Circulation Systems Circulation Systems

Part Four: The Coriolis Force

The Coriolis force describes an apparent force that is due to the rotation of the Earth

Understanding Coriolis Forces

Imagining that you are on a merry-go-round (a flat rotating platform). Two points, X and Y are marked on the platform. You are at the point X and you want to slide a frictionless puck from X to Y. If the platform is stationary the puck would slide along a straight line path from X to Y with a constant speed.

What happens when the platform is rotating anticlockwise?

Velocity vector Suppose you push the puck horizontally with a velocity vx. Since the platform is rotating, at the instant you release it, the puck will have the same vertical velocity vy as you. Therefore, the velocity v of the puck with respect to the ground will have two components vx and vy. This time the puck will not reach the point Y but instead veers off to the right, that is the puck now appears to travel in a curved path with constant speed from your point of view (noninertial frame of reference). The puck has an angular momentum L,

L = m vy r

where m is its mass, r is the distance from the axis of rotation and vy is the tangential component of its velocity vector at any instant.

Coriolis effect

An important physical law is that the angular momentum of an object does not change unless acted upon by a torque (force times perpendicular distance). This is known as the Law of Conservation of Angular Momentum (think of ice skaters spinning). For our sliding puck there are no torques acting on it, therefore the product

vyr = constant

Therefore, when the radius r increases, the velocity vy must decrease. This means that the puck must deflect to the right "as it is left behind" as it now has a smaller tangential speed than a point below it on the rotating platform. Also, a puck pushed toward the centre will also veer to the right. In this case the radius decreases and the velocity of the puck increases, therefore, it moves faster then the rotating platform and is deflected to the right. To an observer in an inertial frame of reference viewing the rotating platform from above always sees the puck slide in a straight line path with constant speed while the platform rotates under the moving puck. For the observer in the inertial frame of reference, the acceleration of the puck is zero, there the total horizontal force acting on the puck must also be zero. For the observer in the noninertial frame of reference, the puck must accelerate because it moves in a curved path and therefore the puck must be acted upon by some horizontal force. This force is called the Coriolis force. It not a ŅrealÓ force, it is only an artefact of an observation made in a noninertial frame of reference. The relatively slow rotation of the Earth makes its effects very small in situations such as throwing stones or walking. However, many of the atmospheric and oceanic characteristics that we take for granted are due to the effects of the Coriolis force.

Coriolis and the Atmosphere

To discuss wind patterns, consider standing on the top of a spinning globe (north pole). You attempt to throw a stone due south, parallel to the surface. From above the North Pole this is qualitatively the same situation as the platform rotating anticlockwise. Thus the stone will veer to the thrower's right (west).

If you were standing at the South Pole then the Earth would be rotating in a clockwise sense. Therefore, the stone would veer to the left (west). The consequences of the Coriolis force due to the EarthÕs rotation is that for winds from any direction:

Winds in the southern hemisphere will always be deflected to the left.
Winds in the northern hemisphere will always be deflected to the right.

The magnitude of the Coriolis force F depends upon the density of the air r, the wind speed v, the angular speed of the EarthÕs rotation w (w = 2p / T where T is the period of the EarthÕs rotation: T = 24 h) and the latitude f as described by the equation

F = 2 vrwsin(f)

The Coriolis force is a maximum at the poles (f = 90°) and zero at the Equator (f = 0). There are several major prevailing surface wind patterns that are in part due to Coriolis forces. One of these is the trade winds, the prevailing east-to-west winds within the tropics. North of the equator, the wind is from the northeast, and south, it is from the southeast. The energy source for these winds is the constant warming of the air near the equator. This warmed air expands and rises, and cooler, denser air from north and south of the equator moves toward the equator near the surface. In the process, this moving air is forced westward in the northern hemisphere and also westward in the southern hemisphere by the Coriolis forces. One infuriating feature of the trade winds to sailors, is that the warmed air at the equator is rising so strongly that the winds from the northeast and southeast are drawn off the surface, producing little wind. This region is known as the equatorial doldrums. The north / south meeting point of the winds is not precisely the equator. The warming is highest in the summer hemisphere, which tends to shift the doldrums toward the summer hemisphere. Also, because there is more land in the northern hemisphere, heating of the air there is greater, and this shifts the median latitude of the doldrums slightly north of the equator.

Storms centre on regions of low pressure. Unsettled weather occurs where the flow of air is towards the centre and then rises and if the air is moist then as it rises the air cools leading to condensation and rain. Because of the Coriolis Effect, the winds will move in a clockwise winds sense around such low pressure centers in the southern hemisphere (anticlockwise in northern hemisphere).

Clear, dry weather is associated with centres of high pressure. Surface winds flow away from such centers. In the southern hemisphere this outward flowing air veers to the left and forms the characteristic anticlockwise flow around high-pressure centers (opposite direction in the northern hemisphere).

Memory aid:

A beforeC
H beforeL
High = Anticlockwise Low = Clockwise

Coriolis effect

A pressure gradient is the change in pressure divided by the distance measured in the direction from high to low pressure. Therefore, the pressure gradient is responsible for a force acting on the air in the direction from high to low pressure. This is sometimes called the pressure gradient force. In the southern hemisphere, moving air is deflected to the left by the Coriolis force (right in the northern hemisphere).

This is Circulation Systems
Part Four: The Coriolis Force
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Go Back to Part One: Introduction   This page was last updated in June 2001
by Chris Stewart. Email him if you find anything amiss.