# The centripetal acceleration

Observations in the free atmosphere (above the level affected by surface friction up to about 500 to 1000 m) show that the wind blows more or less at right angles to the pressure gradient (i.e. parallel to the isobars) with, for the northern hemisphere, high pressure on the right and low pressure on the left when viewed downwind. This implies that for steady motion the pressure-gradient force is balanced exactly by the Coriolis deflection acting in the diametrically opposite direction (Figure 6.3A). The wind in this idealized case is called a geostrophic wind, the velocity (Vg) of which is given by the following formula:

dp dn

For a body to follow a curved path there must be an inward acceleration (c) towards the centre of rotation. This is expressed by:

where dp/dn = the pressure gradient. The velocity is inversely dependent on latitude, such that the same pressure gradient associated with a geostrophic wind where m = the moving mass, V= its velocity and r = the radius of curvature. This effect is sometimes regarded for convenience as a centrifugal 'force' operating radially outward (see Note 1). In the case of the earth itself, this is valid. The centrifugal effect due to rotation has in fact resulted in a slight bulging of the earth's mass in low latitudes and a flattening near the poles. The small decrease in apparent gravity towards the equator (see Note 2) reflects the effect of the centrifugal force working against the gravitational attraction directed towards the earth's centre. It is therefore necessary only to consider the forces involved in the rotation of the air c--

Figure 6.3 (A) The geostrophic wind case of balanced motion (northern hemisphere) above the friction layer. (B) Surface wind V represents a balance between the geostrophic wind, Vg, and the resultant of the Coriolis force (C) and the friction force (F). Note that F is not generally directly opposite to the surface wind.

Figure 6.3 (A) The geostrophic wind case of balanced motion (northern hemisphere) above the friction layer. (B) Surface wind V represents a balance between the geostrophic wind, Vg, and the resultant of the Coriolis force (C) and the friction force (F). Note that F is not generally directly opposite to the surface wind.

about a local axis of high or low pressure. Here the curved path of the air (parallel to the isobars) is maintained by an inward-acting, or centripetal, acceleration.

Figure 6.4 shows (for the northern hemisphere) that in a low-pressure system balanced flow is maintained in a curved path (referred to as the gradient wind) by the Coriolis force being weaker than the pressure force. The difference between the two gives the net centripetal acceleration inward. In the high-pressure case, the inward acceleration exists because the Coriolis force exceeds the pressure force. Since the pressure gradients are assumed to be equal, the different contributions of the Coriolis force in each case imply that the wind speed around the low pressure must be lower than the geostrophic value (subgeostrophic), whereas in the case of high pressure it is supergeostrophic. In reality, this effect is obscured by the fact that the pressure gradient in a high is usually much weaker than in a low. Moreover, the fact that the earth's rotation is cyclonic imposes a limit on the speed of anticyclonic flow. The maximum occurs when the angular velocity is f/2 (= V sin 9), at which value the absolute rotation of the air (viewed from space) is just cyclonic. Beyond this point anticyclonic flow breaks down ('dynamic instability'). There is no maximum speed in the case of cyclonic rotation.

The magnitude of the centripetal acceleration is generally small, but it becomes important where highvelocity winds are moving in very curved paths (i.e. around an intense low-pressure vortex). Two cases are of meteorological significance: first, in intense cyclones near the equator, where the Coriolis force is negligible; and, second, in a narrow vortex such as a tornado. Under these conditions, when the large pressure-gradient force provides the necessary centripetal acceleration for balanced flow parallel to the isobars, the motion is called cyclostrophic.

The above arguments assume steady conditions of balanced flow. This simplification is useful, but in reality two factors prevent a continuous state of balance. Latitudinal motion changes the Coriolis parameter, and the movement or changing intensity of a pressure system leads to acceleration or deceleration of the air, causing some degree of cross-isobaric flow. Pressure change itself depends on air displacement through the breakdown of the balanced state. If air movement were purely geostrophic there would be no growth or decay of pressure systems. The acceleration of air at upper levels from a region of cyclonic isobaric curvature (sub-geostrophic wind) to one of anticyclonic curvature (supergeostrophic wind) causes a fall of pressure at

Figure 6.4 The gradient wind case of balanced motion around a low pressure (A) and a high pressure (B) in the northern hemisphere.

lower levels in the atmosphere to compensate for the removal of air aloft. The significance of this fact will be discussed in Chapter 9G. The interaction of horizontal and vertical air motions is outlined in B.2 (this chapter).

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### Responses

• maximilian
How does centripetal force effect weather?
2 years ago
• ELEN
How does centrifugal force affect weather?
2 years ago
• christina jaeger
What is the origin of centripetal force in air circulating around a low pressure zone?
2 years ago
• Isabella
Are low pressure centrifugal or centripetal?
3 years ago
• joonas
Do meteorological models account for centripetal force?
5 years ago
• ralf
Are high and low pressure systems subject to centripetal force?
6 years ago
• anne
Is weather affected by centripetal force?
7 years ago