New multiscale models and self-similarity in tropical convection

Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

One of the unexplained striking features of tropical convection is the observed statistical self-similarity in clusters, superclusters, and intraseasonal oscillations through complex multiscale processes ranging from the mesoscales to the equatorial synoptic scales to the intraseasonal/planetary scales. Here new multispatialscale, multitime-scale, simplified asymptotic models are derived systematically from the equatorial primitive equations on the range of scales from mesoscale to equatorial synoptic to planetary/intraseasonal, which provide a useful analytic framework for addressing these issues. New mesoscale equatorial synoptic dynamical (MESD) models and balanced MESD (BMESD) models are developed for the multitime, multispace interaction from mesoscales to equatorial synoptic scales; new multitime versions of the intraseasonal planetary equatorial synoptic dynamics (IPESD) models are developed for multiple spatiotemporal interactions on equatorial synoptic scales and planetary scales. The mathematical character derived below for all these simplified models explicitly demonstrates that the main nonlinear interactions across scales are quasi-linear where eddy flux divergences of momentum and temperature from nonlinear advection from the smaller-scale spatiotemporal flows as well as mean source effects accumulate in time and drive the waves on the successively larger spatiotemporal scales. Furthermore, these processes that transfer energy to the next larger, longer, spatiotemporal scales are self-similar in a suitable sense established here. On the other hand, the larger scales set the environment for this transport through processes such as mean advection of the smaller scales.

Original languageEnglish (US)
Pages (from-to)1393-1404
Number of pages12
JournalJournal of the Atmospheric Sciences
Volume64
Issue number4
DOIs
StatePublished - Apr 2007

Fingerprint

convection
advection
momentum
eddy
divergence
oscillation
energy
temperature

ASJC Scopus subject areas

  • Atmospheric Science

Cite this

New multiscale models and self-similarity in tropical convection. / Majda, Andrew J.

In: Journal of the Atmospheric Sciences, Vol. 64, No. 4, 04.2007, p. 1393-1404.

Research output: Contribution to journalArticle

@article{2844d6fb946249b6ac909a477949e8b9,
title = "New multiscale models and self-similarity in tropical convection",
abstract = "One of the unexplained striking features of tropical convection is the observed statistical self-similarity in clusters, superclusters, and intraseasonal oscillations through complex multiscale processes ranging from the mesoscales to the equatorial synoptic scales to the intraseasonal/planetary scales. Here new multispatialscale, multitime-scale, simplified asymptotic models are derived systematically from the equatorial primitive equations on the range of scales from mesoscale to equatorial synoptic to planetary/intraseasonal, which provide a useful analytic framework for addressing these issues. New mesoscale equatorial synoptic dynamical (MESD) models and balanced MESD (BMESD) models are developed for the multitime, multispace interaction from mesoscales to equatorial synoptic scales; new multitime versions of the intraseasonal planetary equatorial synoptic dynamics (IPESD) models are developed for multiple spatiotemporal interactions on equatorial synoptic scales and planetary scales. The mathematical character derived below for all these simplified models explicitly demonstrates that the main nonlinear interactions across scales are quasi-linear where eddy flux divergences of momentum and temperature from nonlinear advection from the smaller-scale spatiotemporal flows as well as mean source effects accumulate in time and drive the waves on the successively larger spatiotemporal scales. Furthermore, these processes that transfer energy to the next larger, longer, spatiotemporal scales are self-similar in a suitable sense established here. On the other hand, the larger scales set the environment for this transport through processes such as mean advection of the smaller scales.",
author = "Majda, {Andrew J.}",
year = "2007",
month = "4",
doi = "10.1175/JAS3880.1",
language = "English (US)",
volume = "64",
pages = "1393--1404",
journal = "Journals of the Atmospheric Sciences",
issn = "0022-4928",
publisher = "American Meteorological Society",
number = "4",

}

TY - JOUR

T1 - New multiscale models and self-similarity in tropical convection

AU - Majda, Andrew J.

PY - 2007/4

Y1 - 2007/4

N2 - One of the unexplained striking features of tropical convection is the observed statistical self-similarity in clusters, superclusters, and intraseasonal oscillations through complex multiscale processes ranging from the mesoscales to the equatorial synoptic scales to the intraseasonal/planetary scales. Here new multispatialscale, multitime-scale, simplified asymptotic models are derived systematically from the equatorial primitive equations on the range of scales from mesoscale to equatorial synoptic to planetary/intraseasonal, which provide a useful analytic framework for addressing these issues. New mesoscale equatorial synoptic dynamical (MESD) models and balanced MESD (BMESD) models are developed for the multitime, multispace interaction from mesoscales to equatorial synoptic scales; new multitime versions of the intraseasonal planetary equatorial synoptic dynamics (IPESD) models are developed for multiple spatiotemporal interactions on equatorial synoptic scales and planetary scales. The mathematical character derived below for all these simplified models explicitly demonstrates that the main nonlinear interactions across scales are quasi-linear where eddy flux divergences of momentum and temperature from nonlinear advection from the smaller-scale spatiotemporal flows as well as mean source effects accumulate in time and drive the waves on the successively larger spatiotemporal scales. Furthermore, these processes that transfer energy to the next larger, longer, spatiotemporal scales are self-similar in a suitable sense established here. On the other hand, the larger scales set the environment for this transport through processes such as mean advection of the smaller scales.

AB - One of the unexplained striking features of tropical convection is the observed statistical self-similarity in clusters, superclusters, and intraseasonal oscillations through complex multiscale processes ranging from the mesoscales to the equatorial synoptic scales to the intraseasonal/planetary scales. Here new multispatialscale, multitime-scale, simplified asymptotic models are derived systematically from the equatorial primitive equations on the range of scales from mesoscale to equatorial synoptic to planetary/intraseasonal, which provide a useful analytic framework for addressing these issues. New mesoscale equatorial synoptic dynamical (MESD) models and balanced MESD (BMESD) models are developed for the multitime, multispace interaction from mesoscales to equatorial synoptic scales; new multitime versions of the intraseasonal planetary equatorial synoptic dynamics (IPESD) models are developed for multiple spatiotemporal interactions on equatorial synoptic scales and planetary scales. The mathematical character derived below for all these simplified models explicitly demonstrates that the main nonlinear interactions across scales are quasi-linear where eddy flux divergences of momentum and temperature from nonlinear advection from the smaller-scale spatiotemporal flows as well as mean source effects accumulate in time and drive the waves on the successively larger spatiotemporal scales. Furthermore, these processes that transfer energy to the next larger, longer, spatiotemporal scales are self-similar in a suitable sense established here. On the other hand, the larger scales set the environment for this transport through processes such as mean advection of the smaller scales.

UR - http://www.scopus.com/inward/record.url?scp=34247608253&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247608253&partnerID=8YFLogxK

U2 - 10.1175/JAS3880.1

DO - 10.1175/JAS3880.1

M3 - Article

VL - 64

SP - 1393

EP - 1404

JO - Journals of the Atmospheric Sciences

JF - Journals of the Atmospheric Sciences

SN - 0022-4928

IS - 4

ER -