1. Lecture 7 Forces (gravity, pressure gradient force)
Imaginary forces (Coriolis, centrifugal)
Force balance and resulting horiz. wind
Geostrophic wind
Gradient wind
Adjustment to balance
The thermal “wind” (change in geostrophic wind in the vertical)

2. Wind direction is the direction from which the wind is blowing
Wind direction is the direction from which the wind is blowing. Wind direction is expressed in degrees
Units: m/s or knots
1 knot = 0.5 m/s
1knot ~ 1 mile/hr
Wind speed is
expressed in terms
of the flagpole

3. Newton’s law of motion
A body at rest tends to stay at rest; a body in motion tends to stay in motion, traveling at a constant speed in a straight line.
A force exerted on a body of mass m causes the body to accelerate in the direction of the applied force.
Force = mass x acceleration

4. A force has direction and magnitude (it is a vector)
A force has direction and magnitude (it is a vector). Adding two forces is vector addition.

5. Forces that move the air
Gravitational force (g=9.8 m/s2)
Pressure gradient force (-1/rho x dp/dx or --1/rho x dp/dy). It points toward lower p. The pressure gradients causing the wind are horizontal.
Coriolis force
Centrifugal force
Frictional force

6. Pressure gradient force pushes from higher to lower pressures
PGF
Magnitude depends on value of pressure gradient

7. Isobaric chart (height contours on a constant pressure surface)

8. Pressure (p) as a function of height

9. Vertical structure in the atmosphere
What about pressure?
Hydrostatic equation: balance between pressure gradient force and gravity.
dp/dz = - rho g
Ideal gas law:
p = rho R T
Let’s go to the board!
z = - H ln (p/p0), where H is scale height and is only constant
if T is constant.
In other words, p = p0 exp(- z/H)

10. Next: Coriolis force Earth’s rotational speed is greatest at the equator and exactly zero at the poles

11. Coriolis deflection Coriolis force deflects moving air to the right
in the Northern Hemisp.
Coriolis force deflects
moving air to the left
in the S. Hemisphere

12. The magnitude of the Coriolis force (CF) is proportional to the wind speed and sine of latitude
CF= f x V,
Where f is
2xEarth’s rotation rate
xsin(latitude)

13. Centrifugal force: arises because the trajectory is curved
Centrifugal force: arises because the trajectory is curved. CENTF= V^2/R, where R (radius of curvature) is positive for cyclones, negative for anticyclones

14. Frictional force is proportional to the wind- speed and directed opposite to the wind dir.
FF = -k V (where k describes the roughness)

15. Summary: The Forces
Gravity – the strong silent type
PGF arises from pressure gradients generated by differential solar heating –leads to wind. Only then do the other forces start acting.
CF, CENTF, FF all depend of V, wind speed.

16. Atmospheric force balances Sum of forces = mass x acceleration Balance when the forces add up to zero
Hydrostatic balance in the vertical (gravity does not cause wind).
Strong horizontal PGF means strong wind
CF changes wind direction not speed
CENTF only acts on curved flow
FF slows down the wind (regardless of direction).

17. Geostrophic wind, geostrophic balance PGF + CF = 0

18. Wind blows counterclockwise around lows (cyclonic wind in cyclones), clockwise around highs (anticyclones)
Force balance not quite right since we have curved flows
Add centrifugal force

19. Gradient balance and the gradient wind

20. Gradient balance results in gradient wind
Represents balance of three forces
It is an excellent approximation to free atmospheric flow.
Around highs it is supergeostrophic
Around lows it is subgeostrophic

21. Adjustment to balance
The atmosphere tries hard to stay in balance, but it is constantly being pushed away from it.
The atmosphere adjusts very quickly (in a matter of minutes) to imbalance.

22. Adjustment to balance with 3 forces: