On the relation between wind and distribution of pressure

In studying the relation between the observed wind at various heights, and the pressure distribution at the surface of the earth, one usually takes as the standard of comparison the “geostrophic” wind, which is determined by the pressure distribution alone. If its velocity be denoted by G, G is defined by the equation 2Ω sinλ .ρ G = ∂p /∂v , where Ω is the earth’s angular velocity of rotation,λ is the latitude,ρ is the density of the air,p is the pressure, and ∂p /∂v is the rate of increase of pressure per unit distance normal to the isobars. Self-consistent units are of course to be employed. The direction of this ideal wind is along the isobars, so that the low pressure is on its left. If certain conditions were satisfied in the atmosphere, it is easily shown that the actual wind would always be strictly equal to the geostrophic wind (apart from conceivable free vibrations compatible with constant pressure). These conditions are that (1) the pressure distribution should not be changing with the time; (2) friction should be absent; (3) the velocity should be so small that its square can be neglected. None of these conditions holds in practice. The failure of the first is the chief reason for official encouragement of meteorology. Sir Napier Shaw has shown that the instantaneous centre of the motion in a cyclone moving from west to east would be expected to be north of the centre of the isobars, causing the wind in front of the cyclone to blow outwards from the region of low pressure, while that on the following side blows inwards. The second disturbing influence—friction—is ordinarily the most important near the surface, but dies out at a height of a few thousand feet. Its amount depends on several factors, but chiefly on the temperature lapse rate and the wind velocity; and G. I. Taylor has shown that it causes the surface wind to deviate towards the region of low pressure, while its velocity is decidedly less than that of the geostrophic wind. The third condition is usually approximately satisfied, except near the centres of cyclonic storms. If the pressure distribution were stationary, the terms neglected would amount simply to the “cyclostrophic” term of the ordinary theory; but, owing to its variation with time, they become more complex.