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Intermittency in turbulence: computing the scaling exponents in shell models.

Roberto Benzi1, Luca Biferale, Mauro Sbragaglia

  • 1Dipartimento di Fisica and IFM, Sezione di Roma, Università Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Rome, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
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We developed a stochastic closure for turbulence shell models to calculate anomalous scaling exponents. This method connects zero-modes and cascade processes in passive scalar models.

Area of Science:

  • Fluid dynamics
  • Statistical physics
  • Turbulence modeling

Background:

  • Turbulence phenomena involve complex multiscale interactions.
  • Shell models offer a simplified framework for studying turbulence.
  • Anomalous scaling exponents characterize energy transfer and dissipation.

Purpose of the Study:

  • To introduce a stochastic closure for multiscale correlation functions in turbulence shell models.
  • To develop a method for calculating anomalous scaling exponents of structure functions.
  • To explore the connection between zero-modes and cascade processes in passive scalar turbulence.

Main Methods:

  • Applying a stochastic closure to the equation of motion for multiscale correlation functions.
  • Utilizing exact constraints from the equation of motion to derive a closure scheme.

Related Experiment Videos

  • Performing explicit calculations for the fifth-order scaling exponent.
  • Adapting the method for Kraichnan passive scalar shell models.

    • Main Results:

    • A plausible closure scheme for calculating anomalous scaling exponents was presented.
    • An explicit calculation of the fifth-order scaling exponent was performed by varying a model parameter.
    • The study established a link between zero-modes and time-dependent cascade processes in passive scalar turbulence.

    Conclusions:

    • The stochastic closure provides a viable approach for studying anomalous scaling in turbulence.
    • The method offers insights into the dynamics of energy transfer and dissipation.
    • The connection between zero-modes and cascade processes is significant for understanding passive scalar transport.