Amazing merry-go-round animation shown in class http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/gifs/coriolis.mov Note that the merry-go-round rotates in the opposite sense as the Northern Hemisphere Earth, so the deflection is to the left. You can also think of it as a good approximation to the effects of rotation near the South Pole. The colorful still pictures I showed about the Coriolis Force can be downloaded here Next I include a series of animated of constant angular momentum oscillations described in chapter 1 of Holton. They are avi files, which vary in size from about 10 to 20 Mbyte. Ideally you should click on the link and your computer will automatically open an application that allows you to play the animation. Failing this, you may be able to save them to disk and open them with your favorite player. I use QuickTime on my mac. I made these animations in MATLAB. At the bottom of the page, I have a link to the script for the last two animations. You can run it yourself and choose your own initial conditions. Send me an email if you have trouble and you think I can help. Because rocks that
compose
Earth cannot sustain a shear force for long, Earth is not a sphere but
instead
it is an oblate spheroid (there's a bulge in the tropics). True gravity
on
Earth has a component normal to the surface that is equal and opposite
to
the centrifugal force of an object rotating with Earth. Imagine that the
Earth
ceases to rotate but remains an oblate spheriod. Without the
centrifugal force
from rotation, nothing balances the component of true gravity that
attracts
objects towards the poles. For small deviations from the pole on a
frictionless
surface, we can assume R is just the distance from the pole.
Acceleration
along longitudes is then dv/dt
= - Omega2R.
This equation gives rise to simple harmonic motion d2R/dt2
= - Omega2R.
The animation gravity.avi illustrates this motion from the inertial frame. The same animation
holds
true for a rotating Earth as well because the object has zero angular
momentum
at the pole and the frictionless surface imparts no torque. To
emphasize that
the Earth is rotating, the Greenwich Meridian (labeled 0 deg) is shown
rotating
in the animation gravity_rot.avi. (You
might
want to skip this one if you have low bandwidth.) Animation gravity_rot_traj.avi is the same motion but the green trajectory illustrates the motion seen from the rotating reference frame. This is an animated version of Holton Fig 1.7. The oscillations here are known as constant angular momentum animations. The constant is zero! You are seeing the Coriolis Force causing deflection to the right in the rotating frame. Download the MATLAB
script and make your own movies from gravity_rot.m Now consider constant angular momentum oscillations that do not go through the pole, but still remain close enough to approximate all motions in a plane tangent to the pole. The angular momentum is not zero. The animation buddha_xtoss.avi is a view from an inertial frame of a Buddha sitting at rest facing south on Earth. He tosses a ball eastward at the start of the animation. The ball sliding on a frictionless Earth then takes the red elliptical-like orbit as observed from the inertial frame. The ball's path is essentially a circular orbit perturbed by something like a 24-hour oscillations along a line that runs parallel to the direction of the initial toss (recall gravity.avi). This new animation shows that the paths of the ball and Buddha are intertwined. In the 24 hrs it takes for the Buddha to return to its starting point, the ball passes behind the Buddha twice, and the ball runs into the Buddha at 12 and 24 hrs. This animation illustrates why there is a factor of 2 in the Coriolis parameter. Finally, because it is mind-warping, buddha_xtoss_rotating.avi shows the motion from the rotating frame. Download the MATLAB script and make your own movies from inertial.m The equations that give rise to the motion in these movies were taken from the following paper. Reference: Durran, Dale R. 1993: Is the Coriolis force really responsible for the inerial Oscillation, BAMS 74 , 2179-84. |
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