Multiscale asymptotics for the Skeleton of the Madden-Julian Oscillation and Tropical–Extratropical Interactions

Shengqian Chen; Andrew J. Majda; Samuel N. Stechmann

Mathematics of Climate and Weather Forecasting (2015)

  • Volume: 1, Issue: 1
  • ISSN: 2353-6438

Abstract

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Anew model is derived and analyzed for tropical–extratropical interactions involving the Madden– Julian oscillation (MJO). The model combines (i) the tropical dynamics of the MJO and equatorial baroclinic waves and (ii) the dynamics of barotropic Rossby waves with significant extratropical structure, and the combined system has a conserved energy. The method of multiscale asymptotics is applied to systematically derive a system of ordinary differential equations (ODEs) for three-wave resonant interactions. Two novel features are (i) a degenerate auxiliary problem with overdetermined equations due to a compatibility condition (meridional geostrophic balance) and (ii) cubic self-interaction terms that are not typically found in threewave resonance ODEs. Several examples illustrate applications to MJO initiation and termination, including cases of (i) the MJO, equatorial baroclinic Rossbywaves, and barotropic Rossbywaves interacting, and (ii) the MJO, baroclinic Kelvinwaves, and barotropic Rossbywaves interacting. Resonance with the Kelvinwave is not possible here if only dry variables are considered, but it occurs in the moist model here through interactions with water vapor and convective activity.

How to cite

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Shengqian Chen, Andrew J. Majda, and Samuel N. Stechmann. "Multiscale asymptotics for the Skeleton of the Madden-Julian Oscillation and Tropical–Extratropical Interactions." Mathematics of Climate and Weather Forecasting 1.1 (2015): null. <http://eudml.org/doc/276447>.

@article{ShengqianChen2015,
abstract = {Anew model is derived and analyzed for tropical–extratropical interactions involving the Madden– Julian oscillation (MJO). The model combines (i) the tropical dynamics of the MJO and equatorial baroclinic waves and (ii) the dynamics of barotropic Rossby waves with significant extratropical structure, and the combined system has a conserved energy. The method of multiscale asymptotics is applied to systematically derive a system of ordinary differential equations (ODEs) for three-wave resonant interactions. Two novel features are (i) a degenerate auxiliary problem with overdetermined equations due to a compatibility condition (meridional geostrophic balance) and (ii) cubic self-interaction terms that are not typically found in threewave resonance ODEs. Several examples illustrate applications to MJO initiation and termination, including cases of (i) the MJO, equatorial baroclinic Rossbywaves, and barotropic Rossbywaves interacting, and (ii) the MJO, baroclinic Kelvinwaves, and barotropic Rossbywaves interacting. Resonance with the Kelvinwave is not possible here if only dry variables are considered, but it occurs in the moist model here through interactions with water vapor and convective activity.},
author = {Shengqian Chen, Andrew J. Majda, Samuel N. Stechmann},
journal = {Mathematics of Climate and Weather Forecasting},
keywords = {tropical intraseasonal variability; tropical-extratropical interactions; multiscale asymptotic analysis},
language = {eng},
number = {1},
pages = {null},
title = {Multiscale asymptotics for the Skeleton of the Madden-Julian Oscillation and Tropical–Extratropical Interactions},
url = {http://eudml.org/doc/276447},
volume = {1},
year = {2015},
}

TY - JOUR
AU - Shengqian Chen
AU - Andrew J. Majda
AU - Samuel N. Stechmann
TI - Multiscale asymptotics for the Skeleton of the Madden-Julian Oscillation and Tropical–Extratropical Interactions
JO - Mathematics of Climate and Weather Forecasting
PY - 2015
VL - 1
IS - 1
SP - null
AB - Anew model is derived and analyzed for tropical–extratropical interactions involving the Madden– Julian oscillation (MJO). The model combines (i) the tropical dynamics of the MJO and equatorial baroclinic waves and (ii) the dynamics of barotropic Rossby waves with significant extratropical structure, and the combined system has a conserved energy. The method of multiscale asymptotics is applied to systematically derive a system of ordinary differential equations (ODEs) for three-wave resonant interactions. Two novel features are (i) a degenerate auxiliary problem with overdetermined equations due to a compatibility condition (meridional geostrophic balance) and (ii) cubic self-interaction terms that are not typically found in threewave resonance ODEs. Several examples illustrate applications to MJO initiation and termination, including cases of (i) the MJO, equatorial baroclinic Rossbywaves, and barotropic Rossbywaves interacting, and (ii) the MJO, baroclinic Kelvinwaves, and barotropic Rossbywaves interacting. Resonance with the Kelvinwave is not possible here if only dry variables are considered, but it occurs in the moist model here through interactions with water vapor and convective activity.
LA - eng
KW - tropical intraseasonal variability; tropical-extratropical interactions; multiscale asymptotic analysis
UR - http://eudml.org/doc/276447
ER -

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