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Low-dimensional models of coherent structures in turbulence

Publication ,  Journal Article
Holmes, PJ; Lumley, JL; Berkooz, G; Mattingly, JC; Wittenberg, RW
Published in: Physics Report
January 1, 1997

For fluid flow one has a well-accepted mathematical model: the Navier-Stokes equations. Why, then, is the problem of turbulence so intractable? One major difficulty is that the equations appear insoluble in any reasonable sense. (A direct numerical simulation certainly yields a "solution", but it provides little understanding of the process per se.) However, three developments are beginning to bear fruit: (1) The discovery, by experimental fluid mechanicians, of coherent structures in certain fully developed turbulent flows; (2) the suggestion, by Ruelle, Takens and others, that strange attractors and other ideas from dynamical systems theory might play a role in the analysis of the governing equations, and (3) the introduction of the statistical technique of Karhunen-Loève or proper orthogonal decomposition, by Lumley in the case of turbulence. Drawing on work on modeling the dynamics of coherent structures in turbulent flows done over the past ten years, and concentrating on the near-wall region of the fully developed boundary layer, we describe how these three threads can be drawn together to weave low-dimensional models which yield new qualitative understanding. We focus on low wave number phenomena of turbulence generation, appealing to simple, conventional modeling of inertial range transport and energy dissipation.

Duke Scholars

Published In

Physics Report

DOI

ISSN

0370-1573

Publication Date

January 1, 1997

Volume

287

Issue

4

Start / End Page

337 / 384

Related Subject Headings

  • Nuclear & Particles Physics
  • 51 Physical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Holmes, P. J., Lumley, J. L., Berkooz, G., Mattingly, J. C., & Wittenberg, R. W. (1997). Low-dimensional models of coherent structures in turbulence. Physics Report, 287(4), 337–384. https://doi.org/10.1016/S0370-1573(97)00017-3
Holmes, P. J., J. L. Lumley, G. Berkooz, J. C. Mattingly, and R. W. Wittenberg. “Low-dimensional models of coherent structures in turbulence.” Physics Report 287, no. 4 (January 1, 1997): 337–84. https://doi.org/10.1016/S0370-1573(97)00017-3.
Holmes PJ, Lumley JL, Berkooz G, Mattingly JC, Wittenberg RW. Low-dimensional models of coherent structures in turbulence. Physics Report. 1997 Jan 1;287(4):337–84.
Holmes, P. J., et al. “Low-dimensional models of coherent structures in turbulence.” Physics Report, vol. 287, no. 4, Jan. 1997, pp. 337–84. Scopus, doi:10.1016/S0370-1573(97)00017-3.
Holmes PJ, Lumley JL, Berkooz G, Mattingly JC, Wittenberg RW. Low-dimensional models of coherent structures in turbulence. Physics Report. 1997 Jan 1;287(4):337–384.
Journal cover image

Published In

Physics Report

DOI

ISSN

0370-1573

Publication Date

January 1, 1997

Volume

287

Issue

4

Start / End Page

337 / 384

Related Subject Headings

  • Nuclear & Particles Physics
  • 51 Physical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences