Aspects of potential vorticity: impermeability, angular momentum, attribution, coordinates (Invited Presentation)

Potential vorticity (PV) plays a dominant role in the dynamic interpretation of atmospheric phenomena. It is, therefore, of interest to discuss a few topics involving PV where further clarification might be helpful. For example, the impermeability theorem states that fluxes of PV cannot cross isentropic surfaces. It is shown here that one can find equivalent fluxes which cross these surfaces. This result sheds new light on this theorem. The relation of angular momentum (AM) and PV has been invoked quite often in the interpretation of the zonal mean circulation of the atmosphere. Zonal wind and AM budget equations are reviewed to clarify the role of vorticity and PV. The invertibility principle has often been interpreted in a causal sense. This makes piecewise potential vorticity inversion a rather meaningful effort. It is argued that inversion of PV does not establish causal links. Finally, the formulation of PV in general vertical coordinates is discussed. It is shown that the result is normally rather complicated except if a metric simplification is applied.