Geostrophic Force (Coriolis Effect) and Geostrophic Wind
Under normal circumstances (i.e. if the Earth were not spinning) air would just move from high to low pressure, across the isobars (due to the Pressure Gradient Force, or PGF). The PGF acts at right angles to the isobars, from high to low pressure. Its size depends on the spacing of the isobars and air density.
However, this is only true around the Equator. In the Northern Hemisphere, air actually moves clockwise round a high pressure area and anticlockwise round a low, because the Earth is spinning, and deflects normal air movement (over the ground), until eventually the wind blows along the isobars (instead of across) at around 2,000 feet. Thus, an imaginary force appears to act at right angles to the rotating Earth, causing a moving body to follow a curved path opposite to the direction of the Earth’s rotation.
Not only that, the Earth moves faster at the equator than it does at the Poles (based on a cosine relationship), so, if you fire an artillery shell from the North Pole to the Equator, progressively more of the Earth’s surface would pass under its track, giving the illusion of the object curving to the right (or West of A) as it lags behind – the Earth is moving slower towards the North. If you threw whatever it was the other way, it would “move” to the East of B, because you are adding the Earth’s movement at both latitudes. That is, B will be moving slower relative to A. In other words, a bullet might fly in a straight line, but its target will move to the right.
This apparent movement (East or West) is like extra centrifugal force, which is called in some places the Coriolis Effect, but actually is Geostrophic Force when it refers to air movement, although no “force” is involved, hence the use of the word “effect”. That is, the wind at 2,000 feet is assigned a geostrophic property, which is only true when the isobars are straight and parallel. They are actually mostly curved, so the geostrophic wind becomes the gradient wind. The extra energy to keep the air curving comes from the cyclostrophic force, which is similar to centripetal force, as it operates inward, at 90° to the instantaneous motion, to the right in the Northern Hemisphere and the left in the Southern Hemisphere, until it balances the PGF and the wind follows the isobars. Around a low, it is the difference between PGF and GF – around a high, between GF and PGF.
The GF increases with the speed of the air, and it is dependent on the sine of the latitude, being maximum at the Poles (sin 90° = 1) and zero at the Equator.
So, the geostrophic wind is the imaginary wind that would result if the Coriolis and Pressure Gradient forces are balanced. When the air starts to move faster, the geostrophic force is increased and deflection starts again. Coriolis force is directly proportional to wind speed, in that it is zero when the wind is still and at its maximum when the wind is at maximum speed. It is also zero at the Equator and at its maximum at the Poles (meaning that the above relationships break down near the Equator, and isobars cannot be used to represent weather patterns. Streamlines are used instead).
As always, there is a mathematical solution:
GF = 2wrVsinq
where w = the Earth’s rotational velocity, r is density, V is the wind speed and q is the latitude. You can see that, as latitude increases, so will the geostrophic force, or that the wind speed will decrease. To get windspeed, at 2,000 feet, the wind is parallel to the isobars (when they are straight and parallel), meaning that the PGF must be balanced by another force, which we shall call GF. Now all you need to do is swap GF for PGF and play with the formula:
V = PGF
It also shows that the windspeed increases with height as density reduces, but it all breaks down within about 15° of the Equator, or you would have an infinite windspeed. Given the same pressure gradient at 40°N, 50°N and 60°N, the geostrophic wind speed will be greatest at 40°N.
As you descend, friction with trees, rocks, etc. will slow the wind down by just over 50%, which lessens the geostrophic effect and gives you an effective change of wind direction to the left, so there are two forces acting on air moving from high to low pressure – Coriolis effect which deflects it to the right and frictional effect which brings it back to the left slightly. Over the sea, the geostrophic effect will be less, giving about 10° difference in direction, as opposed to the 30° you can expect over land (the speed reduces to about 70% over water, and 50% over land). If the winds are high, you could get into a stall on landing as you encounter windshear, described later.
The Coriolis effect depends directly on latitude and wind speed. It is greater for stronger winds, ranging from zero at the Equator to a maximum at the Poles.
