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Potential Vorticity

For adiabatic motion ( i.e., Theta is a constant) the density is rho = P(Cv/Cp). For motions between layers of constant Theta

q = (zeta + f) ยท partial Theta/partial p = constant

In the Shallow Water Model, where rho is a constant ( i.e., incompressible), the conserved quantity is usually written as:

q ident (zeta + f)/(g h)   seconds/meter2
example : flow over a mountain

<u> is eastward (westerly) then flow turns towards equator as it passes mountain, then oscillates around original latitude.

<u> is westward (easterly) then flow turns equatorward (note flow turning poleward `bucks' the flow causing it to turn equatorward. System is returned to original latitude after it passes mountain. No oscillations.