Transcript Atmospheric Force Balances - UW

Atmospheric Force
Balances
QUIZ !
Newton’s Laws of motion
 1. Every object in a state of uniform
motion tends to remain in that state of
motion unless an external force is
applied to it.
 2. F = ma
 3. For every action there is an equal
and opposite reaction.
Newton’s second law
 F = ma
 Lets examine the terms
 We know what mass means
Acceleration
 The rate of change of velocity with time
 Given one force an object must have an
acceleration in the same direction
 If more than one force:
(F1 + F2 + …) = ma
- Remember no acceleration does not
necessarily imply no movement (velocity)
Main Atmospheric Forces
 Lets name the important atmospheric
forces…
 Pressure Gradient Force (PGF)
 Coriolis Force (Apparent)
 Frictional Force
 Centrifugal Force (Apparent)
 Gravitational Force
 Buoyancy Force
Buoyancy Force
Fbuoyancy  g
Tparcel  Tenv
Tenv
 The larger the difference in Tparcel and Tenv ,
the larger the force and acceleration
(F = ma)
 More buoyancy leads to stronger updrafts,
up to 50 m/s
All we are is dust in the Wind
 What is wind?
 Measures how air moves
 Can feel it but can not really see it
unless big enough particles are present
(i.e. dust or bigger)
How is the air forced to
move?
 Our atmospheric forces conspire to




