Coriolis Acceleration and Scales of Circulation

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.

Animation

 

Coriolis Acceleration in Natural Coordinates =

2 X (Angular Velocity of Earth) X Wind Speed X sine of the latitude

Angular Velocity of Earth = 360 deg/day =
7.292 X 10-5 radians s-1

 

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

General Circulation

Synoptic Scale

1,000 km

100s km

Weeks to

Days

Hurricanes Wave Cyclones
Thunderstorm Complexes

Mesoscale

10-100 km

Hours

Thunderstorm

Microscale

1 km

Minutes