Ch. Bishop et Aj. Thorpe, POTENTIAL VORTICITY AND THE ELECTROSTATICS ANALOGY - QUASI-GEOSTROPHIC THEORY, Quarterly Journal of the Royal Meteorological Society, 120(517), 1994, pp. 713-731
Potential vorticity (PV) is a property of the atmosphere which is char
acterized by the divergence of a vector field. It is illuminating to d
raw an analogy between electrical charges and PV anomalies. Here the f
ield induced by quasi-geostrophic PV charges is chosen to be a quantit
y 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 vertica
lly oriented temperature dipole. A further consequence of this electro
statics 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 o
f 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-stabili
ty parameter, such as occur at the tropopause, affect the flow produce
d by PV anomalies. The problem of attribution, namely attributing part
s of the flow to particular PV features, is considered in the light of
the electrostatics analogy. Imposing conditions at boundaries is equi
valent to including possibly spurious PV anomalies exterior to such bo
undaries.