Curl condition properties

The vorticity equation describes how vorticity is changed by various properties of the flow. Only in very special circumstances would the vorticity be conserved following the flow. Kelvin s circulation theorem describes how an integral measure of vorticity is conserved but is valid only for barotropic flow and furthermore requires a knowledge of the time evolution of material surfaces. There does exist a quantity, referred to as the Ertel potential vorticity, that is conserved under more general conditions than either the vorticity or the circulation. It may be shown by combining the curl of the momentum equation [Eq. (26a)] with the continuity equation [Eq. (26c)] and the thermodynamic equation [Eq. (26b)] expressed in terms of potential temperature 0 that... 

PDI has also been used for treatment of wool [179] and hair fibres [180]. King and Brockway [179] showed that PDI was able to restore part of the original properties on aged or harshly treated wool. The same enzyme was used by Brockway [180] to perform a curling, waving or straightening treatment safely under mild condition. 

---