Abstract
Navier-Stokes turbulence at ordinarily large Reynolds numbers can involve excitation of perhaps 1018 Fourier modes. A variety of proposals for reduced description have been offered, both to gain physical insight and to make computation feasible. The present brief and idiosyncratic survey discusses Galerkin approximations, Liapunov bases, Karhunen-Loeve decompositions, and statistically based decimation techniques.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. Lindenberg and B. J. West,J. Atmos. Sci. 41:3021 (1984).
R. H. Kraichnan,Adv. Math. 16:305 (1975).
D. Forster, D. R. Nelson, and M. J. Stephen,Phys. Rev. A 16:732 (1977).
V. Yakhot and S. A. Orszag,J. Sci. Comput. 1:3 (1986).
R. H. Kraichnan, inTheoretical Approaches to Turbulence, D. L. Dwoyer, M. Y. Hussaini, and R. G. Voight, eds. (Springer-Verlag, New York, 1985), pp. 91–135.
J. L. Lumley, inTransition and Turbulence, R. E. Meyer, ed. (Academic Press, New York, 1981), pp. 215–242.
N. Aubry, P. Holmes, J. L. Lumley, and E. Stone, Cornell University Report FDA-86-15 (1986).
N. Aubry and L. R. Keefe, Stanford University Center for Turbulence Research Report CTR-S87 (1987).
R. Grappin and J. Léorat,Phys. Rev. Lett. 59:1100 (1987).
R. H. Kraichnan and D. Montgomery,Rep. Prog. Phys. 43:547 (1979).
L. Keefe, P. Moin, and J. Kim, preprint (1987).
R. H. Kraichnan,13:569 (1970).
R. H. Kraichnan,J. Math. Phys. 2:124 (1961);2:205 (1962).
R. H. Kraichnan,J. Fluid Mech. 41:189 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kraichnan, R.H. Reduced descriptions of hydrodynamic turbulence. J Stat Phys 51, 949–963 (1988). https://doi.org/10.1007/BF01014893
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01014893