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EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

Explore the material derivative, continuity, Lagrangian and Eulerian formulations, advection, and momentum equations for fluid mechanics in ocean and atmosphere. Delve into Newton's Second Law and rotating frames of reference in this enlightening lecture based on Peixoto & Oort's Chapter 3.

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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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