# Chapter 10: Atmospheric Dynamics

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Chapter 10: Atmospheric Dynamics

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

Force Newton’s Second Law of Motion: F = ma
Force = mass x acceleration Imbalance of forces causes net motion Slide23.mp3 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

Forces We Will Consider
Gravity Pressure Gradient Force Coriolis Force Centrifugal Force / Centripetal Acceleration Friction Slide22.mp3 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.

1. Gravitational 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

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 Slide26.mp3 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

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

Low Pressure Center Center of lowest pressure
Pressure increases outward from the low center Also called a cyclone Slide38.mp3 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.

High Pressure Center Center of highest pressure
Pressure decreases outward from the low center Also called an anticyclone Slide39.mp3 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.

Low Pressure Trough An elongated axis of lower pressure
Isobars are curved but not closed as in a low 1000 1004 1008 Slide40.mp3 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

High Pressure Ridge An elongated axis of higher pressure
Isobars are curved but not closed as in a high pressure center 1000 1004 1008 Slide41.mp3 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

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

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)

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 Slide31.mp3 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

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

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

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

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.

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

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…

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

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.

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

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]

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

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

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

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

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

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

Near Surface Wind

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]

Comparison

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]

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

Pressure Gradient Force + Coriolis Force
Geostrophic Wind

Pressure Gradient + Coriolis + Friction Forces
Surface Wind

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