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2015 | 1 | 1 |

Article title

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


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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.







Physical description


11 - 6 - 2015
13 - 10 - 2015
30 - 11 - 2015


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


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