Ertel's potential vorticity in unstratified turbulence

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 time scale ~ (L/U_rms)R_γ^1/2, L being the integral scale, u_rms the large rms velocity, and R_γ the microscale Reynolds number. -Authors