Validity of the one and one-half layer quasi-geostrophic model and effective topography

Andrew Majda; Xiaoming Wang

doi:10.1080/03605300500258782

Validity of the one and one-half layer quasi-geostrophic model and effective topography

Andrew Majda, Xiaoming Wang

Research output: Contribution to journal › Article › peer-review

Abstract

We rigorously justify the so-called one and one-half layer quasi-geostrophic model from the two layer model as the ratio of the depth of the bottom layer over that of the top layer approaches infinity. The effective dynamics is given by the classical barotropic quasi-geostrophic dynamics for the bottom layer without topography, and the one layer quasi-geostrophic dynamics with the stream function of the bottom layer serving as an effective (possibly time-dependent) topography for the the top layer. Such a one and one-half layer model is utilized in successful quantitative prediction of the Great Red Spot on Jupiter (see Turkington et al., 2001).

Original language	English (US)
Pages (from-to)	1305-1314
Number of pages	10
Journal	Communications in Partial Differential Equations
Volume	30
Issue number	7-9
DOIs	https://doi.org/10.1080/03605300500258782
State	Published - 2005

Keywords

Effective topography
One and one-half layer model
Quasi-geostrophic model
Two-layer model

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605300500258782

Cite this

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title = "Validity of the one and one-half layer quasi-geostrophic model and effective topography",

abstract = "We rigorously justify the so-called one and one-half layer quasi-geostrophic model from the two layer model as the ratio of the depth of the bottom layer over that of the top layer approaches infinity. The effective dynamics is given by the classical barotropic quasi-geostrophic dynamics for the bottom layer without topography, and the one layer quasi-geostrophic dynamics with the stream function of the bottom layer serving as an effective (possibly time-dependent) topography for the the top layer. Such a one and one-half layer model is utilized in successful quantitative prediction of the Great Red Spot on Jupiter (see Turkington et al., 2001).",

keywords = "Effective topography, One and one-half layer model, Quasi-geostrophic model, Two-layer model",

author = "Andrew Majda and Xiaoming Wang",

note = "Funding Information: The authors acknowledge the financial support from NSF, DARPA, NAVY. Most of the work was done while the second author was visiting the Courant Institute of the Mathematical Sciences during the 2001–2002 academic year. Part of the work was done during the second author{\textquoteright}s visit to the Institute for Advanced Study at Princeton. The financial support and hospitality of IAS is graciously acknowledged.",

year = "2005",

doi = "10.1080/03605300500258782",

language = "English (US)",

volume = "30",

pages = "1305--1314",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "7-9",

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TY - JOUR

T1 - Validity of the one and one-half layer quasi-geostrophic model and effective topography

AU - Majda, Andrew

AU - Wang, Xiaoming

N1 - Funding Information: The authors acknowledge the financial support from NSF, DARPA, NAVY. Most of the work was done while the second author was visiting the Courant Institute of the Mathematical Sciences during the 2001–2002 academic year. Part of the work was done during the second author’s visit to the Institute for Advanced Study at Princeton. The financial support and hospitality of IAS is graciously acknowledged.

PY - 2005

Y1 - 2005

N2 - We rigorously justify the so-called one and one-half layer quasi-geostrophic model from the two layer model as the ratio of the depth of the bottom layer over that of the top layer approaches infinity. The effective dynamics is given by the classical barotropic quasi-geostrophic dynamics for the bottom layer without topography, and the one layer quasi-geostrophic dynamics with the stream function of the bottom layer serving as an effective (possibly time-dependent) topography for the the top layer. Such a one and one-half layer model is utilized in successful quantitative prediction of the Great Red Spot on Jupiter (see Turkington et al., 2001).

AB - We rigorously justify the so-called one and one-half layer quasi-geostrophic model from the two layer model as the ratio of the depth of the bottom layer over that of the top layer approaches infinity. The effective dynamics is given by the classical barotropic quasi-geostrophic dynamics for the bottom layer without topography, and the one layer quasi-geostrophic dynamics with the stream function of the bottom layer serving as an effective (possibly time-dependent) topography for the the top layer. Such a one and one-half layer model is utilized in successful quantitative prediction of the Great Red Spot on Jupiter (see Turkington et al., 2001).

KW - Effective topography

KW - One and one-half layer model

KW - Quasi-geostrophic model

KW - Two-layer model

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 7-9

ER -

Validity of the one and one-half layer quasi-geostrophic model and effective topography

Abstract

Keywords

ASJC Scopus subject areas

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