move air
Sometimes air accelerates
(changes speed OR direction)
Sometimes it moves without
accelerating.
Examples…
Lets first look at the horizontal wind…
The first main force – PGF
 What is a gradient?
 Change in quantity over a distance
 PG – change in pressure over a distance
Gradient of X = (X2 –X1)/ D
The Pressure Gradient Force (PGF)
This is analogous to the pressure gradient force!
The pressure gradient force is the atmosphere’s way to try and
balance out the pressure field.
http://www.indiana.edu/~geog109/topics/10_Forces&Winds/pgf.html
Review: The Pressure Gradient Force (PGF)
PGF =
The change in pressure
Distance
• Direction of the PGF: Always from HIGH to LOW pressure
• Perpendicular to the isobars (lines of constant pressure)
• Magnitude of the PGF: Related to how closely packed the
isobars are.
• With isobars very close together, the numerator in the PGF
equation is large (a very large change in pressure), so the
pressure gradient is large, and thus, the PGF is very strong.
Hydrostatic Balance
 Vertical PGF = Gravitational Force
 Will discuss more next week and the
important conclusions that can be
drawn from this balance
Review: The Pressure Gradient Force (PGF)
Example of the pressure
gradient force around an
area of low pressure.
Notice how the PGF arrows
(“vectors”) are
approximately
perpendicular to the isobars.
Review: The Pressure Gradient Force (PGF)
An example of how the pressure gradient force is much stronger
where the isobars are closely packed together. The “closeness”
of the isobars represents the magnitude of the PGF.
The Coriolis Force
The Coriolis force is an apparent force that results from the
constant rotation of the Earth.
In the northern hemisphere, it always acts exactly 90o to the right
of the object in movement (such as the wind)
Wind
Coriolis Force
The Coriolis Force cont.
What does the Earth’s rotation
have to do with the Coriolis
force?
R2
As a parcel of air moves from
one latitude to another, its
distance from the axis of
rotation changes.
The speed of a stationary parcel
changes, because the speed of
the Earth is different for
different latitudes
R1
Axis of rotation
The Coriolis Force cont.
Remember: Since angular momentum is conserved, the path of a
parcel changes as it moves north/south!
Angular momentum = constant = Vradial + Vrelative
A northward moving object will thus be deflected to the right
(east) in the northern hemisphere! (opposite for S.H.) This is
because as an object moves north, Vradial decreases (the distance
from the axis of rotation decreases), so Vrelative must increase!
Example: Ice Skater – why is skater able to spin so fast when not moving
initially with a great initial speed and no outside force acting upon skater
Review: The Coriolis Force
Examples of the Coriolis force at work in the
northern hemisphere:
Review: The Coriolis Force
The Coriolis force has much a greater effect farther away from the
equator (closer to the poles)
The Coriolis force only acts on an object in movement. It can’t help
start the movement of air, only deflect it in a certain direction once
it’s in movement.
Geostrophic Balance
The balance that exists between the two forces we’ve talked
about:
1. Pressure Gradient Force
2. Coriolis Force
The “geostrophic wind” is a wind that occurs as a result of this
balance. The wind can be approximated as “geostrophic” in the
absence of friction: Generally high above the ground, or over
oceans.
Geostrophic Balance
L
996 mb
x
1000 mb
1004 mb
H
Geostrophic Balance
L
Pressure
Gradient Force
996 mb
1000 mb
Coriolis Force
1004 mb
H
Geostrophic Balance
L
Pressure
Gradient Force
996 mb
Geostrophic
Wind
1000 mb
Coriolis Force
1004 mb
H
What if an Object is Initially Not
in Geostrophic Balance
 http://ww2010.atmos.uiuc.edu/(Gh)/g
uides/mtr/fw/gifs/geo.mov
Geostrophic Balance
The geostrophic wind is . . .
•…always parallel to the isobars
• …stronger if there is a stronger pressure gradient
• …weaker if there is a weaker pressure gradient
The wind can be approximated as nearly geostrophic in the
upper levels of the troposphere.
Geostrophic Balance
Winds at 300 mb are nearly geostrophic:
http://www.spc.noaa.gov
Geostrophic Balance
Winds at 850 mb are generally NOT geostrophic, they often flow across the isobars:
http://www.spc.noaa.gov
The Frictional Force
The reason that geostrophic balance doesn’t hold close to the
surface of the Earth is due to friction.
The frictional force always acts in the opposite direction of the
wind.
The Frictional Force
• Certain terrain is especially rough, like cities or forests.
• Generally, friction is much less over oceans or large seas and lakes.
• This is why it is much windier over large bodies of water. The wind has very
little counteractive force over water!
Small frictional force
Large frictional force
http://slamonline.com/online/wp-content/uploads/2006/07/PacificOcean.jpeg
http://www.ccauthority.com/images/minneapolis.jpg
The Frictional Force
More factors that affect the frictional force:
Height above the surface
The further away from the surface, the less friction
For instance, the winds at 300 mb experience less friction than the winds at
the surface
Wind speed
The stronger the wind, the more friction will oppose the motion
Therefore, slower winds experience less friction than fast winds
Surface Type
The rougher the surface, the greater the friction
For example, the friction over an open body of water is weaker than that over
a mountainous terrain
The Frictional Force
How does friction affect geostrophic balance?
Since friction acts in the opposite direction of the wind, it
slows the wind
Change in speed  change in magnitude of the Coriolis
force
Friction + Coriolis force ~ PGF  no longer geostrophic
balance and winds can cross the isobars
Atmospheric Force Balancing with the Frictional
Force
L
996 mb
1000 mb
x
1004 mb
H
Atmospheric Force Balancing with the Frictional
Force
L
996 mb
Pressure Gradient
Force
1000 mb
1004 mb
H
Atmospheric Force Balancing with the Frictional
Force
L
996 mb
Pressure Gradient
Force
1000 mb
Frictional Force
1004 mb
H
Coriolis Force
Atmospheric Force Balancing with the Frictional
Force
L
996 mb
Pressure Gradient
Force
Wind
1000 mb
Frictional Force
1004 mb
H
Coriolis Force
Atmospheric Force Balancing with the Frictional Force
Notice that, with the presence of friction…
• …the wind blows ACROSS isobars! Thus, the flow can
not be geostrophic
• …the wind is slightly weaker than it would be without
friction
• …the frictional force is always in the exact opposite
direction of the wind
• …the Coriolis force, however, is still always 90o to the
right of the wind (in the northern hemisphere)
This kind of atmospheric flow is common at the surface of the
Earth.
Atmospheric Force Balancing with the Frictional Force
Surface winds around cyclones (L) and anticyclones (H)
in the northern hemisphere.
Atmospheric Force Balancing with the Frictional Force
Due to the frictional
force, surface winds
converge around areas of
low pressure!
This results in the lifting
of air parcels around low
pressure centers.
http://ww2010.atmos.uiuc.edu/guides/mtr/fw/gifs/fric1.gif
Centripetal and Centrifugal
Forces
 When flow is curved, it is




changing direction
To change direction, must
accelerate!
To accelerate, need a force!
Centripetal force is what is
pulling in toward the center
of the circle
Centrifugal force is
apparent force
Centripetal directed toward
Center of circle wind is blowing
around
Centripetal and Centrifugal
Continued
 A tighter curve requires a greater
change of direction --> needs bigger
force
 Centrifugal force (inertial pull) greater
when winds are more curved or moving
faster (change of direction must occur
in shorter time)
Centripetal and Centrifugal
cont.
 Centrifugal and
centripetal forces
are greater when
speed is greater
 Both are greater
when radius of the
curve is smaller
 Centripetal = V2 / R
Couple Other Force Balances to
think
of…
1. Gradient Wind Balance

- Balance between PGF, Centrifugal Force (a result of
centripetal acceleration inward if curvature present),
and Coriolis
- http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/g
rad.rxml
2. Cyclostrophic Balance
- Balance between PGF and the Centrifugal Force
- In a small area and short time span the Coriolis force is
not that important
- Example: tornadoes can spin both ways
- http://profhorn.aos.wisc.edu/wxwise/AckermanKnox/c
hap6/cyclostrophic.html#fig