Download Pressure, Forces and Motion

Pressure, Forces and Motion
Readings
A&B: Ch. 4 (p. 93-114)
CD Tutorials: Pressure Gradients,
Coriolis, Forces & Winds
Topics
1. Review: What is
Pressure?
2. Horizontal Pressure
Gradients
3. Depicting Pressure
Gradients
a. Constant Height Charts
b. Constant Pressure Charts
4. Newton’s 2nd Law
5. Forces & Winds
a. Pressure Gradient Force
b. Coriolis Force
→ Geostrophic Wind
→ Gradient Wind
c. Friction Force
6. Anticyclones & Cyclones
G109: Weather and Climate
Review: What is Pressure?
• Pressure = Force / Area
• Atmospheric Pressure: weight of air above an area
• “Weight above” decreases steadily with height
∴Pressure decreases steadily with height
• Can be used to “measure” height in the atmosphere
G109: Weather and Climate
10: Pressure & Motion
Review: The Ideal Gas Law
The Ideal Gas Law:
P:
ρ:
T:
Rd:
•
P = ρ T Rd
pressure
density
abs. temperature
spec. gas constant
for dry air
[Pa = kg m-1 s-2]
[kg m-3]
[K]
287 [J kg-1 K-1]
If Pressure (P) is constant
ƒ Increased T → Decreased Density → Increased Volume
ƒ Decreased T → Increased Density → Decreased Volume
G109: Weather and Climate
10: Pressure & Motion
Horizontal Pressure Gradients
•
When surface under one air column is heated
the air column expands, following:
P = ρ Rd T
•
Example: Two columns of air with equal ρ, P,
and T
G109: Weather and Climate
10: Pressure & Motion
Horizontal Pressure Gradients
•
After heating and expansion of right-hand column:
•
Height at which 500 mb pressure is reached is now
•
At 5640 m the pressure in the warm column is now
•
OR: The height of 500 mb level
column
G109: Weather and Climate
cool
10: Pressure & Motion
Horizontal Pressure Gradients
•
Gradual poleward decrease in mean
temperature
ƒ Denser air at higher latitude
ƒ More rapid decrease of pressure with height
ƒ Horizontal changes in pressure
G109: Weather and Climate
10: Pressure & Motion
Horizontal Pressure Gradients
•
As a result of horizontal temperature
differences:
ƒ A given pressure (e.g. 500 mb) occurs at different
ƒ At a given height (e.g. 5640 m) in the atmosphere,
•
(If no air is flowing away or into the air
column, the surface pressure does not vary
horizontally … yet)
G109: Weather and Climate
10: Pressure & Motion
Horizontal Pressure Gradients
•
With a horizontal pressure gradient aloft
(created by T differences), air can start to
flow from
to
→The weight of the entire air column (surface
pressure) changes as well, because of the air
flow
→There are now
at
the surface and at height
• These give rise to
→ Pressure differences cause
→ Pressure differences occur because of
G109: Weather and Climate
10: Pressure & Motion
Depicting Horizontal Pressure Variation
•
Pressure varies
ƒ Spatial & temporal patterns
ƒ Need a way to depict variations
•
Two types of charts or maps
ƒ At sea-level, show horizontal variation of pressure
as isobars
= pressure variation at
ƒ For a given level of pressure (e.g. 500 mb), show
at what height this occurs, as contours of
geopotential
= height variation of
G109: Weather and Climate
10: Pressure & Motion
Depicting Horizontal Pressure Variation
1.
ƒ
ƒ
Shows variations of pressure at the surface
Altitude corrections: all pressures are corrected
to same level (usually sea level)
• Prevents mountainous areas from appearing
with lower pressure because of height
G109: Weather and Climate
10: Pressure & Motion
Depicting Horizontal Pressure Variation
2.
ƒ
Shows variation of height along an Isobaric
Surface, i.e., the height at which a certain
pressure occurs
• Isobaric Surface: a surface of constant
pressure
G109: Weather and Climate
10: Pressure & Motion
Newton’s 2nd Law of Motion
•
Acceleration of an air parcel is equal to the
ƒ Acceleration: change of velocity over (unit) time
• i.e., a change in
and/or
ƒ Net force: vector sum of all component forces
G109: Weather and Climate
10: Pressure & Motion
Newton’s 2nd Law of Motion
•
Forces in the atmosphere (the most
important ones):
ƒ Pressure Gradient Force: FPG
• Driving force – affects speed and direction
• Accelerates air from High to Low pressure
ƒ Coriolis Force: FC
• Deflecting force – affects direction only
ƒ Friction Force: Ff
• Retarding force – affects speed only
• Friction Increases with increasing wind speed
G109: Weather and Climate
10: Pressure & Motion
Pressure Gradient Force (FPG)
•
Force resulting from the horizontal difference
in pressure
ƒ Proportional to
ƒ i.e., depends on
FPG
H
1008
•
1004
L
1000
(mb)
FPG goes from
ƒ At right angles to the isobars
G109: Weather and Climate
10: Pressure & Motion
Pressure Gradient Force (FPG)
•
The closer the isobars, the stronger the
pressure gradient and thus the FPG
FPG =
H
∆P change in PRESSURE
=
d
DISTANCE
FPG
L
FPG
H
1008 1004 1000
1008
1004
G109: Weather and Climate
L
1000
10: Pressure & Motion
Pressure Gradient Force (FPG)
•
•
•
Can set a stationary air parcel in motion
Mostly responsible for the
If FPG were the only force, winds
ƒ Air would move at
•
But the earth rotates →
G109: Weather and Climate
10: Pressure & Motion
Coriolis Effect
•
Coriolis effect:
•
An unaccelerating object moves in a straight
line (due to balanced forces)
Because of Earth’s rotation, a “straight line
motion” on Earth as viewed from (e.g.)
