytime an object is slowing or speeding up or changing direction (or both) a net force is present.

You should be able to look at an object's (or the wind's) motion and tell if there is a net force or not.  There are two possibilities where there is no net force.  The first is shown below.


The two objects above are stationary.  In both cases there is no net force.  That could mean there aren't any forces at all (left figure).  Or forces may be present but they cancel each other out and add up to zero (the total force is zero).  With zero net force both objects will remain stationary.

The other possibility is that something is moving in a straight line at constant speed.




As long as the net force remains zero both objects will continue to move in a straight line at constant speed.  Note in the bottom figure the two forces could have been pointing right and left.  If they cancel each other out the total force is zero and the object would continue to move in a straight line at constant speed.

Here are some more examples of straight line motion.
 


The speed is also constant in examples (a) and (f) so there is no net force in those two cases only. 

The speed is changing in (b), (c), (d), and (e).  A net force is present and you should be able to determine its direction.  Maybe you can figure that out just by looking at the pictures, maybe not.  What you might do is think of a situation you're familiar with.




Here's a picture of someone throwing a ball upward.  You know from personal experience that the downward force of gravity will cause the ball to slow down as it rises, come to a stop, and then begin to fall picking up speed as it falls.  Gravity is present during both the rise and fall of the object.


We can match up the motion and force arrows with (b) and (e) in the earlier example.


Notice how the motion in (b) resembles that of a falling ball.  The motion in (e) is just like the motion of the ball thrown upward in the air.  Notice also that when the force is pointing in the same direction as the motion the object speeds up.  The object slows down when the force arrow points opposite the motion.  Now you can figure out the direction of the forces in (c) and (d).




The next figure shows a more important example - circular motion.  Is there a net force in any of these examples?  The answer is yes, a net force is present in all three cases because the motion is not straight line motion at constant speed.  What is the direction of the net force?


My sister can help with this question



She's out longeing (I believe that is the correct spelling) one of her horses, training it to run in a circle and to obey her commands.  At least initially the horse doesn't really want to do that and you must pull with a lot of force to keep it moving in a circle (without a force it would move in a straight line).  It's relatively easy to understand when you imagine a strong heavy horse at the end of a longe line that a net inward force is needed anytime anything moves in a circular path.



It doesn't matter what the direction of spin is, it doesn't matter what's in the middle of the picture, anytime something is moving in a circle there is a net inward force (gravity is the inward force keeping the satellite in orbit in the 3rd picture).
Here's a question I know many people will have trouble with (but better to have trouble here in the online notes rather than in the middle of a quiz).  Keeping an image of a horse on the end of a longe line might help.





Is there a net inward or outward force in each case?  You should now know that there is a net inward force in the 1st example because that's what we just looked at.  What about the next two.  The 3rd example is the one that causes people the most trouble.  Here's a clue --> Goldilocks and the Three Bears.  That will make a lot more sense when you look at the answer to this question at the end of today's notes.

Now we'll start to look at the forces that cause the wind to blow.
Step #3 Pressure Gradient Force (PGF) 
The figure below is on p. 123a in the ClassNotes)


Isobars on a weather map are very much like height contours on a topographic map.  A center of low pressure on a weather map is analogous to a circular valley on a topographic map (high pressure on a weather chart is like a circular hill).
The effect that the PGF force has on air
is very much like the effect of gravity on a rock placed on a slope. 
The rock will roll downhill, air will move toward low pressure.

The PGF always points in a direction that is perpendicular to the contour lines and toward low pressure.  The PGF can start stationary air moving.  The air will always start moving toward low pressure.  Air moving inward toward low pressure or outward away from high pressure is similar to a rock rolling downhill into the center of a depression or downhill and outward away from the summit of a hill.


It's good to understand the pressure gradient force as best you can.  But at the same time it's nice to have some rules that you can fall back on and apply.  The rules for the PGF are shown above.  Follow them (especially the one for direction) to the letter and you'll never go wrong.

Use the following figure to test yourself.  With an arrow draw the direction of the PGF at each of the points in the figure.  You'll find the answers at the end of today's notes.





Step #4 - Coriolis force (CF)
In this case we'll start with the rules and put some discussion of what causes this force into some online Optional Reading.  The rules for the CF are shown below.



The top of p. 123b in the ClassNotes has several examples showing the direction of the CF.  You can use them to check and make sure you understand how to apply the direction rule above.  I would suggest turning the page in your class notes so that you are looking in the direction the wind is blowing, looking downstream, whenever you try to determine the direction of the Coriolis force.




The Coriolis force is caused by the rotation of the earth.  Again you can read more online.  The CF points perpendicular to the wind and is to the right or left depending on hemisphere.  Be sure you are looking in the direction the wind is blowing, looking downstream, when determining the direction of the CF. 

The CF can only change the wind's direction.  It can't cause the wind to speed up or slow down. 

There isn't any Coriolis force when the wind is calm.  Coriolis force is zero at the equation because that's where the CF changes direction.  Hurricanes don't form at the equator because there is no Coriolis force there.
Time now to begin to apply what we've learned so far.

We'll consider the simplest possible situation - upper level winds with straight contours.  We'll do a Northern Hemisphere (NH) example.




