ATOC 4720 class36
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Transcript of ATOC 4720 class36
1. The continuity equation 2. The vertically averaged divergence 3. The primitive equations
ATOC 4720 class36
Equations we have learnt up to now:
( )
Where,
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
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 massContinuity equation
Example: pancake; cloud anvil
The continuity equationHowever, there is a significant difference:
Pancake: uncompressible;Air parcel: compressible: volume changes.
Two types of volume changes:1. Gradual, hydrostatic changes due to expansion and compression; [hydrostatic] In P-coordinate, this process is automatically taken into account;2. Nonhydrostatic fluctuations--vertically propagating sound waves. [Small amplitude, high frequency, not important for large-scale atmospheric motion.
The continuity equation
Mass:
As the flow deform the shape of the parcel, its mass is conserved:
Mathematically, the above equation can be expanded as:
Because,
The continuity equation: mass conservation
To gain a clearer understanding of the physics, let’s rewrite Equation:
Let
Using
We have,
divergence
convergence
Convergence
Divergence
IfZ-coordinate: