FLUX OF POTENTIAL VORTICITY SUBSTANCE - A SIMPLE DERIVATION AND A UNIQUENESS PROPERTY

It is well known that even in the presence of diabatic effects a conse rvation law exists for potential vorticity Q in the form partial deriv ative (rhoQ)/partial derivative t + del . J = 0, where J is a flux of potential vorticity substance. A new and extremely simple proof of thi s result is presented that uses only one fact: the vorticity vector is nondivergent. The flux vector derived by this method differs from tha t of Haynes and McIntyre by a divergence-free vector, calling attentio n to the nonuniqueness of J. It is proved, however, that the Haynes-Mc Intyre flux vector is the unique choice that is the sum of a purely ad vective flux and a nonadvective flux that depends linearly on local he ating rate and frictional forces.