Ertel's Potential Vorticity in Unstratified Turbulence

Abstract

The evolution of Ertel's potential vorticity (PV) is examined in direct numerical simulations (DNS) of decaying turbulence advecting passive scalars and in a generalized Taylor-Green vortex (TGV). It is noted that although PV itself is advected as a passive scalar, its dissipation occurs over all scales and is not concentrated in the velocity or scalar dissipations range. Thus, attempts to invoke cascade arguments to infer an inertial range for PV variance are vitiated. Moreover, for the TGV it is noted that molecular dissipation can create PV from an initial state for which it is everywhere zero. For the random initial value problem, the DNS results suggest a simple characterization of PV dissipation, which implies that for isotropic turbulence (and small Prandtl numbers) PV decays roughly exponentially on a lime scale ? (L/Urms)R?½, L being the integral scale, urms the large rms velocity, and Rrms, the microscale Reynolds number. The statistics of PV are also examined, and it is noted that it is far from Gaussian, even at modest values of Reynolds number R?.