1. Fundamental Force Balances
AOS 101 Section 301
April 6th, 2009

2. Why Talk About Forces?
All motion in the atmosphere (really, all motion anywhere) is due to the interaction of forces
Luckily for forecasters, the motion in the atmosphere is due to a few specific forces, and fundamental balances between those forces

3. Fundamental Forces The fundamental forces in the atmosphere are:
Pressure-gradient force (PGF)
Coriolis force (COR)
Friction force (FR)
Each of these forces has an important role to play in the motion of the air (wind), and observed wind is a result of various balances between them

4. Pressure-Gradient Force
“Pressure” = Atmospheric pressure
“Gradient” = Change in some quantity over some distance
A strong gradient in pressure implies that pressure changes greatly over a short distance
This pressure gradient creates a force:

5. Pressure-Gradient Force
A divider is placed in a tank of water, separating a deep column of water from a shallow column of water.

6. Pressure-Gradient Force
A divider is placed in a tank of water, separating a deep column of water from a shallow column of water.
The divider is lifted …

7. Pressure-Gradient Force
A divider is placed in a tank of water, separating a deep column of water from a shallow column of water.
The divider is lifted …
The deep column of water pushes into the area inhabited by the shallow column.

8. Pressure-Gradient Force
A divider is placed in a tank of water, separating a deep column of water from a shallow column of water.
The divider is lifted …
The deep column of water pushes into the area inhabited by the shallow column.
Motion in the tank continues until the water level is flat.

9. Pressure-Gradient Force
Recall that pressure is equal to the weight of fluid above you.
Let’s look at this example again, but this time we look at it from the perspective of being at the bottom of the tank:

10. Pressure-Gradient Force

11. Pressure-Gradient Force
At the bottom of the tank, the deep column exerts greater pressure than the shallow column H L

12. Pressure-Gradient Force
At the bottom of the tank, the deep column exerts greater pressure than the shallow column
The divider is lifted… H L

13. Pressure-Gradient Force
At the bottom of the tank, the deep column exerts greater pressure than the shallow column
The divider is lifted…
The deep column of water pushes into the area inhabited by the shallow column. H L

14. Pressure-Gradient Force
At the bottom of the tank, the deep column exerts greater pressure than the shallow column
The divider is lifted…
The deep column of water pushes into the area inhabited by the shallow column.
Motion in the tank continues until the water level is flat.
At this point, there is the same weight of fluid above you at all points along the bottom of the tank – the pressure is equal everywhere, so there is no pressure gradient. Therefore, there is no pressure-gradient force.

15. Pressure-Gradient Force
The pressure-gradient force acts by pushing the fluid on the “high pressure side” stronger than the fluid is pushed on the “low pressure side”
The fluid is forced to move from the area of excess fluid (area of high pressure) to the area with a deficit of fluid (area of low pressure

16. Pressure-Gradient ForceH

17. Pressure-Gradient ForceH

18. Pressure Gradient

19. Wind Speed

20. Coriolis Force
The Coriolis force is an apparent force that is caused by the fact that we are on a rotating planet
We cannot see the planet rotating, so when something is moving, we perceive it as being deflected to the right of its intended trajectory

23. Imagine Dallas, TX fires an ICBM nuclear missile at Winnipeg, Manitoba…

24. Imagine Dallas, TX fires an ICBM nuclear missile at Winnipeg, Manitoba…
Missile starts at Dallas, which is at a latitude of N, rotates with the Earth at a speed of m/s.

25. Imagine Dallas, TX fires an ICBM nuclear missile at Winnipeg, Manitoba…
Missile starts at Dallas, which is at a latitude of N, rotates with the Earth at a speed of m/s.
Missile travels toward Winnepeg which, at a latitude of N, rotates with the Earth at a speed of m/s.
The missile will conserve its angular momentum as it travels north, meaning it will travel around the Earth at the speed of the Earth’s rotation at Dallas, TX

