A SOLENOID - MASS CONTINUITY INVARIANCE CRITERION-RELATED TO THE POTENTIAL VORTICITY CONSERVATION

As characteristic of a quasi-hydrostatic and isentropic shallow-fluid atmosphere, a criterion of conservation along trajectories is derived for an integral solenoid term, or, by incorporating the mass continuit y equation, a corresponding differential quantity. In the latter case, the individual invariant consists of the product of a static stabilit y parameter (-partial derivative theta/partial derivative p) and the v ertical component of the solenoidal vector del(theta) x (wdel(theta)z) . By this coupling one is led to the dynamical importance this invaria nce principle attains through its direct interdependency with ERTEL's potential vorticity theorem. In combination the two invariance princip les mediate a fuller description of the potential vorticity conservati on than the ''classical'' principle concerning the invariant eta(theta )partial derivative theta/partial derivative p.