Nonconservation of Ertel Potential Vorticity in Hydrogen Atmospheres

Abstract

The compositions of the atmospheres of the outer planets are dominated by molecular hydrogen. The hydrogen ortho and para forms (proton spins parallel and antiparallel) are observed to have ratios that are not in thermodynamic equilibrium, with spatial variations, probably due to vertical motions that transport fluid from a different temperature regime. Conversion between the two forms produces significant ?latent heat? release, but conversion is thought to be so slow that this heating is extremely small. Because the two forms of hydrogen have different specific heats and their abundance ratio is spatially variable, Ertel's potential vorticity is not conserved, even in the adiabatic and frictionless limit. In this paper the degree of nonconservation is assessed by scale analysis, for typical observed ortho?para inhomogeneity. A numerical example similar to Jupiter's Great Red Spot is presented. Analysis is restricted to large-scale motions in the stable upper tropospheres of the planets, where the quasigeostrophic approximation applies. A major result is that a generalization of quasigeostrophic potential vorticity is still conserved, and that the para fraction is merely an inert tracer in this regime. The Ertel isentropic potential vorticity is not conserved, even to leading order, except in special regions where the ortho? para ratio is exceptionally homogeneous.