## Coriolis Acceleration Term in Horizontal Equation of Motion, Scales of Circulation and Wind

Newton's Second Law of Motion (the Equation of Motion) can be restated in the folloiwng manner: an object moving at a certain velocity, will continue to move in a straight line at tht speed, forever, unless acted upon by another force or combination of forces. We have already observed one of these forces, the pressure gradient force. If the pressure gradient force were the only force that affected air motion, then all air parcels would move at right angles to isobars (or height contours....the "equivalent" of isobars if the vertical coordinate is pressure and not height).

We have already observed on the sealevel weather map that although air does indeed drift across isobars from high to low pressure, it does not move at right angles to the isobars, but in a spiraling motion relative to pressure centers. In addition, we now note that the air motion in the "free atmosphere" (the portion of the atmosphere unaffected by friction) tends to be parallel to the isobars or height contours.

How can this be?According to Newton's Second Law of Motion, the motion of air relative to the isobars on a rotating earth, must be accounted for by forces. Clearly there must be an additional "force." This additional force is that due to Coriolis.

Demonstration: Northern Hemisphere

 Coriolis Acceleration

Coriolis Acceleration -- an accleration experienced by frictionless objects moving relative to a rotating surface. On earth, Coriolis acceleration deflects all frictionless moving objects to the right of their path in the Northern Hemisphere, and its magnitude ranges from zero at the Equator to a maximum value at the North Pole. The magnitude of the deflection is greater the speed of the moving object. The equation for Coriolis acceleration can be used to deduce flow characteristics on any planet if the value for that particular planet's rotation is substituted for that of the earth.

 Length of Deflection Due to Coriolis

 Class Example: Wind moving 10 m s-1 (approximately 20 mph)

 Straight Line Distance Travel Time Straight Line Distance Deflection Distance 10,000 km 278.8 hr 450,000 km 1,000 km 27.8 hr 4,500 km 100 km 2.8 hr 45 km 10 km 0.28 hr 457 m 1 km 0.03 hr (1.8 min) 4.57 m 100 m 11 s 4.57 cm 10 m 1.1 s 0.05 cm 1m .1 s 0.0005 cm

Shading indicates scales at which Coriolis accelerations are relatively insignificant in determining wind patterns (i.e., Coriolis acceleration can be dropped out on an order of magnitude basis).  Assumptions:  wind of 10 m s-1 at 400 latitude.

Applications:

 Scale of Circulation Distance Scale Time Scale Examples Macroscale 10,000 km Years to Seasons Synoptic Scale 1,000 km 100s km Weeks to Days Mesoscale 10-100 km Hours Microscale 1 km Minutes