### 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 language | English (US) |
---|---|

Pages (from-to) | 85-127 |

Number of pages | 43 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 98 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2004 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Geophysical and Astrophysical Fluid Dynamics*, vol. 98, no. 2, pp. 85-127. https://doi.org/10.1080/03091920410001686712

}

TY - JOUR

T1 - Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic Rossby waves

AU - Biello, Joseph A.

AU - Majda, Andrew J.

PY - 2004/4

Y1 - 2004/4

N2 - 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.

AB - 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.

KW - Amplitude equations

KW - Atmospheric boundary layer

KW - Equatorial Rossby waves

UR - http://www.scopus.com/inward/record.url?scp=5044229214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5044229214&partnerID=8YFLogxK

U2 - 10.1080/03091920410001686712

DO - 10.1080/03091920410001686712

M3 - Article

AN - SCOPUS:5044229214

VL - 98

SP - 85

EP - 127

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 2

ER -