Probability density of velocity increments in turbulent flows

Measurements have been made of the probability density function (PDF) of velocity increments Δu(r) for a wide range of separation distances r. Stretched exponentials provide good working approximations to the tails of the PDF. The stretching exponent varies monotonically from 0.5 for r in the dissipation range to 2 for r in the integral scale range. Theoretical forms based on multifractal notions of turbulence agree well with the measured PDFs. When the largest scales in the velocity u are filtered out, the PDF of Δu(r) becomes symmetric and, for large r, close to exponential.