Theory of Winds
Pressure Gradient Force (PGF)
Air is a fluid. One important property of fluids is that the pressure at a point in the fluid acts in all directions. This means that air can exert a pressure horizontally as well as vertically.
Imagine a parcel of air with different pressure on either side of it:
Pressure is just the force acting on each square metre. So if the parcel has different pressures on either side of it, it has different forces on either side.
There is therefore a resultant force acting on the parcel from higher pressure to lower pressure. This is the pressure gradient force. The size of the pressure gradient force depends upon the rate of change of pressure with distance.
It is always directed towards the lower pressure.
If the pressure gradient force were the only force acting, the wind would blow straight across the isobars from high to low pressure.
Coriolis or Geostrophic Force
This is an imaginary force. We use the force to make an allowance for the effect of the earth’s rotation.
To an observer on the earth’s surface the effect of this force is to deflect moving air to the right of its direction of motion in the northern hemisphere and to the left of its direction of motion in the southern hemisphere. The force becomes zero at the equator. Coriolis force only affects objects moving relative to the earth’s surface.
Geostrophic Winds
These winds only occur in certain conditions. They only occur when PGF and Coriolis force are equal and opposite and these are the only forces acting. The isobars must be straight and parallel. The winds cannot occur less than 600m above the earth’s surface so that friction at the earth’s surface is negligible.
Imagine an experiment where a parcel of air is placed at a point in a set of straight parallel isobars:
Initially the parcel of stationary so it is not affected by Coriolis force. PGF will act upon the parcel so the parcel begins to accelerate in the direction of the PGF. Once the parcel is moving Coriolis force begins to act. As the parcel is moving slowly Coriolis force is small. Coriolis force acts at 90° to the direction in which the parcel is moving. PGF is fixed by the isobars and so the parcel has two forces acting upon it. The parcel accelerates in the direction of the resultant of the two forces, to the right of its original direction of travel. As the parcel’s speed increases the size of Coriolis force acting upon it increases. The parcel continues to accelerate and deviates further to the right.
Eventually a balanced situation occurs. PGF and Coriolis force are equal and opposite. There is no resultant force acting upon the air, so the parcel moves with steady speed parallel to the isobars.
Buys Ballot’s Law
It can be seen from the diagram that if an observer faces the wind in the northern hemisphere, the low pressure lies to his right, whilst in the southern hemisphere the low pressure lies to his left. These facts were first propounded by Buys Ballot
Geostrophic Wind Speed
It is possible to estimate the geostrophic wind speed, and hence the surface wins speed, at any point on a chart. The geostrophic wind is the wind, which blows when Coriolis Force and Pressure Gradient Force are the only forces acting and these forces are equal in magnitude. The equation for this becomes
1/ r ∂p/∂n = 2 Ω v sin lat
This equation has been used to draw up a geostrophic wind scale.
Using the scale:
Winds with curved isobars
These winds blow more that 600m above the earth’s surface, so friction is negligible. The isobars are curved and so centrifugal force must be taken into account. The wind, which blows along curved isobars is known as a Gradient Wind. Centrifugal Force is an imaginary force, which is used for air travelling in a circle. The force always acts out of the circle.
(A) Low Pressure: Cyclonic flow
PGF acts inwards and centrifugal force acts outwards. As with geostrophic winds a parcel of air placed in the isobars would initially move off with PGF. Coriolis force will deflect it to the right in the northern hemisphere until a balanced situation is achieved.
When the forces balance:
CORIOLIS FORCE = PRESSURE GRADIENT FORCE - CENTRIFUGAL FORCE
Since centrifugal force is acting with Coriolis force the parcel will not have accelerated to the geostrophic wind speed when the balance is achieved. The gradient wind around a depression is less than the geostrophic wind would be for the same isobar spacing. This is referred to as sub-geostrophic.
(B) High Pressure: Anticyclonic flow
Here PGF and Centrifugal force both act outwards. Air moves with the PGF but is deflected until a balance is achieved.
CORIOLIS FORCE = PRESSURE GRADIENT FORCE + CENTRIFUGAL FORCE
The parcel will accelerate to a speed higher than the geostrophic wind speed before the forces balance. The gradient wind around a high is greater than the geostrophic wind would be for the same isobar spacing. This is referred to as super-geostrophic.
Surface winds
Friction
Most of the frictional drag results from eddies which produce rapid irregular fluctuations in wind speed and direction. This is known as turbulence. The size of the frictional force depends upon the roughness of the surface.
Friction always acts to oppose motion.
Straight Isobars
These forces will act:
1. PGF fixed by the isobars.
2. Coriolis Force.
3. Friction.
The size and direction of Coriolis Force and Friction depend upon the wind speed.
The resultant wind blows at an angle to the isobars. This angle, a, is called the “angle of indraught”.
Over the land the surface wind varies widely. Usually ¯ to ½ of Geostrophic and the value of a is 20° to 30°, but it may reach 40°.
Over the sea the surface wind is about ½ to ° of Geostrophic and a is 10° to 20°.
Convergence & divergence
Convergence is a term used to describe the situation where air is accumulating in a certain area. Divergence is used to describe the situation where air is leaving an area. If all winds were geostrophic there would be no convergence and no divergence.
Convergence and divergence can be caused by the direction in which the air is moving:
Confluence
Diffluence
A change in the velocity of the air can also produce convergence and divergence. Divergence occurs where air is leaving an area more quickly than it is arriving. Convergence occurs where air is arriving more quickly than it is leaving.
Divergence
Convergence
It is possible that 2 effects can occur at once
e.g. Confluence and a change in speed
Divergence in the upper troposphere will produce convergence near the surface, with air rising in the troposphere. Convergence in the upper troposphere will produce divergence near the surface and air sinking in the troposphere.
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Meteorology 2
dariusz.lipinski