Discussion
Which of the following is not conserved by the unforced QG system?
The vertical velocity
Total energy
Potential enstrophy
Potential vorticity following the flow
Answer: C
The vertical velocity is diagnosed afresh at every instant from the omega equation and is not a conserved quantity in any sense. Total energy and potential enstrophy are conserved as domain integrals, and potential vorticity is conserved following individual parcels. The three genuine conservation laws between them determine much of the qualitative behaviour of the system.
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