On the Conservation and Impermeability Theorems for Potential Vorticity

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Abstract
If the partial analogy between the behavior of Rossby-Ertel potential vorticity (PV) and the behavior of chemical tracers is to be correctly used in the general case of diabatic, frictional motion, then certain fundamental differences, as well as similarities, between the behavior of PV and that of chemical tracers must be recognized. These differences stem from the well-known kinematical relationship between PV and isentropic circulation (via Stokes' theorem), which has no counterpart for chemical substances. One way of stating the analogy while recognizing the differences is to say first that PV behaves like the mixing ratio of a peculiar chemical “substance” that has zero source; i.e., is exactly conserved, away from boundaries (conserved not in the material or Lagrangian sense, but in the general sense associated with the idea of an indestructible chemical substance), and second that isentropic surfaces behave exactly as if they were impermeable to this “PV-substance” or “PVS,” even when diab... Abstract If the partial analogy between the behavior of Rossby-Ertel potential vorticity (PV) and the behavior of chemical tracers is to be correctly used in the general case of diabatic, frictional motion, then certain fundamental differences, as well as similarities, between the behavior of PV and that of chemical tracers must be recognized. These differences stem from the well-known kinematical relationship between PV and isentropic circulation (via Stokes' theorem), which has no counterpart for chemical substances. One way of stating the analogy while recognizing the differences is to say first that PV behaves like the mixing ratio of a peculiar chemical “substance” that has zero source; i.e., is exactly conserved, away from boundaries (conserved not in the material or Lagrangian sense, but in the general sense associated with the idea of an indestructible chemical substance), and second that isentropic surfaces behave exactly as if they were impermeable to this “PV-substance” or “PVS,” even when diab...

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