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EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

EVAT 554 OCEAN-ATMOSPHERE DYNAMICS. EQUATIONS OF MOTION (CONT); ENERGY EQUATION. LECTURE 4. (Reference: Peixoto & Oort, Chapter 3). Zonal Momentum Balance:. Meridional Momentum Balance:. Vertical Momentum Balance:. Continuity. 1. “Boussinesq Approximation”.

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EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

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  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…

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