A theory for the atmospheric energy spectrum: Depth-limited temperature anomalies at the tropopause

R. Tulloch, K. S. Smith

Research output: Contribution to journalArticle


The horizontal spectra of atmospheric wind and temperature at the tropopause have a steep -3 slope at synoptic scales, but transition to -5/3 at wavelengths of the order of 500-1,000 km [Nastrom, G. D. & Gage, K. S. (1985) J. Atmos. Sci. 42, 950-960]. Here we demonstrate that a model that assumes zero potential vorticity and constant stratification N over a finite-depth H in the troposphere exhibits the same type of spectra. In this model, temperature perturbations generated at the planetary scale excite a direct cascade of energy with a slope of -3 at large scales, -5/3 at small scales, and a transition near horizontal wavenumber kt = f/NH, where f is the Coriolis parameter. Ballpark atmospheric estimates for N, f, and H give a transition wavenumber near that observed, and numerical simulations of the previously undescribed model verify the expected behavior. Despite its simplicity, the model is consistent with a number of perplexing features in the observations and demonstrates that a complete theory for mesoscale dynamics must take temperature advection at boundaries into account.

Original languageEnglish (US)
Pages (from-to)14690-14694
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number40
StatePublished - Oct 3 2006



  • Atmospheric dynamics
  • Geophysical turbulence
  • Meteorology

ASJC Scopus subject areas

  • General

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