## potential vorticity

(Sometimes called absolute potential vorticity.) The specific volume times the scalar product of the absolute vorticity vector and the gradient of potential temperature: where α is the specific volume,

**Ω**the angular velocity vector of the earth's rotation,**u**the three- dimensional vector velocity relative to the rotating earth, and θ the potential temperature.In the absence of friction and heat sources, the Ertel potential vorticity This nonhydrostatic version is not necessary for the analysis of large-scale weather systems, and an approximate hydrostatic version is usually used. This approximate version neglects terms involving the vertical velocity The potential vorticity has the SI units m

*P*is a materially conservative property (it remains constant for each particle). In spherical coordinates (λ, φ,*r*), where λ is longitude, φ is latitude, and*r*is the distance from the center of the earth, the above expression for*P*becomes*w*, neglects the Coriolis terms proportional to the cosine of the latitude, and makes selective use of*r*≈*a*, where*a*is the constant radius of the earth. In this way we obtain the approximate form^{2}s^{-1}K kg^{-1}. It has become accepted to define 1.0 × 10^{-6}m^{2}s^{-1}K kg^{-1}as one potential vorticity unit (1 PVU).*See*vorticity equation.Gill, A. E. 1982. Atmosphere–Ocean Dynamics. Academic Press, . 237–241.