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EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

EVAT 554 OCEAN-ATMOSPHERE DYNAMICS. EQUATIONS OF MOTION. LECTURE 2. (Reference: Peixoto & Oort, Chapter 3). Let Us Consider the Equations of Fluid Mechanics at A Level Of Generality Appropriate for Both the Ocean and Atmosphere. (Material Derivative). Continuity (conservation of mass).

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EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

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  1. EVAT 554OCEAN-ATMOSPHERE DYNAMICS EQUATIONS OF MOTION LECTURE 2 (Reference: Peixoto & Oort, Chapter 3)

  2. Let Us Consider the Equations of Fluid Mechanics at A Level Of Generality Appropriate for Both the Ocean and Atmosphere

  3. (Material Derivative) Continuity (conservation of mass) A=dxdz V V A=dydz dz A=dxdy dy dx “Parcel”

  4. Continuity (conservation of mass) A=dxdz V V A=dydz dz A=dxdy dy dx

  5. Where: Continuity (conservation of mass) Lagrangian Formulation

  6. Advection Continuity (conservation of mass) (local derivative) Eulerian Formulation

  7. Conservation of Momentum NEWTON’S SECOND LAW (“NAVIER-STOKES EQUATION”) FOR A FLUID

  8. MOMENTUM EQUATION Body Force Total Force per Unit Mass Friction PGF But what if we measure velocity relative to a rotating frame?

  9. Consider a frame of reference rotating at angular velocity W Apply this to the acceleration:

  10. where

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