With linear shallow water theory (LSW) we find del(omega)/del(t) = 0, that is vorticity is preserved, whereas if we consider non-linear shallow water theory (NLSW) it is the potential vorticity that is conserved following each fluid particle. In oceanographic context potential vorticity is a very important parameter. I wish to distinguish the vorticity and potential vorticity terms physically? How can I do this?
By the word 'physically' I mean some real life examples by which this distinctions seems obvious.
I have not studied the case you are interested in. However, typically the issue you raise is the result of moving from a simple application where Kelvin's circulation theorem holds to a case where it does not. A brief but reasonably detailed discussion of Kelvin's circulation theorem may be found at wikipedia. However the more general equation for the evolution of vorticity can be found in the attached document.
http://en.wikipedia.org/wiki/Kelvin's_circulation_theorem
Potential vorticity includes the coriolis parameter, and since the coriolis effect is mostly important at large scales, PV is the right variable for large-scale flows. There are variants to the PV formulation depending on the flow (e.g. stratified versus unstratified).
The attached document distinguishing the vorticity and potential vorticity terms physically is attached here. Sorry for its absence in the previous post.
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