30 June 2009

Rogue waves


Vagues scélérates - Ma-Tvideo France3
Les disparitions de navires en pleine mer étaient longtemps attribuées à des vagues géantes. Une inanité, selon les scientifiques, jusqu'au jour où une vague de 26 mètres de haut fut effectivement enregistrée, en 1995.

19 June 2009

The coriolis effect

 Bart experimenting on the coriolis force..


 One can find both counterclockwise and clockwise flowing drains in both hemispheres. Some people would like you to believe that the Coriolis force affects the flow of water down the drain in sinks, bathtubs, or toilet bowls.
Don’t believe them! The Coriolis force is simply too weak to affect such small bodies of water.

   Normally, objects in contact with the ground travel the same speed as the ground they stand on. As a result, the Coriolis effect generally doesn't have a noticeable effect to people on the ground; the speed of the point you're standing on and the speed of the point you're stepping onto are too close for you to tell the difference. Or, looking back at the Coriolis effect equation above, if the velocity relative to the rotating frame (the Earth) is zero, so is the Coriolis effect.
   However, when an object moves north or south and is not firmly connected to the ground (air, artillery fire, etc), then it maintains its initial eastward speed as it moves. This is just an application of Newton's First Law. An object moving east continues going east at that speed (both direction and magnitude remain the same) until something exerts a force on it to change its velocity. Objects launched to the north from the equator retain the eastward component of velocity of other objects sitting at the equator. But if they travel far enough away from the equator, they will no longer be going east at the same speed as the ground beneath them.
   The result is that an object traveling away from the equator will eventually be heading east faster than the ground below it and will seem to be moved east by some mysterious "force". Objects traveling towards the equator will eventually be going more slowly than the ground beneath them and will seem to be forced west. In reality there is no actual force involved; the ground is simply moving at a different speed than its original "home ground" speed, which the object retains.
   Consider Figure 1. Yellow arrow 1 represents an object sent north from the equator. By the time it reaches the labeled northern latitude, it has traveled farther east than a similar point on the ground at that latitude has, since it kept the eastward speed it had when it left the equator. Similarly, green arrow 2 started south of the equator at a slower eastward speed, and doesn't go as far east as the ground at the equator...seeming to deflect west from the point of view of the ground.


 Things moving towards the poles curve to the east, things moving away from the poles curve to the west, things moving east curve towards the equator and things moving west curve towards the poles. In other words, air (or anything else) moving freely in the northern hemisphere deflect to the right, air moving freely in the southern hemisphere deflect to the left. And this is what the result of the vector cross products in the Coriolis effect equation says as well, in its mathematical shorthand.
   What does this mean for, say, weather systems? Take, for example, a low pressure center, where there's less air than in the area around it. If there's less air in one place than in the surroundings, air will try to move in to balance things out.
   Air starting at rest with respect to the ground will move towards a low pressure center. Such motion in the Northern Hemisphere will deflect to its right, as shown in Figure 4. However, the forces which got the air moving towards the low pressure center in the first place are still around, and the result will be a vortex of air spinning counter-clockwise. Air will try to turn to the right, the low pressure system will try to draw the air into itself, and the result is that air is held into a circle that actually turns to the left. Without the Coriolis effect, fluid rushing in towards a point could still form a vortex, but the direction would either be random or depend solely on the initial conditions of the fluid.
   The eye of a hurricane is a clear example of fast winds bent into a tight circle, moving so fast that they can't be "pulled in" to the center. The very low pressure at the center of the hurricane means that there is a strong force pulling air towards the center, but the high speed of the wind invokes the Coriolis effect strongly enough that the forces reach a kind of balance. The net force on air at the eye wall is a centripetal force large enough to keep the air out at a given radius determined by its speed.



This low pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force.