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Atms 4320 / 7320

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

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Atms 4320 / 7320

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

  2. The Omega Equation: A physical interpretation. • 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!

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