Atmospheric Force Balances

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Atmospheric Force Balances

• AOS 101 Discussion 305
• April 11th, 2008
• Dan Hartung

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Logistics

• Quiz Friday May 2nd on all disc lectures
• Hand back write-ups and homework
• few comments
• Reminder- I am always available via email or
  office hours for assistance on homework.. Dont
  hesitate to ask, but dont just expect the answer
  either!

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Newtons Laws of Motion

• 1. An object will remain at rest, or continue to
  move at a constant velocity, unless an external
  force acts upon it.
• 2. The relationship between an objects mass m,
  its acceleration a, and the applied force F is
  Fma. (In this law, the direction of the force
  vector is the same as the direction of the
  acceleration vector)
• 3. For every action there is an equal and
  opposite reaction.

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Newtons 2nd Law

• Fma
• Lets define the terms
• We know what mass means
• What is the definition of acceleration?
• Unit of force is the Newton (kg m s-2)

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Main Atmospheric Forces

• Lets name the important atmospheric forces

• Pressure Gradient Force (PGF)
• Coriolis Force (Apparent)
• Frictional Force
• Centrifugal Force (Apparent)
• Gravitational Force
• Bouyancy Force (discussed previously)

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Bouyancy Force

• The larger the difference in Tparcel and Tenv,
  the larger the force and acceleration (Fma)
• More bouyancy leads to stronger updrafts, as
  large as 50m/s

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Acceleration

• Definition The rate of change of velocity with
  time
• Given one force, an object must have an
  acceleration in the same direction
• Given more than one force, there may be no
  acceleration
• (F1F2)ma
• Important no acceleration doesnt necessarily
  mean no movement (velocity)

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Did someone break wind?

• What is wind?
• Measures how air moves (velocity)
• Can feel it but can not really see it unless big
  enough particles are present
• (I.e. dust or bigger)

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How is air forced to move?

• Our atmospheric forces all conspire to move air
  (create wind)
• Sometimes air accelerates.. (sudden gust)
  Sometimes it moves without accelerating..
  (constant breeze)
• Lets first look at the horizontal wind

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1. Pressure Gradient Force (PGF)

• What is a gradient?
• Change in a quantity over a distance.
• PGF Change in pressure over a distance

Where D is the distance between P2 and P1
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Pressure Gradient Force (PGF)

• A good way to think of why there is a pressure
  gradient force is to imagine a fluid with a
  barrier

Wants to go to lower energy state

• On one side of the barrier, the fluid is at a
  higher level than the other side.
• Removal of the barrier results in fluid moving
  from the area where the fluid was higher to where
  the fluid was originally lower.

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The Pressure Gradient Force (PGF)

• This is analogous to the pressure gradient force!
• The pressure gradient force is the atmospheres
  way to try and balance out the pressure field.

http//www.indiana.edu/geog109/topics/10_ForcesW
inds/pgf.gif
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Review The Pressure Gradient Force (PGF)
The change in pressure
PGF
Distance

• Direction of the PGF Always from HIGH to LOW
  pressure
• Orientated 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
  of the PGF equation is large (a very large change
  in pressure), so the pressure gradient is large,
  and thus, the PGF is very strong.

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Review The Pressure Gradient Force (PGF)

• Example of PGF around an area of low pressure
• Notice how the PGF arrows (vectors) are
  approximately perpendicular to the isobars.

L
996mb
1000mb
1004mb
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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.

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2. The Coriolis Force

• The Coriolis force is an apparent force that
  results from the constant rotation of the Earth.
• Small Group Demonstration

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The Coriolis Force

• In the northern hemisphere, it always acts
  exactly 90? to the right of the object in
  movement (such as the wind)

Wind
Coriolis Force
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The Coriolis Force cont.

• What does the Earths rotation have to do with
  the Coriolis force?
• As a parcel of air moves from one latitude to
  another, its distance from the axis of rotation
  changes.
• Thus, the speed of a stationary parcel changes
  because the speed of the Earth is different for
  different latitudes (needs to be the case for the
  Earth to not self destruct).

R2
R1
Axis of Rotation
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The Coriolis Force cont.

• Remember Since angular momentum is conserved,
  the path of a parcel changes as it moves
  north/south!
• Angular Momentum (AM) constant Vradial
  Vrelative
• A northward moving object will thus be deflected
  to the right (east) in the northern hemisphere!
  (opposite for SH) 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
  the skater?

