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Singularities in multifractal turbulence dissipation networks and their degeneration

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  • Bershadskii, A.
  • Gibson, C.H.

Abstract

We suggest that large-scale turbulence dissipation is concentrated along caustic networks (that appear due to vortex sheet instability in three-dimensional space), leading to an effective fractal dimension Deff = 53 of the networl backbone (without caustic singularities) and a turbulence intermittency exponent μ = 16. If there are singularities on these caustic networks then Deff < 53 and μ > 16. It is shown (using the theory of caustic singularities) that the strongest (however, stable on the backbone) singularities lead to Deff = 43 (an elastic backbone) and to μ = 13. Thus, there is a restriction of the network fractal variability: 43 < Deff < 53, and consequently: 16 < μ < 13.

Suggested Citation

  • Bershadskii, A. & Gibson, C.H., 1994. "Singularities in multifractal turbulence dissipation networks and their degeneration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(3), pages 251-260.
    • Handle: RePEc:eee:phsmap:v:212:y:1994:i:3:p:251-260
    DOI: 10.1016/0378-4371(94)90331-X
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    References listed on IDEAS

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    1. Bershadskii, A. & Kit, E. & Tsinober, A., 1993. "Self-organization and fractal dynamics in turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(3), pages 453-475.
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