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Application of E-infinity theory to turbulence

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  • He, Ji-Huan

Abstract

El-Naschie’s E-infinity theory is applied to turbulence. The Hausdorff-fractal dimension for turbulent flow is defined, the critical values for laminar flow (D=3.98) and turbulent flow (D=4.23) are obtained, and the fractal dimension for fully developed turbulent flow is D>6.8. It is also shown that the Navier–Stokes equations are invalid for an exact model of turbulent flow and that two-dimensional planar turbulence does not exist in nature.

Suggested Citation

  • He, Ji-Huan, 2006. "Application of E-infinity theory to turbulence," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 506-511.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:2:p:506-511
    DOI: 10.1016/j.chaos.2005.11.033
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    2. He, Ji-Huan & Huang, Zhende, 2006. "A novel model for allometric scaling laws for different organs," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1108-1114.
    3. Ziaei, Ali Naghi & Keshavarzi, Ali Reza & Homayoun, Emdad, 2005. "Fractal scaling and simulation of velocity components and turbulent shear stress in open channel flow," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1031-1045.
    4. Keshavarzi, Ali Reza & Ziaei, Ali Naghi & Homayoun, Emdad & Shirvani, Amin, 2005. "Fractal-Markovian scaling of turbulent bursting process in open channel flow," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 307-318.
    5. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    6. He, Ji-Huan, 2006. "An allometric scaling law between gray matter and white matter of cerebral cortex," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 864-867.
    7. El Naschie, M.S., 2005. "‘t Hooft ultimate building blocks and space–time as an infinite dimensional set of transfinite discrete points," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 521-524.
    8. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
    9. El Naschie, M.S., 2006. "Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 297-330.
    10. El Naschie, M.S., 2005. "On Penrose view of transfinite sets and computability and the fractal character of E-infinity spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 531-533.
    11. Bakunin, O.G., 2005. "Percolation models of turbulent transport and scaling estimates," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1703-1731.
    12. He, Ji-Huan, 2006. "Application of E-infinity theory to biology," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 285-289.
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    Cited by:

    1. He, Ji-Huan, 2008. "String theory in a scale dependent discontinuous space–time," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 542-545.
    2. Sergeyev, Yaroslav D., 2009. "Evaluating the exact infinitesimal values of area of Sierpinski’s carpet and volume of Menger’s sponge," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3042-3046.
    3. He, Ji-Huan & Xu, Lan, 2009. "Number of elementary particles using exceptional Lie symmetry groups hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2119-2124.
    4. He, Ji-Huan, 2007. "The number of elementary particles in a fractal M-theory of 11.2360667977 dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 346-351.
    5. Zamankhan, Piroz, 2011. "Bubbles and solid structures in a vibrated bed of granular materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(8), pages 1402-1416.
    6. Khrennikov, Andrei Yu., 2009. "Gene expression from polynomial dynamics in the 2-adic information space," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 341-347.
    7. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    8. He, Ji-Huan & Liu, Jun-Fang, 2009. "Allometric scaling laws in biology and physics," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1836-1838.
    9. Lonngren, Karl E. & Toh, Sadayoshi, 2008. "Invariants of the Richardson equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 148-150.

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