26. Imagine Dallas, TX fires an ICBM nuclear missile at Winnipeg, Manitoba…
Missile starts at Dallas, which is at a latitude of N, rotates with the Earth at a speed of m/s.
Missile travels toward Winnepeg which, at a latitude of N, rotates with the Earth at a speed of m/s.
The missile will conserve its angular momentum as it travels north, meaning it will travel around the Earth at the speed of the Earth’s rotation at Dallas, TX
Since the Earth rotates slower the farther north you go, the missile appears to deflect to the right of its intended target

27. Imagine Dallas, TX fires an ICBM nuclear missile at Winnipeg, Manitoba…
Missile starts at Dallas, which is at a latitude of N, rotates with the Earth at a speed of m/s.
Missile travels toward Winnepeg which, at a latitude of N, rotates with the Earth at a speed of m/s.
The missile will conserve its angular momentum as it travels north, meaning it will travel around the Earth at the speed of the Earth’s rotation at Dallas, TX
Since the Earth rotates slower the farther north you go, the missile appears to deflect to the right of its intended target
Missile lands north of Ottawa.

28. Coriolis Force
IMPORTANT NOTE: While the example given is only valid for an object which moves north or south, the Coriolis force will act on an object moving in any direction
The Coriolis force will act to deflect the object to the right in the northern hemisphere, and to the left in the southern hemisphere

29. Geostrophic Balance
The pressure-gradient force and the Coriolis force can oppose each other, and reach a force balance
Due to Newton’s laws of motion, an object which experiences no net force will move at constant velocity – without accelerating
The balance between the pressure-gradient force and the Coriolis force is known as geostrophic balance

30. Geostrophic Balance L H

31. Geostrophic Balance L
PGF H

32. Geostrophic Balance L
PGF CF H

33. Geostrophic Balance L
PGF
wind CF H

34. Geostrophic Balance L
PGF CF
wind H
The wind defined by geostrophic balance, known as the “geostrophic wind”, moves parallel to lines of constant pressure, with low pressure on the left

35. Geostrophic Balance L H
PGF CF
wind H
The wind defined by geostrophic balance, known as the “geostrophic wind”, moves parallel to lines of constant pressure, with low pressure on the left
Where the pressure-gradient is small, the PGF is also small, resulting in a weak wind. L
PGF
wind CF H

36. Geostrophic Balance L H
PGF CF
wind H
The wind defined by geostrophic balance, known as the “geostrophic wind”, moves parallel to lines of constant pressure, with low pressure on the left
Where the pressure-gradient is small, the PGF is also small, resulting in a weak wind.
Where the pressure-gradient is large, the PGF is also large, resulting in a strong wind. L
PGF
wind CF H

37. H CF CF CF CF
PGF
PGF
PGF
PGF L

38. Height vs Pressure Levels
Meteorologists typically look at data on levels of constant pressure
It would be impossible to see the pressure-gradient, and therefore the PGF, on such a map
However, there is a relationship between pressure and height

39. Height vs Pressure Levels
2 km P3 H L Z P4 Y P5
Pressure surfaces in cross-section
Pressure-gradient at 2 km X X
Because pressure is largest at the ground and decreases with height, a region of low pressure is a region where a given value of pressure is closer to the ground

40. Height vs Pressure Levels
2 km
1 km
3 km H
2 km P3 H L Z Y L
1 km
Height surfaces in cross-section
Height-gradient at P3 X X
Low pressures on a height-surface are the same as low heights on a pressure surface, and high pressures on a height-surface are the same as high heights on a pressure surface.

41. Height vs Pressure Levels
So the PGF is visible on a map of constant pressure as a gradient in height, with the force pointing from high heights to low heights: H

42. Friction
Friction affects geostrophic balance by putting a drag-force on the air: friction always acts in the direction opposite the direction of the wind: FR
wind

43. Friction
This throws the wind out of geostrophic balance – there is now a net force acting on the wind in the direction opposite its motion
PGF FR
wind CF

44. Friction
A new balance can be achieved if the wind tilts slightly toward lower heights/pressure, allowing the CF to balance the FR:
PGF
wind FR CF

45. Friction
In regions where friction is important, we expect the winds to point slightly toward lower pressure
PGF
wind FR CF

46. Winds Near Surface

47. Winds Away From Surface