Lognormality in Turbulence Energy Spectra

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.