### Abstract

In the tropical atmosphere, waves can couple with water vapor and convection to form large-scale coherent structures called convectively coupled waves (CCWs). The effects of water vapor and convection lead to CCW-mean flow interactions that are different from traditional wave-mean flow interactions in many ways. CCW-mean flow interactions are studied here in two types of models: a multiscale model that represents CCW structures in two spatial dimensions directly above the Earth's equator, and an amplitude model in the form of ordinary differential equations for the CCW and mean flow amplitudes. The amplitude equations are shown to capture the qualitative behavior of the spatially resolved model, including nonlinear oscillations and a Hopf bifurcation as the climatological background wind is varied. Furthermore, an even simpler set of amplitude equations can also capture some of the essential oscillatory behavior, and it is shown to be equivalent to the Duffing oscillator. The basic interaction mechanisms are that the mean flow's vertical shear determines the preferred propagation direction of the CCW, and the CCWs can drive changes in the mean shear through convective momentum transport, with energy transfer that is sometimes upscale and sometimes downscale. In addition to CCW-mean flow interactions, also discussed are CCW-water vapor interactions, which form the basis of the Madden-Julian Oscillation (MJO) skeleton model of the first two authors. The key parameter of the MJO skeleton model is estimated theoretically and is in agreement with previously conjectured values.

Original language | English (US) |
---|---|

Pages (from-to) | 513-532 |

Number of pages | 20 |

Journal | Theoretical and Computational Fluid Dynamics |

Volume | 27 |

Issue number | 3-4 |

DOIs | |

State | Published - Jun 2013 |

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### Keywords

- Convective momentum transport
- Convectively coupled equatorial waves
- Madden-Julian Oscillation
- Tropical convection
- Wave-mean flow interaction

### ASJC Scopus subject areas

- Condensed Matter Physics
- Fluid Flow and Transfer Processes
- Engineering(all)
- Computational Mechanics

### Cite this

*Theoretical and Computational Fluid Dynamics*,

*27*(3-4), 513-532. https://doi.org/10.1007/s00162-012-0268-8

**Convectively coupled wave-environment interactions.** / Stechmann, Samuel N.; Majda, Andrew J.; Skjorshammer, Dmitri.

Research output: Contribution to journal › Article

*Theoretical and Computational Fluid Dynamics*, vol. 27, no. 3-4, pp. 513-532. https://doi.org/10.1007/s00162-012-0268-8

}

TY - JOUR

T1 - Convectively coupled wave-environment interactions

AU - Stechmann, Samuel N.

AU - Majda, Andrew J.

AU - Skjorshammer, Dmitri

PY - 2013/6

Y1 - 2013/6

N2 - In the tropical atmosphere, waves can couple with water vapor and convection to form large-scale coherent structures called convectively coupled waves (CCWs). The effects of water vapor and convection lead to CCW-mean flow interactions that are different from traditional wave-mean flow interactions in many ways. CCW-mean flow interactions are studied here in two types of models: a multiscale model that represents CCW structures in two spatial dimensions directly above the Earth's equator, and an amplitude model in the form of ordinary differential equations for the CCW and mean flow amplitudes. The amplitude equations are shown to capture the qualitative behavior of the spatially resolved model, including nonlinear oscillations and a Hopf bifurcation as the climatological background wind is varied. Furthermore, an even simpler set of amplitude equations can also capture some of the essential oscillatory behavior, and it is shown to be equivalent to the Duffing oscillator. The basic interaction mechanisms are that the mean flow's vertical shear determines the preferred propagation direction of the CCW, and the CCWs can drive changes in the mean shear through convective momentum transport, with energy transfer that is sometimes upscale and sometimes downscale. In addition to CCW-mean flow interactions, also discussed are CCW-water vapor interactions, which form the basis of the Madden-Julian Oscillation (MJO) skeleton model of the first two authors. The key parameter of the MJO skeleton model is estimated theoretically and is in agreement with previously conjectured values.

AB - In the tropical atmosphere, waves can couple with water vapor and convection to form large-scale coherent structures called convectively coupled waves (CCWs). The effects of water vapor and convection lead to CCW-mean flow interactions that are different from traditional wave-mean flow interactions in many ways. CCW-mean flow interactions are studied here in two types of models: a multiscale model that represents CCW structures in two spatial dimensions directly above the Earth's equator, and an amplitude model in the form of ordinary differential equations for the CCW and mean flow amplitudes. The amplitude equations are shown to capture the qualitative behavior of the spatially resolved model, including nonlinear oscillations and a Hopf bifurcation as the climatological background wind is varied. Furthermore, an even simpler set of amplitude equations can also capture some of the essential oscillatory behavior, and it is shown to be equivalent to the Duffing oscillator. The basic interaction mechanisms are that the mean flow's vertical shear determines the preferred propagation direction of the CCW, and the CCWs can drive changes in the mean shear through convective momentum transport, with energy transfer that is sometimes upscale and sometimes downscale. In addition to CCW-mean flow interactions, also discussed are CCW-water vapor interactions, which form the basis of the Madden-Julian Oscillation (MJO) skeleton model of the first two authors. The key parameter of the MJO skeleton model is estimated theoretically and is in agreement with previously conjectured values.

KW - Convective momentum transport

KW - Convectively coupled equatorial waves

KW - Madden-Julian Oscillation

KW - Tropical convection

KW - Wave-mean flow interaction

UR - http://www.scopus.com/inward/record.url?scp=84878333845&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878333845&partnerID=8YFLogxK

U2 - 10.1007/s00162-012-0268-8

DO - 10.1007/s00162-012-0268-8

M3 - Article

AN - SCOPUS:84878333845

VL - 27

SP - 513

EP - 532

JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

SN - 0935-4964

IS - 3-4

ER -