Probability density function of turbulent velocity fluctuations

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Experimental Physics

Background:

• Understanding turbulent flow dynamics is crucial in various scientific and engineering fields.
• The statistical properties of velocity fluctuations, particularly their probability density functions (PDFs), offer key insights into turbulence characteristics.

Purpose of the Study:

• To systematically investigate the probability density function (PDF) of velocity fluctuations in grid turbulence.
• To analyze how the PDF evolves with distance from the grid, correlating with turbulence development and decay.

Main Methods:

• Experimental study of grid turbulence.
• Measurement and analysis of velocity fluctuations.
• Calculation of probability density functions (PDFs).
• Fourier transform analysis of velocity fluctuations.

Main Results:

• The PDF of velocity fluctuations exhibits distinct behaviors at different distances from the grid: sub-Gaussian (developing), Gaussian (fully developed), and hyper-Gaussian (decayed).
• Fourier transforms of velocity fluctuations consistently show Gaussian PDFs.
• Statistical independence of Fourier transforms at intermediate distances is confirmed as the condition for Gaussianity.

Conclusions:

• The PDF of velocity fluctuations in grid turbulence is not static but evolves predictably with spatial development and decay.
• The statistical independence of Fourier transforms is a critical factor determining the Gaussian nature of velocity fluctuations.