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Cascade model of fully developed turbulence

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Abstract

A simple system of quadratically nonlinear equations representing a hierarchy of frequency scales is derived from a cutoff version of Burgers' equation. When forced, the model system reproduces a number of qualitative features of fully developed turbulence. In equilibrium, the model exhibits, in addition to the energy, an extensive isolating integral of the motion that is cubic in the velocity.

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References

  1. L. D. Landau and E. M. Lifshitz,Fluid Dynamics (Addison-Wesley, Reading, Mass., 1959).

    Google Scholar 

  2. A. S. Monin and A. M. Yaglom,Statistical Fluid Mechanics, Vol. 2 (MIT, Cambridge, Mass., 1975).

    Google Scholar 

  3. P. G. Saffman, inTopics in Nonlinear Physics, N. J. Zabusky, ed. (Springer-Verlag, New York, 1968).

    Google Scholar 

  4. U. Frisch, P. L. Sulem, and M. Nelkin, to appearJ. Fluid Mech. 87 (1978).

  5. V. N. Desnyansky and E. A. Novikiov,Prinkl. Mat. Mekh. 38:507 (1974) (J. Appl. Math. Mech.).

    Google Scholar 

  6. V. N. Desnyansky and E. A. Novikov,Atmos. Oceanic Phys. 10:127 (1974).

    Google Scholar 

  7. M. Nelkin and T. L. Bell,Phys. Fluids 20:345 (1977).

    Google Scholar 

  8. T. L. Bell and M. Nelkin, to appearJ. Fluid Mech. (1978).

  9. E. D. Siggia,Phys. Rev. A 15:1730 (1977).

    Google Scholar 

  10. E. D. Siggia,Phys. Rev. A 17:1166 (1978).

    Google Scholar 

  11. R. H. Kraichnan,J. Fluid Mech. 67:155 (1975).

    Google Scholar 

  12. J. R. Herring and R. H. Kraichnan, inStatistical Models and Turbulence, M. Rosenblatt and C. Van Atta, eds. (Springer-Verlag, New York, 1972).

    Google Scholar 

  13. R. H. Kraichnan,Phys. Fluids 7:1723 (1964).

    Google Scholar 

  14. E. G. Harris, inAdvances in Plasma Physics, Vol. 3, A. Simon and W. B. Thompson, eds. (Wiley-Interscience, New York, 1969).

    Google Scholar 

  15. R. H. Kraichnan,Phys. Fluids 10:1417 (1967).

    Google Scholar 

  16. O. H. Hald,Phys. Fluids 19:914 (1976).

    Google Scholar 

  17. J. Lee,Phys. Fluids 20:1250 (1977).

    Google Scholar 

  18. D. Fyfe and D. Montgomery,Phys. Fluids 21:316 (1978).

    Google Scholar 

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Author notes

  1. Eric D. Siggia

    Present address: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York

Authors and Affiliations

  1. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York

    Robert M. Kerr

  2. Laboratory of Atomic and Solid State Physics and Laboratory of Nuclear Studies, Cornell University, Ithaca, New York

    Eric D. Siggia

  3. National Center for Atmospheric Research, Boulder, Colorado

    Eric D. Siggia

Authors
  1. Robert M. Kerr
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  2. Eric D. Siggia
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Additional information

This work was aided by a direct grant of computer time from NCAR. This work was in part supported by the National Science Foundation under Grant No. ENG 7408501A02.

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Kerr, R.M., Siggia, E.D. Cascade model of fully developed turbulence. J Stat Phys 19, 543–552 (1978). https://doi.org/10.1007/BF01011698

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  • DOI: https://doi.org/10.1007/BF01011698

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