Potential vorticity and the electrostatics analogy: Quasi‐geostrophic theory

Potential vorticity (PV) is a property of the atmosphere which is characterized by the divergence of a vector field. It is illuminating to draw an analogy between electrical charges and PV anomalies. Here the field induced by quasi‐geostrophic PV charges is chosen to be a quantity that does not depend on conditions imposed at boundaries at a finite distance from the anomaly, or on the mean static‐stability or density profiles. This field describes ‘action‐at‐a‐distance’. Elementary PV charges involve circulation about a vertical axis as well as a vertically oriented temperature dipole. A further consequence of this electrostatics analogy is that the atmosphere is analogous to an anisotropic dielectric material and hence the existence of a ‘bound’ PV charge is implied. The mean static stability measures this dielectric property of the atmosphere, and the dielectric tensor for the quasi‐geostrophic system is here presented. The bound‐charge concept provides an elegant physical picture of how vertical gradients in the mean static‐stability parameter, such as occur at the tropopause, affect the flow produced by PV anomalies. The problem of attribution, namely attributing parts of the flow to particular PV features, is considered in the light of the electrostatics analogy. Imposing conditions at boundaries is equivalent to including possibly spurious PV anomalies exterior to such boundaries.