A reduced dynamical model of convective flows in tall laterally heated cavities

A. Liakopoulos; P. A. Blythe; H. Gunes

doi:10.1098/rspa.1997.0037

A reduced dynamical model of convective flows in tall laterally heated cavities

A. Liakopoulos^*, P. A. Blythe, H. Gunes

^*Corresponding author for this work

Lehigh University

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

49 Citations (Scopus)

Abstract

Proper orthogonal decomposition (the Karhunen-Koeve expansion) is applied to convective flows in a tall differentially heated cavity. Empirical spatial eigenfunctions are computed from a multicellular solution at supercritical conditions beyond the first Hopf bifurcation. A low-dimensional model for the dynamical behaviour is then constructed using Galerkin projection. The reduced model successfully predicts the first Hopf bifurcation of the multicellular flow. Results determined from the low-order model are found to be in qualitative agreement with known properties of the full system even at conditions far from criticality.

Original language	English
Pages (from-to)	663-672
Number of pages	10
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	453
Issue number	1958
DOIs	https://doi.org/10.1098/rspa.1997.0037
Publication status	Published - 1997
Externally published	Yes

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title = "A reduced dynamical model of convective flows in tall laterally heated cavities",

abstract = "Proper orthogonal decomposition (the Karhunen-Koeve expansion) is applied to convective flows in a tall differentially heated cavity. Empirical spatial eigenfunctions are computed from a multicellular solution at supercritical conditions beyond the first Hopf bifurcation. A low-dimensional model for the dynamical behaviour is then constructed using Galerkin projection. The reduced model successfully predicts the first Hopf bifurcation of the multicellular flow. Results determined from the low-order model are found to be in qualitative agreement with known properties of the full system even at conditions far from criticality.",

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AU - Liakopoulos, A.

AU - Blythe, P. A.

AU - Gunes, H.

PY - 1997

Y1 - 1997

N2 - Proper orthogonal decomposition (the Karhunen-Koeve expansion) is applied to convective flows in a tall differentially heated cavity. Empirical spatial eigenfunctions are computed from a multicellular solution at supercritical conditions beyond the first Hopf bifurcation. A low-dimensional model for the dynamical behaviour is then constructed using Galerkin projection. The reduced model successfully predicts the first Hopf bifurcation of the multicellular flow. Results determined from the low-order model are found to be in qualitative agreement with known properties of the full system even at conditions far from criticality.

AB - Proper orthogonal decomposition (the Karhunen-Koeve expansion) is applied to convective flows in a tall differentially heated cavity. Empirical spatial eigenfunctions are computed from a multicellular solution at supercritical conditions beyond the first Hopf bifurcation. A low-dimensional model for the dynamical behaviour is then constructed using Galerkin projection. The reduced model successfully predicts the first Hopf bifurcation of the multicellular flow. Results determined from the low-order model are found to be in qualitative agreement with known properties of the full system even at conditions far from criticality.

UR - https://www.scopus.com/pages/publications/0030742632

U2 - 10.1098/rspa.1997.0037

DO - 10.1098/rspa.1997.0037

M3 - Article

AN - SCOPUS:0030742632

SN - 1364-5021

VL - 453

SP - 663

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JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 1958

ER -

A reduced dynamical model of convective flows in tall laterally heated cavities

Abstract

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