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Area of Science:

  • Fluid dynamics
  • Turbulence research
  • Experimental physics

Background:

  • Nikuradse's experiments in 1933 established foundational data on turbulent friction.
  • Previous theoretical work attempted to simplify this data using single-variable functions.
  • Comparing the efficacy of different data collapse methods has been challenging due to a lack of quantitative comparison techniques.

Purpose of the Study:

  • To develop a rigorous quantitative method for comparing alternative data collapses.
  • To identify the optimal analytic functions that best describe the Nikuradse dataset.
  • To re-evaluate the effectiveness of historical data collapse models.

Main Methods:

  • An unsupervised machine learning approach was employed to identify optimal analytic functions for data collapses.
  • The method involved analyzing the Nikuradse dataset for turbulent friction.
  • Descaling of analytic functions was performed to assess the validity of data collapses.

Main Results:

  • A low dispersion in scaled data does not necessarily indicate a good data collapse.
  • The original data collapse proposed by Prandtl and Nikuradse in 1933 provides the best description of the experimental data.
  • The Prandtl-Nikuradse model shows good agreement with recent experimental data when model parameters are adjusted.

Conclusions:

  • The developed unsupervised method offers a robust way to quantitatively compare data collapse models.
  • The historical Prandtl-Nikuradse data collapse remains a highly effective model for turbulent friction.
  • Further validation of the Prandtl-Nikuradse model with adaptable parameters is supported by current experimental findings.