Corporate Profile

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METR 2413 22 February 2004
Dynamics I Basic forces
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Review

• Synoptic meteorology
• Synoptic refers to the spatial and temporal
  scale of the systems
• Length scale is of the order of 1000 km (106 m)
  time scale is of the order of several days
  (105 s)
• Typical weather features at the synpotic scale
  are
• Surface cyclones and anticyclones
• Upper level troughs and ridges
• Fronts
• Hurricanes

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Pressure gradient force
A main concept of synoptic meteorology is the
Pressure Gradient Force (PGF). The PGF can
be defined as the change in pressure measured
across a given distance. In mathematical terms
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Pressure gradient force
So Hence, the total pressure gradient is
defined as the change in pressure measured
in the x direction plus the change in
pressure measured in the y direction plus
the change in pressure measured in the z
direction. But why do we call it a Force? Is it
really a force? A closer look reveals that
pressure is actually a momentum flux (recall
from the kinetic theory of gases).
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Pressure gradient force
Force, F m a Pressure, or So pressure is
momentum (mv) per unit area per unit time, or
momentum flux. Hence, the pressure gradient
force is a force per unit mass, or an
acceleration.
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Pressure gradient force
Now, lets consider PGF in the atmosphere. Consid
er regions of high and low pressure. Air will
tend to move in the direction of low pressure due
to the PGF.
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Pressure gradient force
In the absence of any other forces, air tends
to move away from regions of high pressure and
toward regions of low pressure. However, if
you look at a weather map, you never see wind
blowing in this direction, (except maybe in the
tropics). Thats because air parcels that are
moving experience other forces.
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Coriolis force
The Coriolis force deflects moving objects to the
right in the Northern Hemisphere (NH). Why?
Because the earth is rotating, and we are on the
that rotating reference frame. The Coriolis force
arises because the earth is an acccelerating
frame of reference. It can be defined as Fcor
v f v 2O sinf, where Coriolis parameter, f 2O
sinf, with angular speed of the Earths rotation,
O 2p/86,400s 7.310-5 s-1 and latitude f.
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Coriolis force
If we look at the scales for the Coriolis force,
it has scales of velocity/time acceleration
F/m So the Coriolis force is really a force per
unit mass or an acceleration, just like the
pressure gradient force. The Coriolis force is
a function of velocity, so as the wind speed
increases, the Coriolis force on air parcels also
increases.
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Coriolis force
Initially an air parcel (A) responds to the PGF
by moving toward low pressure. As it
accelerates, the Coriolis force increases.
Eventually, the PGF and the Coriolis force
balance each other.
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Coriolis force
For typical synoptic scale winds, the flow is
fairly steady, so the net force on an air parcel
is zero. The Coriolis force (to the right of the
velocity vector in the NH) balances the pressure
gradient force (from high to low pressure).
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Coriolis force
In the NH, the Coriolis force ALWAYS acts to the
right of the wind vector!!!
Coriolis Force
PGF
Wind Vector
Wind Vector
Coriolis Force
PGF
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Geostrophic wind
In the absence of any other forces, the
Coriolis force balances the PGF and the flow is
steady. This is called the Geostrophic Wind.
On a weather map, say at 500 mb, the wind vectors
are usually parallel to the contours, and the
flow around a cyclone is anticlockwise in the NH.
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Geostrophic wind
What about in the Southern Hemisphere? In the SH,
the sense of the Earths rotation is opposite to
the NH and the Coriolis parameter, f, is
negative. So, the Coriolis force is in the
opposite direction in the SH and points to the
left of the wind vector.
Coriolis Force
The geostrophic wind in the SH is still a balance
between the PGF and the Coriolis force, but the
flow around a cyclone is clockwise in the SH.
High pressure
Wind Vector
PGF
Low pressure
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Frictional effects
Near the earths surface, friction opposes
motion, so the flow is not longer geostrophic.
So what happens?

• PGF does not change
• Velocity decreases
• Coriolis force decreases
• The wind no longer behaves geostrophically, and
  there is cross-contour flow toward lower
  pressure
• The vector sum of the Coriolis force and
  friction balances the PGF

1000 hPa
Wind Vector
PGF
1004 hPa
Friction
Coriolis Force
1008 hPa
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Summary

• PGF acts in the direction of low pressure
• Coriolis force due to the Earths rotation, Fcor
  f v, acts to the right (left) of the wind
  vector in the NH (SH)
• For geostrophic flow, PGF balances the Coriolis
  force, the flow is parallel to the
  pressure contours, and the flow
  around a cyclone is anticlockwise in the NH
  (clockwise in the SH)
• For flow near the surface, where friction is
  important, geostrophic balance does not hold, and
  there is cross-isobar flow towards
  low pressure