We start with some stationary air in the lower left corner of the picture.  Low pressure is at the top and high pressure at the bottom of the picture.

The PGF can start stationary air moving.  The PGF will point toward the top of the picture (perpendicular to the contours and toward the low pressure at the top).  There won't be any Coriolis force when the air is stationary.

Once the wind starts to blow (blue line above) the CF will appear.  The CF will be weak at first because the wind speed is low but the CF will begin to turn the wind to the right.  As the wind picks up speed the CF will increase in strength.  Eventually the wind will be blowing parallel to the contours from left to right.  The PGF and CF point in opposite directions and are of equal strength.  The net force is zero and the wind will continue to blow to the right in a straight line at constant speed.

Here's a simpler less cluttered way of depicting what we have just figured out.



The dots show the direction of the initial motion.  That will always be toward low pressure.  Then you look in the direction the wind starts to blow and look to see if the wind turns right or left.  It turned right in this case.  That's the effect of the Coriolis force and means this is a northern hemisphere map.

Here's one last example to test your understanding.

The direction of the initial motion is shown with dots.  Where is the high and low pressure in this case?  Is this a NH or SH chart.  You'll find the completed map at the end of today's notes.


Step #5 - Upper level winds, low pressure, northern hemisphere

Next we'll be looking at the upper level winds that develop around circular centers of high and low pressure.





We start with some stationary air at the bottom of the picture.  Because the air is stationary, there is no Coriolis force.  There is a PGF force, however.  The PGF at Point 1 starts stationary air moving toward the center of low pressure (just like a rock would start to roll downhill).  The dots show the initial motion

A rock would roll right into the center of the picture.  Once air starts to move, the CF causes it to turn to the right (because this is a northern hemisphere chart).    As the wind speeds up the CF strengthens.  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.

Upper level winds spin counterclockwise around low pressure in the northern hemisphere.


Step #6 - Upper level winds, low pressure, southern hemisphere


We start again with some stationary air at Point 1 in this figure.  The situation is very similar.  Air starts to move toward the center of the picture but then takes a left hand turn (the CF is to the left of the wind in the southern hemisphere).  The winds end up spinning in a clockwise direction around low in the southern hemisphere.  The directions of the PGF, CF, and the net inward force are all shown in the picture.

Upper level winds spin clockwise around low pressure in the southern hemisphere.


Step #7 - Upper level winds, high pressure, northern hemisphere


Here initially stationary air near the center of the picture begins to move outward in response to an outward pointing pressure gradient force (PGF is pointing toward low pressure which is on the edges of the picture).  Once the air starts to move, the Coriolis force (CF) will cause the wind to turn to the right.  The dots show the initial outward motion and the turn to the right.  The wind ends up blowing in a clockwise direction around the high.  The inward pointing CF is 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 with high pressure centers as well as with centers of low pressure.  An inward force is needed anytime something moves in a circular path.


Step #8 - Upper level winds, high pressure, southern hemisphere


This is a southern hemisphere upper level center of high pressure. The air starts to move outward again but this time takes a left hand turn and ends up spinning counterclockwise.  The net force is inward again.


Upper level winds review
Here's a quick review of much of what we have covered.  Many of the figures below were on a handout distributed in class today.
Winds spin counterclockwise around L pressure in the northern hemisphere then switch direction and spin clockwise around L pressure in the southern hemisphere.   I think by just remembering a couple of things you can figure this out rather than just trying to memorize it.

The pressure gradient will start stationary air moving toward low pressure (just like a rock placed on a slope will start to move downhill)

The PGF can start stationary air moving.  The PGF always points toward low pressure, so the direction of the initial motion will always be toward low pressure. 

The dots in the figure above show this initial motion and its in toward the center of the picture.  These must both be centers of Low pressure. 

Once the air starts moving the wind will turn to the right or left depending on the hemisphere.  This is the effect of the Coriolis force, the CF turns wind to the right in the northern hemisphere and to the left in the southern hemisphere (remember to always look down stream).   



The northern hemisphere winds are shown at left in the figure above, the southern hemisphere winds are shown at right.  The inward pointing force is always stronger than the outward force so that there is a net inward pointing force.

This initial motion is outward away from the center in the two figures below. 

Low pressure is on the outside edges of the picture.  High pressure must be found in the center of both pictures.



The outward moving air takes a right turn in the left figure above, a left turn in the right figure (you may need to rotate the picture so that you are looking downstream, in the direction the wind is blowing to clearly see the left hand turn).

I'm not sure we'll even get this far in class on Friday.    We'll cover Steps #9 & #10, the Frictional force and surface winds on Monday.

Here are the answers to the questions on the handout and embedded in today's notes.




A net inward force is needed in all three cases.  The thing that changes is the strength of the inward force.






This figure shows the directions of the PGF at each of the highlighted points.  The mistake many people make is to draw the arrow pointing straight toward the L.  But the PGF arrow must also always be perpendicular to the contour lines.





The initial motion is always toward L pressure which must be at the bottom of this map.  Then if you turn the map so that you can look downstream in the direction of the initial motion you'll notice the wind turning to the left indicating this is a southern  hemisphere map.