another planet, leaves a curved trace on
Earth: the motion appears to be accelerated
(curved!)
•
G109: Weather and Climate
10: Pressure & Motion
Coriolis Force (FC)
•
•
•
Apparent acceleration
accounted for by
apparent force: Coriolis
force FC
Northern Hemisphere:
(counter-clockwise
rotation)
Southern Hemisphere:
(clockwise rotation)
G109: Weather and Climate
10: Pressure & Motion
Coriolis Force (FC)
•
FC (on Earth) dependent on:
•
Latitude
ƒ Strongest
twisting motion at
poles.
ƒ No twisting
motion at the
equator.
ƒ FC increases
•
Velocity: proportional to velocity.
ƒ FC increases with
… the greater
the distance traveled per unit time the greater the
deflection
G109: Weather and Climate
10: Pressure & Motion
Coriolis Force (FC)
•
•
Always at right angles to the direction of air
flow
Affects only the
not
•
Affected by
•
ƒ Stronger the wind speed the greater the force
Strongest at the
and weakest at the
FC = 2 ν Ω sin φ
ƒ ν - wind speed
ƒ Ω - earth's angular rate of spin (constant )
ƒ φ - latitude
G109: Weather and Climate
10: Pressure & Motion
Geostrophic Wind
•
Wind aloft (above a few km) above the effects
of friction
• Assume evenly spaced, and straight isobars
→ Idealized model (an approximation of winds
aloft)
•
balances the
and directs the airflow
• FPG = FC
• Net force = 0
G109: Weather and Climate
10: Pressure & Motion
Geostrophic Wind
•
•
FPG = FC
Wind flows in a
•
Proportional to the pressure gradient force
ƒ steep gradient strong winds; weak gradient light
winds
•
With back to wind, Low is
(in northern hemisphere)
G109: Weather and Climate
10: Pressure & Motion
Gradient Wind
→ A second idealized model of winds aloft
• Above the level of frictional influence wind,
with isobars that are curved
• Wind blows at
constant
but with
constantly
changing
…
therefore has
acceleration
G109: Weather and Climate
10: Pressure & Motion
Gradient Wind
•
•
Above the level of frictional influence wind,
when isobars are NOT parallel
Wind blows
G109: Weather and Climate
10: Pressure & Motion
Troughs and Ridges
•
•
•
In upper atmosphere pressure height variations are
distributed as a series of ridges and troughs:
Ridge: elongated zone of
pressure, extending
toward the pole: associated with
weather
Trough: elongated zone of
pressure, extending
toward the equator: associated with
weather
ƒ Greatest surface instability (T-storms) is usually
ahead of (to the right of) the 500 mb trough
G109: Weather and Climate
10: Pressure & Motion
Friction Force (Ff)
•
•
As we move toward the surface (away from aloft)
friction slows down the movement of air
Roughness of the surface retards the airflow
ƒ Wind speed reduced
• Impacts Coriolis force (FC) –
• Pressure gradient force (FPG) is not affected →
•
•
Wind crosses isobars
Angle depends on friction
ƒ Smooth ocean:
• Slight angle: 10-20o
ƒ Rough terrain:
• Greatest angle: 45o
G109: Weather and Climate
.
10: Pressure & Motion
Anticyclones and Cyclones
•
•
•
•
•
Anticyclone: enclosed area of
with circular isobars or height contours
Northern Hemisphere
ƒ Winds rotate
as FPG is outward and FC
deflects to right
NH surface
Southern Hemisphere
ƒ Winds rotate
as FPG is
outward and FC deflects
to left
SH surface
NH upper atm
SH upper atm
Near surface: wind is not parallel to isobars but
spirals
→
Upper atmosphere: flow is parallel to isobars
G109: Weather and Climate
10: Pressure & Motion
Anticyclones and Cyclones
•
•
•
•
•
Cyclone: enclosed area of Low pressure,
with circular isobars or height contours
Northern Hemisphere
ƒ Winds rotate
as FPG is
inward and FC deflects to
right
Southern Hemisphere
ƒ Winds rotate
as FPG is inward and FC
deflects to left
NH surface
SH surface
NH upper atm
SH upper atm
Near surface: wind is not parallel to isobars but
→
spirals
Upper atmosphere: flow is parallel to isobars
G109: Weather and Climate
10: Pressure & Motion