On the Formation of Potential-Vorticity Anomalies in Upper-Level Jet-Front Systems

Abstract

We review and discuss a difference in interpretation of the role of turbulence in modifying the potential-vorticity distribution in the vicinity of upper-level jet-front systems. In the late 1970s, M. A. Shapiro presented observational evidence that turbulent mixing of heat can result in a positive anomaly of the Ertel potential vorticity on the cyclonic-shear side of upper-level jets near the level of maximum wind. E. F. Danielsen and collaborators disputed this evidence and the accompanying interpretation. They argued that the turbulent mixing of potential vorticity can be described in terms of downgradient diffusion, in the same sense as for a passive chemical tracer. Accordingly, turbulent mixing cannot produce anomalies from initially smooth distributions of potential vorticity. In our view, this dispute stems from differences in the averaging procedures used to analyze turbulent flows, which lead to fundamentally different definitions of potential vorticity. Shapiro defined potential vorticity as the scalar product of the averaged absolute vorticity and the averaged potential-temperature gradient, whereas Danielson et al. defined it, in their analytical framework, as the average of the scalar product of these quantities. We conclude that the positive anomaly of potential vorticity identified by Shapiro is plausible if one accepts the definition of potential vorticity used in his studies. Moreover. we believe Shapiro's alternative to be the only practical option when working with observed or simulated data. Even if Danielsen's alternative could be adopted in practice, we suggest that its utility as a tracer is problematic in view of the questionable validity of the downgradient diffusion of potential vorticity.