Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic Rossby waves

Joseph A. Biello, Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

Two-layer equatorial primitive equations for the free troposphere in the presence of a thin atmospheric boundary layer and thermal dissipation are developed here. An asymptotic theory for the resonant nonlinear interaction of long equatorial baroclinic and barotropic Rossby waves is derived in the presence of such dissipation. In this model, a self-consistent asymptotic derivation establishes that boundary layer flows are generated by meridional pressure gradients in the lower troposphere and give rise to degenerate equatorial Ekman friction. That is to say, the asymptotic model has the property that the dissipation matrix has one eigenvalue which is nearly zero: therefore the dynamics rapidly dissipates flows with pressure at the base of the troposphere and creates barotropic/baroclinic spin up/spin down. The simplified asymptotic equations for the amplitudes of the dissipative equatorial barotropic and baroclinic waves are studied by linear theory and integrated numerically. The results indicate that although the dissipation slightly weakens the tropics to midlatitude connection, strong localized wave packets are nonetheless able to exchange energy between barotropic and baroclinic waves on intraseasonal timescales in the presence of baroclinic mean shear. Interesting dissipation balanced wave-mean flow states are discovered through numerical simulations. In general, the boundary layer dissipation is very efficient for flows in which the barotropic and baroclinic components are of the same sign at the base of the free troposphere whereas the boundary layer dissipation is less efficient for flows whose barotropic and baroclinic components are of opposite sign at the base of the free troposphere.

Original languageEnglish (US)
Pages (from-to)85-127
Number of pages43
JournalGeophysical and Astrophysical Fluid Dynamics
Volume98
Issue number2
DOIs
StatePublished - Apr 2004

Fingerprint

barotropic wave
Troposphere
Rossby wave
planetary waves
dissipation
boundary layers
Boundary layers
boundary layer
troposphere
baroclinic waves
interactions
baroclinic wave
Tropics
Atmospheric boundary layer
Wave packets
Boundary layer flow
barotropic flow
Pressure gradient
primitive equations
baroclinic motion

Keywords

  • Amplitude equations
  • Atmospheric boundary layer
  • Equatorial Rossby waves

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics
  • Space and Planetary Science
  • Computational Mechanics
  • Mechanics of Materials
  • Astronomy and Astrophysics

Cite this

Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic Rossby waves. / Biello, Joseph A.; Majda, Andrew J.

In: Geophysical and Astrophysical Fluid Dynamics, Vol. 98, No. 2, 04.2004, p. 85-127.

Research output: Contribution to journalArticle

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