Transcript Corporate Profile - University of Oklahoma

METR 2413
22 February 2004
Dynamics I:
Basic forces
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
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:
1
PGF   p where, in Cartesiancoordinates,

  
 is thegradient operator,   
x y z
Pressure gradient force
So
p p p
p 


x y z
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).
Pressure gradient force
Force, F = m a
F
Pressure, p 
or
Area
v
mv
mv
m
ma
t  t  Area
p

Area Area Area
t
So pressure is momentum (mv) per unit area per unit time,
or momentum flux.
1
Vol
F
F
PGF   p 


m Area L m
Hence, the pressure gradient force is a force per unit mass,
or an acceleration.
Pressure gradient force
Now, let’s consider PGF in the atmosphere.
Consider regions of high and low pressure. Air will tend to
move in the direction of low pressure due to the PGF.
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).
That’s because air parcels that
are moving experience other
“forces”.
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 2Ω sinφ,
where Coriolis parameter, f = 2Ω sinφ, with
angular speed of the Earth’s rotation, Ω =2π/86,400s = 7.3×10-5 s-1
and latitude φ.
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.
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.
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).
Coriolis force
In the NH, the Coriolis force ALWAYS acts to the right of the
wind vector!!!
Coriolis
Force
PGF
Wind
Vector
Wind
Vector
PGF
Coriolis
Force
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.
Geostrophic wind
What about in the Southern Hemisphere?
In the SH, the sense of the Earth’s 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
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.
Force
High pressure
Wind
Vector
PGF
Low pressure
Frictional effects
Near the earth’s 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
Friction
•The vector sum of the
Coriolis force and friction
balances the PGF
1000 hPa
PGF
Wind
Vector
1004 hPa
Coriolis
Force
1008 hPa
Summary
• PGF acts in the direction of low pressure PGF  
1

p
• Coriolis force due to the Earth’s 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