A theory for the atmospheric energy spectrum

Depth-limited temperature anomalies at the tropopause

R. Tulloch, K. S. Smith

Research output: Contribution to journalArticle

Abstract

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
Volume103
Issue number40
DOIs
StatePublished - Oct 3 2006

Fingerprint

Temperature

Keywords

  • Atmospheric dynamics
  • Geophysical turbulence
  • Meteorology

ASJC Scopus subject areas

  • Genetics
  • General

Cite this

@article{f4d6b5e462a34073944b02f2396ac577,
title = "A theory for the atmospheric energy spectrum: Depth-limited temperature anomalies at the tropopause",
abstract = "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.",
keywords = "Atmospheric dynamics, Geophysical turbulence, Meteorology",
author = "R. Tulloch and Smith, {K. S.}",
year = "2006",
month = "10",
day = "3",
doi = "10.1073/pnas.0605494103",
language = "English (US)",
volume = "103",
pages = "14690--14694",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
number = "40",

}

TY - JOUR

T1 - A theory for the atmospheric energy spectrum

T2 - Depth-limited temperature anomalies at the tropopause

AU - Tulloch, R.

AU - Smith, K. S.

PY - 2006/10/3

Y1 - 2006/10/3

N2 - 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.

AB - 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.

KW - Atmospheric dynamics

KW - Geophysical turbulence

KW - Meteorology

UR - http://www.scopus.com/inward/record.url?scp=33749508464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749508464&partnerID=8YFLogxK

U2 - 10.1073/pnas.0605494103

DO - 10.1073/pnas.0605494103

M3 - Article

VL - 103

SP - 14690

EP - 14694

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 40

ER -