The pressuregradient force
The pressure-gradient force has vertical and horizontal components but, as already noted, the vertical component is more or less in balance with the force of gravity. Horizontal differences in pressure arise from thermal heating contrasts or mechanical causes such as mountain barriers and these differences control the horizontal movement of an airmass. The horizontal pressure gradient serves as the motivating force that causes air to move from areas of high pressure towards areas where it is lower, although other forces prevent air from moving directly across the isobars (lines of equal pressure). The pressure-gradient force per unit mass is expressed mathematically as
1 dp p dn where p = air density and dp/dn = the horizontal gradient of pressure. Hence the closer the isobar spacing the more intense is the pressure gradient and the greater the wind speed (Figure 6.1). The pressure-gradient force is also inversely proportional to air density, and this relationship is of particular importance in understanding the behaviour of upper winds.
Continue reading here: The earths rotational deflective Coriolis force
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