EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

1. EVAT 554OCEAN-ATMOSPHERE DYNAMICS EQUATIONS OF MOTION (CONT); ENERGY EQUATION LECTURE 4 (Reference: Peixoto & Oort, Chapter 3)

2. Zonal Momentum Balance: Meridional Momentum Balance: Vertical Momentum Balance: Continuity

3. 1. “Boussinesq Approximation” (accept in gravity or “buoyancy” term) 2. Ignore “Metric Terms” (terms that scale as 1/a are orders of magnitude smaller than other terms) 3. Assume equations averaged over e.g. several hours (replace molecular diffusion with Eddy Diffusion based on contribution of averaged non-linear terms) SIMPLIFYING APPROXIMATIONS

4. Zonal Momentum Balance: Meridional Momentum Balance: Vertical Momentum Balance: Continuity: But this is not a closed set of equations!

5. CONSERVATION OF ENERGY First Law of Thermodynamics Energy is neither destroyed nor created, but changes form during ordinary physical and chemical processes Heating = Change in Internal Energy + Work Done

6. CONSERVATION OF ENERGY First Law of Thermodynamics Energy is neither destroyed nor created, but changes form during ordinary physical and chemical processes Heating = Change in Internal Energy + Work Done

7. CONSERVATION OF ENERGY First Law of Thermodynamics Energy is neither destroyed nor created, but changes form during ordinary physical and chemical processes Heating = Change in Internal Energy + Work Done Includes radiative heating, latent heating, frictional heating, conduction and turbulent heat flux (“diabatic” heating)

8. CONSERVATION OF ENERGY Example: How much energy is needed to warm 2 kg of dry air by 5oC? mair = 2 kg, DT = 5oC Cp = 1005 J kg-1 K-1 (dry air) DQH = mair Cp DT= (2kg)(1005 J kg-1 K-1 )(5oC) = 10.05 kJ Heating = Change in Internal Energy + Work Done

9. Define the heating rate, CONSERVATION OF ENERGY

10. Define the heating rate, CONSERVATION OF ENERGY Combine molecular and eddy diffusive heat transport:

11. CONSERVATION OF ENERGY Combine molecular and eddy diffusive heat transport:

12. CONSERVATION OF ENERGY

13. CONSERVATION OF ENERGY Boundary Terms

14. CONSERVATION OF ENERGY Incident Solar Planck Blackbody

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