Built-in support for (relative) potential vorticity

A user has requested direct support for potential vorticity, stating that it is rare for scientists to use the already-supported relative vorticity directly & instead they will usually work with vorticity via this potential quantity.

I've had a look at the definitions & (as conveyed well in this resource, see sections 3.5.2 & 3.5.3) it is the normalised dot product of the (absolute - but I assume relative potential vorticity is defined & used with the relative equivalent) vorticity with the gradient of some conserved quantity, in practice potential temperature.

That should not be too difficult to implement(?) as a function akin to cf.relative_voriticty taking, as well as u & v wind fields, two other input fields, temperature & pressure level. Though we might need to be careful to document mathematical assumptions made by any algorithm applied, as per the literature.

After a brief look around across other libraries, I found a pair of NCL functions that calculate the potential vorticity, possibly useful as a reference.

Start by reviewing the existing cf.relative_voriticity functionality and the definitions in sections 3.5.2 and 3.5.3 of the linked resource. Compare the proposed calculation with the NCL potential-vorticity functions, resolve the relative versus absolute interpretation and required inputs, and document the mathematical assumptions when the feature is complete.