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Basic Conservation Laws
Atmospheric motions are governed by three principals:
- conservation of momentum
- conservation of mass
- conservation of energy
These conservation laws can be applied to a control volume of the
atmosphere at a fixed location (Eulerian) or to a control volume of the
atmosphere that is moving with the flow (Lagrangian)
What are the independent variables for the atmospheric field variables in
Eulerian and Lagrangian frames of reference?
Total Differentiation
Total, substantial, or material derivative:
D
Dt
This derivative is the time derivative following the motion (Lagrangian)
It will often be easiest to derive our conservation laws in a Lagrangian
frame.
Local or partial derivative:
?
?t
This derivative is the time derivative at a fixed location (Eulerian)
How can we relate the time derivative in a Lagrangian frame to the time
derivative in an Eulerian frame?
Consider the field variable temperatur...

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