1. EVAT 554 OCEAN-ATMOSPHERE DYNAMICS
LECTURE 5
EQUATION OF STATE; FILTERING OF EQUATIONS FOR ATMOSPHERE
(Reference: Peixoto & Oort, Chapter 3)

2. We still do not have a closed system of equations!
equation of state...
Let us first consider the atmosphere…

3. Recall Ideal Gas Law:
For Dry Air:
Define
Thus, we can write:

4. What about water vapor? Dalton’s Law of Partial Pressures:
For water vapor we can write:
Where
Take
Thus, we can write:

5. What about water vapor? Dalton’s Law of Partial Pressures:
For water vapor we can write:
Where:
Take
Now define:

6. What about water vapor?
Take
Now define:

7. What about water vapor?

8. What about water vapor?
This equation of state has general validity for the atmosphere, for the current atmospheric composition

9. Governing Equations for Atmosphere
Zonal Momentum Balance
Meridional Momentum Balance
Vertical Momentum Balance
Continuity
Equation of State
Temperature Equation
How many equations?
How many variables?

10. The Earth's Atmosphere from Space
The thin blue arc near the horizon shows the shallowness of the earth's atmosphere.

11. Zonal Momentum Balance:
Length scale: L106m, l102m
Depth scale: H104m, h 102m
Horizontal velocity scale: u,v 10 ms-1
Vertical velocity scale: w 10-2 ms-1
Horizontal pressure scale: p 10 mb = 1000 Pa
Time Scale: L/u 105s or H/w 106s
Radius of Earth: a=6.37x 106m
Coriolis parameter: f,f' 10-4 s-1
Density of Air: r 1 kg m-3
Horizontal Eddy Viscosity: nH 10-1 m2s-1
Vertical Eddy Viscosity: nV 10-1 m2s-1
10-4 ms-2
10-3 ms-2
10-6 ms-2
10-3 ms-2
10-4 ms-2
10-4 ms-2

12. Meridional Momentum Balance:
Length scale: L106m, l102m
Depth scale: H104m, h 102m
Horizontal velocity scale: u,v 10 ms-1
Vertical velocity scale: w 10-2 ms-1
Horizontal pressure scale: p 10 mb = 1000 Pa
Time Scale: L/u 105s or H/w 106s
Radius of Earth: a=6.37x 106m
Coriolis parameter: f,f' 10-4 s-1
Density of Air: r 1 kg m-3
Horizontal Eddy Viscosity: nH 10-1 m2s-1
Vertical Eddy Viscosity: nV 10-1 m2s-1
10-4 ms-2
10-3 ms-2
10-3 ms-2
10-4 ms-2
10-4 ms-2