Turbulent Spectrum of the Earth's Ozone Field

Abstract

The total ozone mapping spectrometer database is subjected to an analysis in terms of the Karhunen-Lo\`eve empirical eigenfunctions. The concentration variance spectrum is transformed into a wave-number spectrum, ${E}_{c}(k)$. In terms of the wave number, ${E}_{c}(k)$ is shown to be $O({k}^{\ensuremath{-}2/3})$ in the inverse cascade regime, and $O({k}^{\ensuremath{-}2})$ in the enstrophy cascade regime with the spectral knee at the wave number of baroclinic instability. The spectrum is related to known geophysical phenomena and shown to be consistent with physical dimensional reasoning for the problem. The appropriate Reynolds number for the phenomena is $\mathrm{Re}\ensuremath{\approx}{10}^{10}$.