Comments on some recent measurements of anomalously steep N₂O and O₃ tracer spectra in the stratospheric surf zone

Recent aircraft measurements, primarily in the extratropics, of the horizontal variance of nitrous oxide (N₂O) and ozone (O₃) in the middle stratosphere indicate that horizontal spectra of the tracer variance scale nearly as k^-2, where k is the spatial wavenumber along the aircraft flight track [Strahan and Mahlman, 1994; Bacmeister et al., 1996]. This spectral scaling has been regarded as inconsistent with the accepted picture of stratospheric tracer motion; large-scale quasi-two-dimensional tracer advection typically yields a k^-1 scaling (i.e., the classical Batchelor spectrum). In this paper it is argued that the nearly k^-2 scaling seen in the measurements is a natural outcome of quasi-two-dimensional filamentation of the polar vortex edge. The accepted picture of stratospheric tracer motion can thus be retained: no additional physical processes are needed to account for deviations from the Batchelor spectrum. Our argument is based on the finite lifetime of tracer filaments and on the "singularity spectrum" associated with a one-dimensional field composed of randomly spaced jumps in concentration.