The Coriolis force arises from the fact that the movement of masses over the earth's surface is referenced to a moving co-ordinate system (i.e. the latitude and
longitude grid, which 'rotates' with the earth). The simplest way to visualize how this deflecting force operates is to picture a rotating disc on which moving objects are deflected. Figure 6.1 shows the effect of such a deflective force operating on a mass moving outward from the centre of a spinning disc. The body follows a straight path in relation to a fixed frame of reference (for instance, a box that contains the spinning disc), but viewed relative to co-ordinates rotating with the disc the body swings to the right of its initial line of motion. This effect is readily demonstrated if a pencil line is drawn across a white disc on a rotating turntable. Figure 6.2 illustrates a case where the movement is not from the centre of the turntable and the object possesses an initial momentum in relation to its distance from the axis of rotation. Note that the turntable model is not strictly analogous since the outwardly directed centrifugal force is involved. In the case of the rotating earth (with rotating reference co-ordinates of latitude and longitude), there is apparent deflection of moving objects to the right of their line of motion in the northern hemisphere and to the left in the southern hemisphere, as viewed by observers on the earth. The idea of a deflective force is credited to the work of French mathematician G.G. Coriolis in the 1830s. The 'force' (per unit mass) is expressed by:
where Q = the angular velocity of spin (15 °hr-1 or 2n/24 rad hr-1 for the earth = 7.29 X 10-5 rad s-1); ^ = the latitude and V = the velocity of the mass. 2Q sin ^ is referred to as the Coriolis parameter f).
The magnitude of the deflection is directly proportional to: (1) the horizontal velocity of the air (i.e. air moving at 10 m s-1 has half the deflective force operating on it as on that moving at 20 m s-1); and (2) the sine of the latitude (sin 0 = 0; sin 90 = 1). The effect is thus a maximum at the poles (i.e. where the plane of the deflecting force is parallel to the earth's surface). It decreases with the sine of the latitude, becoming zero at the equator (i.e. where there is no component of the deflection in a plane parallel to the surface). The Coriolis 'force' depends on the motion itself. Hence, it affects the direction but not the speed of the air motion, which would involve doing work (i.e. changing the kinetic energy). The Coriolis force always acts at right-angles to the direction of the air motion, to the right in the northern hemisphere (f positive) and to the left in
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Figure 6.2 The Coriolis deflecting force on a rotating turntable. (A) An observer at X sees the object P and attempts to throw a ball towards it. Both locations are rotating anticlockwise. (B) The observer's position is now X' and the object is at P'. To the observer, the ball appears to follow a curved path and lands at Q. The observer overlooked the fact that position P was moving counterclockwise and that the path of the ball would be affected by the initial impulse due to the rotation of point X.
Figure 6.2 The Coriolis deflecting force on a rotating turntable. (A) An observer at X sees the object P and attempts to throw a ball towards it. Both locations are rotating anticlockwise. (B) The observer's position is now X' and the object is at P'. To the observer, the ball appears to follow a curved path and lands at Q. The observer overlooked the fact that position P was moving counterclockwise and that the path of the ball would be affected by the initial impulse due to the rotation of point X.
the southern hemisphere f negative). Absolute values off vary with latitude as follows:
Latitude 0° 10° 20° 43° 90° fPO-4 s-1) 0 0.25 0.50 1.00 1.458
The earth's rotation also produces a vertical component of rotation about a horizontal axis. This is a maximum at the equator (zero at the poles) and it causes a vertical deflection upward (downward) for horizontal west/east winds. However, this effect is of secondary importance due to the existence of hydrostatic equilibrium.
speed of 15 m s-1 at latitude 43° will produce a velocity of only 10 m s-1 at latitude 90°. Except in low latitudes, where the Coriolis parameter approaches zero, the geo-strophic wind is a close approximation to the observed air motion in the free atmosphere. Since pressure systems are rarely stationary, this fact implies that air motion must change continually towards a new balance. In other words, mutual adjustments of the wind and pressure fields are constantly taking place. The common 'cause-and-effect' argument that a pressure gradient is formed and air begins to move towards low pressure before coming into geostrophic balance is an unfortunate oversimplification of reality.
3 The geostrophic wind
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