1. Chapter 10: Atmospheric Dynamics

2. General Concept Definition:
- Wind: air in motion relative to earth’s surface
Air moves in response to difference in pressure. Thus, pressure difference is a driving source. But winds do not blow directly from a higher pressure region to a lower pressure regions because of influence from different forces.
Solid lines: isobar, arrows: winds

3. Force Newton’s Second Law of Motion: F = ma
Force = mass x acceleration
Imbalance of forces causes net motion
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What do we mean by a force? According to Newton’s second law of motion a force is that which acts on an object with a certain mass to cause an acceleration. In mathematical form this law is expressed as
F = ma
where m is the mass and a is the acceleration. Acceleration is rate of change of the velocity.
Fig. 6-2, p. 160

4. Forces We Will Consider
Gravity
Pressure Gradient Force
Coriolis Force
Centrifugal Force / Centripetal Acceleration
Friction
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We are now ready to begin a discussion of the forces that affect the movement of air. These are pressure gradient force, Coriolis force, the force due to friction, centrifugal force and the downward directed force of gravity. We will primarily discuss the first three.

5. 1. Gravitational Force

7. 2. Pressure Gradient Force
Gradient – the change in a quantity over a distance
Pressure gradient – the change in atmospheric pressure over a distance
Pressure gradient – the resultant net force due to the change in atmospheric pressure over a distance

8. Pressure Gradient Force on the Weather Map
H = High pressure (pressure decreases in all directions from center)
L = Low pressure (pressure increases in all directions from center)
The contour lines are called isobars, lines of constant air pressure
Strength of resultant wind is proportional to the isobar spacing
Less spacing = stronger pressure gradient = stronger winds
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The magnitude of the pressure gradient force is proportional to the isobar or contour spacing because the isobar or contour spacing represents how strong or weak the pressure gradient is. If the isobars or contours are closely packed together, the pressure gradient is higher and therefore the pressure gradient force is stronger. This would cause the wind speeds to be higher than in an area where the isobars or contours are farther apart.
Fig. 6-4, p. 161

9. Pressure Gradient Force (PGF)
pressure gradient: high pressure  low pressure
pressure differences exits due to unequal heating of
Earth’s surface
spacing between isobars indicates intensity of gradient
flow is perpendicular to isobars

10. Low Pressure Center Center of lowest pressure
Pressure increases outward from the low center
Also called a cyclone
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An “L” on a weather map with closed isobars around it represents the center of lowest pressure relative to the pressures surrounding it. Pressures increase in all directions from the center of the low. A low pressure center is sometimes called a cyclone.

11. High Pressure Center Center of highest pressure
Pressure decreases outward from the low center
Also called an anticyclone
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An “H” on a weather map with closed isobars around it represents the center of highest pressure relative to the pressures surrounding it. Pressures decrease in all directions from the center of the high. A high pressure center is sometimes called an anticyclone.

12. Low Pressure Trough An elongated axis of lower pressure
Isobars are curved but not closed as in a low
1000
1004
1008
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A low pressure trough is an elongated axis of lower pressure. The isobars are curved but not circular. Pressure is lowest along the axis of the trough. Moving away from the trough in either direction, pressures increase.
1012

13. High Pressure Ridge An elongated axis of higher pressure
Isobars are curved but not closed as in a high pressure center
1000
1004
1008
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A high pressure ridge is an elongated axis of higher pressure. Again, the isobars are curved but not circular. Pressure is highest along the axis of the ridge. Moving away from the ridge in either direction, pressures decrease.
1012

14. Convergence
Convergence -- the net horizontal inflow of air into an area.
Results in upward motion
Convergence occurs in areas of low pressure (low pressure centers and troughs)
Lows and troughs are areas of rising air

15. Divergence
Divergence -- the net horizontal outflow of air from an area.
Results in downward motion (subsidence)
Divergence occurs in areas of high pressure (high pressure centers and ridges)
Highs and ridges are areas of sinking air (subsidence)

16. 3. Coriolis Force Due to the rotation of the Earth
Objects appear to be deflected to the right (following the motion) in the Northern Hemisphere
Speed is unaffected, only direction
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The second force that governs air motion is the Coriolis force, named after a 19th century French scientist. The Coriolis force is due to the rotation of the earth. It is called an “apparent” force because unlike pressure gradient force, the Coriolis force would not be a factor if the earth did not rotate.
Fig. 6-9, p. 165

17. Coriolis effect seen on a rotating platform, as 1 person throws a ball to another person.

18. Coriolis force (CF)
- The Coriolis force causes the wind to deflect to the right of its intended path in the Northern Hemisphere and to the left of its intended path in the Southern Hemisphere. It acts at a right angle to the wind.
- The Coriolis force is largest at the pole and zero at the equator
- The stronger the wind speed, the greater the deflection
- The Coriolis force changes only wind direction, not wind speed.
- We measure motion on the rotating Earth. Thus, we need to be concerned with the Coriolis force

19. The Coriolis Effect
objects in the atmosphere are influenced by the Earth’s rotation
Rotation of Earth is counter-clockwise
results in an ‘apparent’ deflection (relative to surface)
deflection to the right in the Northern Hemisphere
(left, S. Hemisphere)
Greatest at the poles, 0 at the equator
Increases with speed of moving object
CE changes direction not speed

20. 4. Centrifugal Force / Centripetal Acceleration
Due to change in direction of motion.
A centrifugal force is a force on an
object that tends to move it away from
a center of rotation and always results
from the inertia of the object.
A centripetal force is a force on an object that tends to move it toward a center of rotation.
roller coasters in parks.

