Evidence and Interpretation of a Spectral Gap in the Turbulent Atmospheric Temperature Spectra

Abstract

An analytical formulation of the turbulent potential energy spectrum in a stably stratified medium, valid in the inertia buoyancy subrange, is deduced in the framework of classical assumptions (no source, no sink, spectra locality and proportionality of the buoyancy flux to the mean potential temperature gradient) using recently published results of J. Weinstock. This formulation predicts a gap between two spectral ranges where temperature fluctuations mainly result from either turbulent advection or vertical displacements of fluid particles. In the former, the spectrum reduces to the well-known Obbukov-Corrsin-5/3 power law while in the latter, it becomes proportional to the kinetic energy spectrum, with a ?3 spectral slope and a reverse potential energy flux. Experimental evidence obtained in the stratosphere supports this theoretical description.