Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Turbulence and the dynamics of coherent structures. I. Coherent structures

Author: Lawrence Sirovich
Journal: Quart. Appl. Math. 45 (1987), 561-571
MSC: Primary 76F99; Secondary 58F13
DOI: https://doi.org/10.1090/qam/910462
MathSciNet review: 910462
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  • [1] G. I. Taylor, Statistical theory of turbulence, Pts. I-V, Proc. Roy. Soc. A 151, 421-478 (1938)
  • [2] B. J. Cantwell, Organized motion in turbulent flow, Ann. Rev. Fluid Mech. 13, 457-515 (1981)
  • [3] J. Guckenheimer, Strange attractors in fluids: Another view, Ann. Rev. Fluid Mech. 18, 15-32 (1986) MR 828784
  • [4] J. L. Lumley, The structure of inhomogeneous turbulent flows, Atmospheric Turbulence and Radio Wave Propagation, A. M. Yaglom and V. I. Tatarski, eds., 166-178, Moskow: Nauka, 1967
  • [5] J. L. Lumley, Coherent structures in turbulence, in Transition and Turbulence, R. E. Meyer, ed., 215-242, Academic Press, N. Y., 1981
  • [6] P. Bakewell and J. L. Lumley, Viscous sublayer and adjacent wall region in turbulent pipe flow, Phys. Fluids 10, 1880-1889 (1967)
  • [7] F. R. Payne and J. L. Lumley, Large eddy structure of the turbulent wake behind a circular cylinder, Phys. Fluids 10, S194-196 (1967)
  • [8] M. N. Glauser, S. J. Lieb, and N. K. George, Coherent structure in the axisymmetric jet mixing layer, Proc. 5th Symp. Turb. Shear Flow, Cornell Univ., Springer-Verlag, N. Y., 1985
  • [9] P. Moin, Probing turbulence via large eddy simulation, AIAA Pap.-84-0174 (1984)
  • [10] R. B. Ash and M. F. Gardner, Topics in Stochastic Processes, Academic Press, N. Y., 1975 MR 0448463
  • [11] K. Fukunaga, Introduction to Statistical Pattern Recognition, Academic Press, N. Y., 1972 MR 1075415
  • [12] N. Ahmed and M. H. Goldstein, Orthogonal Transforms for Digital Signal Processing, Springer-Verlag, N. Y., 1975
  • [13] J. L. Lumley, Stochastic Tools in Turbulence, Academic Press, N. Y., 1970 MR 0451408
  • [14] G. S. Schuster, Deterministic Chaos: An Introduction, Physik-Verlag, Weinheim, FRG, 1984 MR 935128
  • [15] P. Bergé, Y. Pomeau, and C. Vidal, Order Within Chaos, Wiley, N. Y., 1986 MR 882723
  • [16] B. Malraison, P. Atten, P. Berge, and M. Dubois, Dimension d'attracteurs étranges: une détermination expérimentale au régime chaotique de deux systems convectifs, Comp. Ren. (Paris) C 297, 209- (1983)
  • [17] A. Bandstater, J. Swift, H. Swinney, H. L. Wolf, D. Farmer, E. Jen, and P. Crutchfield, Low-dimensional chaos in a hydrodynamic system, Phys. Rev. Lett. 51, 1442 (1983) MR 718791
  • [18] K. R. Sreenivasan, Transition and turbulence in fluid flows and low dimensional chaos, in Frontiers in Fluid Mechanics, S. H. Davis and J. L. Lumley, eds., 41-67, Springer-Verlag, N. Y., 1985
  • [19] P. Constantin, C. Foiaş, O. P. Manley, and R. Temam, Determining modes and fractal dimension of turbulent flows, J. Fluid Mech. 150, 427-440 (1985) MR 794051
  • [20] L. Sirovich and J. D. Rodriguez, Coherent structures and chaos: A model problem, Phys. Lett: A 120, no. 5 (1987) MR 879949
  • [21] H. Whitney, Differentiable manifolds, Ann. of Math. 37, 645- (1936) MR 1503303
  • [22] J. O. Hinze, Turbulence: An Introduction to its Mechanisms and Theory, McGraw-Hill, N. Y., 1959 MR 0105962
  • [23] H. Tennekes, and J. L. Lumley, A First Course in Turbulence, MIT Press, Cambridge, 1972
  • [24] L. Sirovich and M. Kirby, Low-dimensional procedure for characterization of human faces, J. Opt. Soc. 4, no. 3 (1987)
  • [25] L. Sirovich, M. Maxey, and H. Tarman, Eigenfunction analysis of turbulence correlations in thermal convection, Bull. Amer. Phys. Soc. 31, 1676 (1986)
  • [26] F. Riesz, and B. Sz. Nagy, Functional Analysis, Ungar, N. Y., 1955 MR 0071727
  • [27] O. A. Ladyshenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, N. Y., 1969
  • [28] S. A. Orzag and G. S. Patterson, Numerical simulation of three-dimensional homogeneous isotropic turbulence, Phys. Rev. Letters 28, 76 (1972)
  • [29] G. S. Patterson and S. A. Orzag, Spectral calculation of isotropic turbulence, Phys. Fluids 14, 2538 (1971)
  • [30] D. Gottlieb and S. A. Orzag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1977
  • [31] C. Canuto, M. Y. Hussaini, A. Quarderonic, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, N. Y., 1987
  • [32] R. S. Rogallo and P. Moin, Numerical simulation of turbulent flows, Ann. Rev. Fluid Mech. 16, 99-127 (1984)
  • [33] J. H. Curry, J. R. Herring, J. Loncaric, and S. A. Orzag, Order and disorder in two- and three-dimensional Bénard convection, J. Fluid Mech. 147, 1-38 (1984)
  • [34] T. M. Eidson, M. Y. Hussaini, and T. A. Zang, Simulation of the turbulent Rayleigh-Bénard problem using a spectral/finite difference technique, ICASE Rep. 86-6 (1986)
  • [35] S. A. Orzag and L. C. Kells, Transition to turbulence in plane Poiseuille and Couette flow, J. Fluid Mech. 96, 159-205 (1980)
  • [36] J. W. Deardoff, A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers, J. Fluid Mech. 41, 453-480 (1970)
  • [37] P. Moin and J. Kim, Numerical investigation of turbulent channel flow, J. Fluid Mech. 118, 341-377 (1982)

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DOI: https://doi.org/10.1090/qam/910462
Article copyright: © Copyright 1987 American Mathematical Society

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