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On taylor correlation functions in isotropic turbulent flows.

Wei Chen1,2

  • 1Department of Applied Mathematics, University of Science and Technology Beijing, 30 Xueyuan Rd, Beijing, China. askelf123@yahoo.com.

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This study analytically derives turbulent flow correlations using superfluid resonance, explaining complex fluid dynamics. The new method aligns well with experimental data, offering insights beyond traditional statistical mechanics.

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Area of Science:

  • Fluid Dynamics
  • Statistical Mechanics
  • Superfluidity

Background:

  • Turbulent flow characterization relies on empirical Taylor correlation functions.
  • Existing understanding is based on statistical mechanics, with universal applicability.
  • Challenges remain in explaining certain experimental observations in turbulent flows.

Purpose of the Study:

  • To analytically derive Taylor correlation functions for turbulent flow.
  • To propose a new model of turbulence as a superfluid resonance phenomenon.
  • To validate the derived correlations against experimental data.

Main Methods:

  • Hypothesizing turbulence as a superfluid resonance phenomenon.
  • Deriving longitudinal and lateral turbulent velocities from heat transfer studies.
  • Utilizing the boundary of the second law to determine integration constants.
  • Analytically determining Taylor correlation functions from velocity profiles.

Main Results:

  • Analytical derivation of Taylor correlation functions for isotropic turbulent flow.
  • Introduction of amplitude and frequency factors based on eigenfunction linearity.
  • Successful curve-fitting of derived factors with two experimental datasets.
  • Strong agreement between the analytical theory and multiple public experimental datasets.

Conclusions:

  • The superfluid resonance hypothesis provides an analytical framework for Taylor correlations.
  • The derived analytical correlations accurately predict experimental results in isotropic flows.
  • This approach offers new explanations for phenomena challenging traditional methods in turbulence research.