1. Atms 4320 / 7320 The Omega Equation: A physical interpretation.

2.  A few weeks ago, we talked about the Z- O equation and it’s interpretation. Now derive Omega equation;  Equations of Motion  1st Law  hydrostatic balance  Continuity  Eqn. of State

3. The Omega Equation: A physical interpretation.  More than one way to derive, but we’ll follow derivation similar to Z-O equation. Consult Krishnamurti (1968, MWR) or Dutton (1968, QJRMS).  Start w/ hydrostatic balance and substitute equation of state.

4. The Omega Equation: A physical interpretation.  Invoke equation of state?

5. The Omega Equation: A physical interpretation.  Rework by

6. The Omega Equation: A physical interpretation.  Rework First law  And then

7. The Omega Equation: A physical interpretation.  Here it is

8. The Omega Equation: A physical interpretation.  Rework vorticity equation (x,y,p coordinates)  and

9. The Omega Equation: A physical interpretation.  Substitute into hydrostatic balance and Viola!

10. The Omega Equation: A physical interpretation.  Continue to manipulate (split off divergence term):

11. The Omega Equation: A physical interpretation.  Finally:

12. The Omega Equation: A physical interpretation.  Krishnamurti (1968, MWR)  Puts all forcing for omega on the RHS of the equation.  Dutton (1968, QJRMS)  Puts all forcing for omega on the LHS.  Solve this using numerical methods.  Can you name the terms?

13. The Omega Equation: A physical interpretation.  Now interpret dynamic forcing:

14. The Omega Equation: A physical interpretation.  Now interpret thermodynamic forcing:

15. The Omega Equation: A physical interpretation.  The End!