Anomalous scaling in a model of hydrodynamic turbulence with a small parameter

@article{Pierotti1999AnomalousSI,
  title={Anomalous scaling in a model of hydrodynamic turbulence with a small parameter},
  author={Daniela Pierotti and Victor S L’vov and Anna Pomyalov and Itamar Procaccia},
  journal={EPL},
  year={1999},
  volume={50},
  pages={473-479}
}
The major difficulty in developing theories for anomalous scaling in hydrodynamic turbulence is the lack of a small parameter. In this letter we introduce a shell model of turbulence that exhibits anomalous scaling with a tunable parameter , 0 ≤ ≤ 1, representing the ratio between deterministic and random components in the coupling between N identical copies of the turbulent field. Our numerical experiments give strong evidence that in the limit N → ∞ anomalous scaling sets in proportional to 4… 
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References

SHOWING 1-10 OF 19 REFERENCES

Dynamical Systems Approach to Turbulence

Introduction 1. Turbulence and dynamical systems 2. Phenomenology of turbulence 3. Reduced models for hydrodynamic turbulence 4. Turbulence and coupled map lattices 5. Turbulence in the complex

Phys. Rev. E

  • Phys. Rev. E
  • 1811

Phys

  • Rev. Lett. 75, 3834
  • 1995

Improved shell model of turbulence

We introduce a shell model of turbulence that exhibits improved properties in comparison to the standard (and very popular) Gledzer, Ohkitani, and Yamada (GOY) model. The nonlinear coupling is chosen

Phys

  • Rev. E 52, 4924
  • 1995

Phys

  • 2, 124
  • 1961

Phys

  • Rev. Lett. 80, 5536
  • 1998

Phys. Fluids

  • Phys. Fluids
  • 2000

J. Math. Phys

  • J. Math. Phys
  • 1961

Random Coupling Model and Self-Consistent ǫ-Expansion Method