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ATOC 4720 class36

ATOC 4720 class36. The continuity equation The vertically averaged divergence 3. The primitive equations. Equations we have learnt up to now:. (. ). Where,. Leading term, . Change T field. Even when . , which is very small, Pronounced T change with time.

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ATOC 4720 class36

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  1. ATOC 4720 class36 • The continuity equation • The vertically averaged divergence 3. The primitive equations

  2. Equations we have learnt up to now: ( )

  3. Where,

  4. Leading term, Change T field Even when , which is very small, Pronounced T change with time Moreover, Precipitation and latent heat release is CONTROLED by

  5. 1. The continuity equation : ( ) However, Newton’s second law of motion: provides no diagnostic information about As we shall see, Is subject to kinematic constraint based on: Conservation of mass Continuity equation Example: pancake; cloud anvil

  6. The continuity equation However, there is a significant difference: Pancake: uncompressible; Air parcel: compressible: volume changes. Two types of volume changes: Gradual, hydrostatic changes due to expansion and compression; [hydrostatic] In P-coordinate, this process is automatically taken into account; Nonhydrostatic fluctuations--vertically propagating sound waves. [Small amplitude, high frequency, not important for large-scale atmospheric motion.

  7. The continuity equation Mass: As the flow deform the shape of the parcel, its mass is conserved:

  8. Mathematically, the above equation can be expanded as: Because,

  9. The continuity equation: mass conservation

  10. To gain a clearer understanding of the physics, let’s rewrite Equation: Let Using

  11. We have, divergence convergence

  12. Convergence Divergence Z-coordinate: If

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