A solenoid?Mass continuity invariance criterion related to the potential vorticity conservation

Abstract

As characteristic of a quasi-hydrostatic and isentropic shallowfluid atmosphere, a criterion of conservation along trajectories is derived for an integral solenoid term, or, by incorporating the mass continuity equation, a corresponding differential quantity. In the latter case, the individual invariant consists of the product of a static stability parameter (−δθ/δp) and the vertical component of the solenoidal vector ∇θx(w∇θz). By this coupling one is led to the dynamical importance this in variance principle attains through its direct interdependency with ERTEL's potential vorticity theorem. In combination the two invariance principles mediate a fuller description of the potential vorticity conservation than the “classical” principle concerning the invariant ηθδθ/δp.