21. 5. Friction factor at Earth’s surface  slows wind
Loss of momentum during travel due to roughness of surface
varies with surface texture, wind speed, time of day/year and atmospheric conditions
Important for air within ~1.5 km of the surface, the planetary boundary layer
Because friction reduces wind speed it also reduces Coriolis deflection
Friction above 1.5 km is negligible
Above 1.5 km = the free atmosphere

22. Atmospheric Force Balances
First, MUST have a pressure gradient force (PGF) for the wind to blow.
Otherwise, all other forces are irrelevant.
Already discussed hydrostatic balance, a balance between the vertical PGF and gravity. There are many others that describe atmospheric flow…

23. Geostrophic Balance Balance between PGF and Coriolis force
Fig. 6-15, p. 172

24. S. Hem. wind PGF Coriolis PGF Coriolis wind N. Hem.
Therefore, wind blows parallel to isobars, which is useful to consider when looking at weather map.
Buy-Ballot’s “law”: If you stand with your back to the wind in the N.H, low pressure will be on your left and high pressure on your right.
In N. Hem., geostrophic wind blow to the right of PGF (points from high to low P), In S. Hem., geostrophic wind to left of PGF.
S. Hem.
wind
PGF
Coriolis
PGF
Coriolis
wind
N. Hem.

25. Converging contours of const
Converging contours of const. pressure (isobars) => faster flow => incr. CF & PGF
Get geostrophic
wind pattern
from isobars

26. Geostrophic balance P diff. => pressure gradient force (PGF)
=> air parcel moves => Coriolis force
Geostrophy = balance between PGF & Coriolis force .
[Tarbuk & Lutgens 2003, Fig.17.5]

27. Upper Atmosphere Winds
upper air moving from areas of higher to areas of lower pressure undergo Coriolis deflection
air will eventually flow parallel to height contours as the pressure gradient force balances with the Coriolis force
this geostrophic flow (wind) may only occur in the free atmosphere (no friction)
stable flow with constant speed and direction
Wind flows in a counterclockwise sense around a low or trough
Wind flows in a clockwise sense around a high or ridge

28. Gradient Wind Balance
Balance between PGF, Coriolis force, and centrifugal force
Examples: hurricanes

29. Supergeostrophic flow
(CF > PGF )
PGF + Ce = CF
Subgeostrophic flow
(CF < PGF)
PGF = CF + Ce

30. Difference between PGF & Coriolis (CF) is the centripetal force needed to keep parcel in orbit.
[Ahrens, 2003, Fig.9.26, 9.27]

31. Geostrophic flow too simplistic  PGF is rarely uniform, height contours curve and vary in distance
wind still flows parallel to contours HOWEVER continuously changing direction (and experiencing acceleration)
for parallel flow to occur pressure imbalance must exist between the PGF and CE  Gradient Flow
Two specific types of gradient flow:
Supergeostrophic: High pressure systems, CE > PGF (to enable wind to turn), air accelerates
Subgeostrophic: Low pressure systems, PGF > CE, air decelerates
supergeostrophic and subgeostrophic conditions lead to airflow parallel to curved height contours

32. Surface Winds Friction slows the wind
Coriolis force (dependent on wind speed) is therefore reduced
Pressure gradient force now exceeds Coriolis force
Wind flows across the isobars toward lower pressure

33. Near Surface Wind

34. Friction Ground friction slows wind => CF weakens.
CF+friction balances PGF.
Surface wind tilted toward low p region.
At the surface, if we stand with our backs to the wind, then turn clockwise about 30 °, lower pressure will be to our left. “Buys-Ballots law”
[Ahrens 2003, Fig.9.29]

35. Comparison

36. Convergence & divergence
Cyclone has convergence near ground but divergence at upper level.
Anticyclone: divergence near ground, convergence at upper level.
Air converges into a low pressure center, leading into ascending motion. This ascending air cools by adiabatic expansion and possible development of clouds and precipitation.
Air diverges at the center of high pressure. Then the air aloft converges and slowly descend.
[Ahrens 2003, Fig.9.33]

37. Winds: examples Aloft Northern Hemisphere Sfc Aloft Sfc
Southern Hemisphere
Aloft
Sfc

38. Pressure Gradient Force + Coriolis Force
Geostrophic
Wind

39. Pressure Gradient + Coriolis + Friction Forces
Surface
Wind

40. Cyclones, Anticyclones, Troughs and Ridges
High pressure areas (anticyclones)  clockwise airflow in the Northern Hemisphere (opposite flow direction in S. Hemisphere)
Characterized by descending air which warms creating clear skies
Low pressure areas (cyclones)  counterclockwise airflow in N. Hemisphere (opposite flow in S. Hemisphere)
Air converges toward low pressure centers, cyclones are characterized by ascending air which cools to form clouds and possibly precipitation
In the upper atmosphere, ridges correspond to surface anticyclones while troughs correspond to surface cyclones