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Related Experiment Videos

Inertial range determination for aerothermal turbulence using fractionally differenced processes and wavelets.

W Constantine1, D B Percival, P G Reinhall

  • 1Insightful Corporation, Suite 500, 1700 Westlake Avenue North, Seattle, Washington 98109-3044, USA. wconstan@insightful.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
Summary

This study models aerothermal turbulence using fractionally differenced processes and wavelet techniques. Results reveal significant departures from Kolmogorov turbulence, introducing a new statistic to quantify these scale-dependent variations.

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Area of Science:

  • Fluid Dynamics
  • Turbulence Modeling
  • Statistical Physics

Background:

  • Aerothermal turbulence data analysis often relies on theoretical models like Kolmogorov's.
  • Understanding deviations from these models is crucial for accurate predictions in high-temperature gas flows.
  • Fractionally differenced (FD) processes offer a flexible framework for modeling complex time series data.

Purpose of the Study:

  • To model aerothermal turbulence data using fractionally differenced processes.
  • To estimate FD model parameters using wavelet techniques.
  • To investigate deviations from Kolmogorov turbulence and develop a statistic to quantify them.

Main Methods:

  • Application of fractionally differenced (FD) processes to aerothermal turbulence data.

Related Experiment Videos

  • Estimation of FD parameters using wavelet techniques.
  • Development and application of three estimators: instantaneous block-independent least squares, and block-dependent weighted least squares and maximum likelihood estimators.
  • Development of confidence intervals for block-dependent estimators.
  • Introduction of a time-scale-dependent inertial range statistic.

    • Main Results:

    • Successful estimation of FD model parameters for aerothermal turbulence data.
    • Demonstration of significant departures from Kolmogorov turbulence over finite scale ranges in most studied data.
    • Quantification of these departures using the newly developed time-scale-dependent inertial range statistic.

    Conclusions:

    • Fractionally differenced processes provide a viable model for aerothermal turbulence.
    • Observed deviations from Kolmogorov turbulence are common and significant.
    • The new statistic effectively quantifies scale-dependent departures from theoretical turbulence models.