Why does the wind "blow", and what factors are involved?
In the 'free' atmosphere on our rotating earth, the movement of air is forced by differences in atmospheric pressure between one location and another: this difference, over a specified distance, is known as the PRESSURE GRADIENT.
It might be assumed that once there is a pressure gradient, that air would travel directly from high pressure to low: this doesn't happen, because as soon as it begins to move, it undergoes an apparent deflection owing to the fact that we live on a rotating planet. In the Northern Hemisphere, the 'deflection' is towards the right of air motion; in the Southern Hemisphere it is towards the left. A balance is achieved whereby the force due to the Pressure Gradient (PRESSURE GRADIENT FORCE, or PGF) exactly equals the deflection due to planetary motion (the CORIOLIS DEFLECTION or ACCELERATION [CA]).
The wind direction is that summarised in Buys Ballots Law (q.v.)
The wind resulting from these ideal conditions is known as the GEOSTROPHIC WIND - a theoretical wind (as measured on a chart using a GEOSTROPHIC SCALE) that assumes the following:
(b): the wind is not speeding-up (accelerating) or slowing-down (decelerating) along the line of travel (isobars/contours are parallel).
(c): the pressure pattern is not changing (no atmospheric development).
(d): there are no frictional forces at work, either molecular, or due to passage over tangible obstacles (e.g. the surface of the earth).
(e): the wind blows horizontally - i.e. there is no vertical motion involved.
Looking at these factors in order:
(a): Unless the air motion is gentle, this factor must be allowed for by finding the curvature of the isobars/contours and subtracting (cyclonic curvature) or adding (anticyclonic curvature) a correction depending upon the strength of the geostrophic wind & the radius of curvature of the isobar/contour. For a tightly curved isobaric/contour pattern around a small-scale low pressure area in mid-latitudes, the value will be in the range 10 to 30 knots at geostrophic wind speeds of over 80 knots. Equally important is the anticyclonic correction: even for a gently curved isobaric pattern around a slow-moving anticyclone, an extra 5 to 10 knots can be added to the theoretical calculation - enough for example to tip the balance between a 'Force 7' and a 'Gale'! (Unlike the cyclonic correction, there is a theoretical maximum for the anticyclonic correction of twice Geostrophic value).
If the pattern is curved, then the corrections applied above will give rise to the term known as the GRADIENT WIND, which is loosely taken to be the 'free-air' value (very roughly around 900 mbar/900 m), from which the wind at the surface can be obtained - (see below).
However, even this is problematic, as it assumes that the pressure system is not moving, i.e. the air takes a path exactly governed by the pattern on the chart. In reality, especially with developing depressions, the movement of the low itself will mean that the air-path adopts a differently curved trajectory to that of the feature generating the winds. In particular, for fast-moving depressions in mid-latitudes, the geostrophic (theoretical) wind speed is probably a better approximation to the 'free-air' flow than trying to apply a correction due to curvature.
(b): When air speeds up or slows down due to changing pressure gradients along the line of travel, then motions are imparted which cause the air to deviate from the ideal path. This flows naturally from the fact that the ideal wind is trying all the time to achieve a balance between the PGF and the Coriolis Acceleration (CA). As the latter is proportional to the wind speed, any change in same will alter the deflection; the 'flow' will become unbalanced, and a 'correction' needs to be achieved, but not before the air has deviated somewhat offline (so-called 'CROSS-CONTOUR FLOW'). The effects are very important at jet-stream levels, where they lead to cross-contour movements of sufficient magnitude to cause development in the column of air below. (e.g. Jet exits, entrances), and also give rise to the potential for clear air turbulence (CAT).
(c): This is important near the surface where there are tight gradients of pressure tendency, i.e. as found in advance of, and particularly to the rear of some rapidly developing cyclonic disturbances in mid-latitudes. These ISALLOBARIC effects can be to add (rapidly rising pressure), or subtract (rapidly falling pressure) well over 10 knots to the theoretical geostrophic wind, and can be as much as 40 knots in the most 'damaging' case, where a explosively deepening low has passed by, and pressure rises sharply behind due to events in the upper air (confluent trough, q.v.).
Couple this effect with the possible downward penetration of momentum from the upper atmosphere associated with the dry intrusion (q.v.), and some highly damaging wind-gusts can result.
(d): Of all the 'controlling' additional forces, this one is the most evident from day-to-day. It is the reason why the wind that we observe blows across the isobars at an angle (from high to low pressure), rather than directly along the isobars. As friction due to the roughness of the earth's surface takes hold, the PGF gains dominance over the CA, and 'turns' the wind away from the beloved 'tramlines' of the tv weather presenters. The greater the roughness (i.e. towns, cities) the greater the effect; for this reason, wind directions over the open sea are more closely allied to the isobaric direction averaging just 8 degrees departure, as opposed to some 20 degrees or more over land.
Additionally, overland the stability of the air must be considered. Highly stable air will damp vertical exchange (or mixing) between the friction-less/'free' air (roughly above 900 mbar/900 metres) and the air in direct contact with the earth's surface (within the atmospheric boundary layer). In such conditions, the surface wind can be backed from the isobaric flow by as much as 40 degrees (perhaps more), and this effect is particularly enhanced at night in conditions of light gradient. Conversely, in unstable conditions, where vertical mixing is particularly effective, then the 'real' wind direction is sometimes only 10 or 15 degrees away from that taken from the isobars.