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

• Authors: Shengqian Chen , Andrew J. Majda , Samuel N. Stechmann
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

tropical intraseasonal variability; tropical-extratropical interactions; multiscale asymptotic analysis

• Publisher: De Gruyter Open
• Journal: Mathematics of Climate and Weather Forecasting
• Year: 2015
• Volume: 1
• Issue: 1

Dates

received

11 - 6 - 2015

accepted

13 - 10 - 2015

online

30 - 11 - 2015

Contributors

author

Shengqian Chen

• Department of Mathematics, University of Wisconsin – Madison, Madison, Wisconsin,
  USA

author

Andrew J. Majda

• Department of Mathematics, and Center for Atmosphere-Ocean Sciences, Courant Institute of Mathematical
  Science, New York University, New York, New York, USA

author

Samuel N. Stechmann

• Department of Mathematics, and Department of Atmospheric and Oceanic Sciences, University of
  Wisconsin – Madison, Madison, Wisconsin, USA

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Identifiers

DOI

10.1515/mcwf-2015-0003