In any case, wind in a low would be lower than the equivalent geostrophic wind, and higher round a high. In the case of a low in the Northern Hemisphere, the centrifugal force goes in the same direction as the Coriolis force. Since the forces must remain in balance, the Coriolis force weakens to compensate and reduce the overall wind speed (the PGF doesn’t change), so the wind will back, tend to go inwards and contribute towards the lifting effect, since it is forced up, to cause adiabatic cooling, and precipitation.
Inside a high, air movement (winds), will tend to increase with the help of centrifugal force, other things being equal, contributing towards the subsidence and adiabatic warming from compression. However, this is offset by the pressure gradient in a low being much steeper, creating stronger winds anyway. This is known as the isallobaric effect, since lines joining places with an equal rate of change of pressure are isallobars. Centrifugal force helps a low by preventing it being filled, and causes a high to decay by removing mass from it.
According to Professor Buys Ballot’s Law (a Dutch meteorologist), if you stand with your back to the wind in the Northern hemisphere, the low pressure will be on your left (on the right in the Southern hemisphere). The implication of this is that, if you fly towards lower pressure, you will drift to starboard as the wind is coming from the left (a common exam question). It’s the opposite way round in an anticyclone. Buys Ballot’s Law, by the way, had already been deduced by US meteorologists William Ferrel and James Coffin, but they didn’t get to be famous. Note that it does not always apply to winds that are deflected by local terrain, or local winds such as sea breezes or those that flow down mountains.
Geostrophic winds occur above the friction layer and develop in response to gradients in atmospheric pressure over large regions of the surface of the earth.
Regions of high and low atmospheric pressure develop at the surface of the earth for a variety of reasons, including heating or cooling, and the rising or sinking of air due to surface topography or movements of air at higher levels in the troposphere. When pressure changes occur gradually over a large area, the isobars describing the horizontal change in pressure, or the pressure gradient, will take on a banded appearance
Much of the convection that takes place on earth is more localised. When low or high pressure develops more locally, the resulting high- and low-pressure regions are cell-like systems, and isobars describing the patterns of air pressure will include one or more closed, circular isobars,
The force acting on a parcel of air, causing it to accelerate from a region of relative high pressure to a region of relative low pressure is referred to as the pressure gradient force (or PGF). The PGF points from high pressure to low pressure, whether the regional isobars are parallel or concentric.
On a non-rotating planet, the principle force which would act on a parcel of air between the subtropical high and the equatorial low would be the pressure gradient force. If that force were the only force present, and friction were not acting on the parcel, the air parcel would accelerate in the direction of this force, toward the equator. On such a planet, the wind would flow in a direction perpendicular to the isobars, the precise direction of the pressure gradient force. High and Low pressure areas on a non-rotating planet would quickly fill in as air motions are principally from the regions of “excess air” (the high pressure centers) to regions of air deficit (the low pressure center).
An air parcel initially at rest will move from high pressure to low pressure because of the pressure gradient force (PGF). However, because the earth is rotating, the winds are deflected by an apparent force called the Coriolis force, producing what is called the Coriolis effect. As an air parcel begins to move, it is deflected by the Coriolis force to the right in the northern hemisphere (to the left on the southern hemisphere).
The horizontal air pressure gradient causes air parcels to accelerate across isobars from areas of high pressure toward areas of low pressure. The Coriolis effect then deflects air parcels to the right in the Northern Hemisphere. As the wind gains speed, the Coriolis effect increases in magnitude until it balances the pressure gradient force. The result is an unaccelerated horizontal wind blowing parallel to isobars that is called the geostrophic wind.
Geostrophic wind at High Latitude
With a geostrophic wind pressure gradient force (PGF) is balanced by coriolis force:
PGF = coriolis
coriolis = 2wpVsinLat where w = rate of rotation of the Earth, p = air density and V = wind speed.
PGF = 2wpVsinLat
V = PGF/ 2wpsinLat
If w and p are constant V varies inversly with the sine of latitude. i.e. for a given pressure gradient, as latitude increases wind speed decreases.