1. Dynamics I: Basic forces
METR 2413
22 February 2004
Dynamics I:
Basic forces

2. 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

3. 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:

4. Pressure gradient forceSo
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).

5. 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.

6. 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.

7. 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”.

8. 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.

9. 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.

10. 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.

11. 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).

12. 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

13. 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.

14. 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 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

15. 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
The vector sum of the Coriolis force and friction balances the PGF
1000 hPa
Wind
Vector
PGF
1004 hPa
Friction
Coriolis Force
1008 hPa

16. Summary PGF acts in the direction of low pressure
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