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Review The Coriolis Force

• Examples of the Coriolis force at work in the
  northern hemisphere

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Review The Coriolis Force

• The Coriolis force has a much greater effect
  farther away from the equator (closer to the
  poles)
• The Coriolis force only acts on an object in
  movement. It cant help start the movement of
  air, only deflect it in a certain direction once
  its in motion.

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Geostrophic Balance

• The balance that exists between the two forces
  weve 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.

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Geostrophic Balance
L
996mb
x
1000mb
1004mb
H
Surface Pressure
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Geostrophic Balance
L
Pressure Gradient Force
996mb
x
1000mb
Coriolis Force
1004mb
H
Surface Pressure
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Geostrophic Balance
L
Pressure Gradient Force
996mb
Geostrophic Wind
x
1000mb
Coriolis Force
1004mb
H
Surface Pressure
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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.

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Geostrophic Balance

• Winds at 300mb are nearly geostrophic

http//www.spc.noaa.gov
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Geostrophic Balance

• Winds at 850mb are generally NOT geostrophic,
  they often flow across the isobars

http//www.spc.noaa.gov
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3. The Frictional Force

• The reason that geostrophic balance doesnt hold
  close to the surface of the Earth is due to
  friction.
• The frictional force always acts in the opposite
  direction of the wind.
• You can think of friction like
• - Rolling a ball across carpet (without
  friction, the ball would never stop rolling)
• - Winds over rough terrain

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The Frictional Force

• Certain terrain is especially rough like cities
  and 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.

Large Frictional Force
Small Frictional Force
http//images.encarta.msn.com/xrefmedia/sharemed/t
argets/images/pho/t025/T025905A.jpg
http//www.oceanexplorer.noaa.gov/explorations/dee
peast01/logs/sep19/media/calm_seas_600.jpg
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The Frictional Force

• More factors that affect the frictional force
• 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 mountainous
  terrain
• Wind Speed
• -The stronger the wind, the more friction will
  oppose the motion
• -Therefore, slower winds experience less friction
  than fast winds
• Height above the surface
• -The farther away from the surface, the less
  friction
• -For instance, the winds at 300mb experience less
  friction than the winds at the surface

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The Frictional Force

• How does friction affect geostrophic balance?
• Since friction acts in the opposite direction as
  the wind, it slows the wind
• 2. Change in speed -gt Change in magnitude of the
  Coriolis force
• 3. Friction Coriolis force PGF -gt No longer
  have geostrophic balance and winds can cross the
  isobars

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Atmospheric Force Balancing with the Frictional
Force
L
996mb
x
1000mb
1004mb
H
Surface Pressure
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Atmospheric Force Balancing with the Frictional
Force
L
Pressure Gradient Force
996mb
x
1000mb
1004mb
H
Surface Pressure
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Atmospheric Force Balancing with the Frictional
Force
L
Pressure Gradient Force
996mb
Frictional Force
x
1000mb
Coriolis Force
1004mb
H
Surface Pressure
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Atmospheric Force Balancing with the Frictional
Force
L
Pressure Gradient Force
996mb
Wind
Frictional Force
x
1000mb
Coriolis Force
1004mb
H
Surface Pressure
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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
  90? to the right of the wind (in the northern
  hemisphere)
• This kind of atmospheric flow is common at the
  surface of the Earth.

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Atmospheric Force Balancing with the Frictional
Force

• Surface winds around cyclones (L) and
  anticyclones (H) in the northern hemisphere

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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 (ascent) of air
  parcels around low pressure centers.

http//ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/fr
ic.rxml
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Other Force Balances to think of

• Gradient Wind Balance
• Balance between PGF, Centrifugal Force (a result
  of centripetal acceleration inward if curvature
  is present), and Coriolis force
• http//ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/gr
  ad.rxml
• Cyclostrophic Balance
• Balance between PGF and the Centrifugal Force
• In a small area and short time span the Coriolis
  force is not that important
• http//profhorn.aos.wisc.edu/wxwise/AckermanKnox/c
  hap6/cyclostrophic.htmlfig

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Hydrostatic Balance

• Vertical PGF Gravitational Force
• We will discuss more next week and the important
  conclusions that can be drawn from this balance
• Have a good weekend!