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The maximum entropy principle explains turbulence energy spectra using a lognormal distribution, aligning with experimental data. This principle allows power spectra reconstruction based on the Reynolds number.

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Area of Science:

  • Fluid dynamics
  • Statistical mechanics

Background:

  • The maximum entropy principle guides physical systems toward states of maximum entropy under constraints.
  • Turbulence energy spectra describe energy distribution across different scales in turbulent flows.

Purpose of the Study:

  • To apply the maximum entropy principle to turbulence energy spectra.
  • To identify a distribution function that maximizes entropy under physical constraints relevant to turbulence.

Main Methods:

  • Applying the maximum entropy principle with constraints of zero energy at boundaries and fixed total energy.
  • Deriving a distribution function for turbulence energy spectra.
  • Validating the derived function against experimental data.

Main Results:

  • The lognormal distribution function maximizes entropy for turbulence energy spectra under the specified constraints.
  • The lognormal model shows strong agreement with experimental data across various energy and length scales.
  • The Reynolds number is identified as a key parameter for reconstructing power spectra.

Conclusions:

  • The maximum entropy principle provides a robust framework for understanding turbulence energy spectra.
  • The lognormal distribution is a theoretically and empirically supported model for turbulence energy spectra.
  • The Reynolds number effectively parameterizes turbulence energy spectra reconstruction.