  The probability density function of single-point velocity fluctuations in
turbulence is studied systematically using Fourier coefficients in the
energy-containing range. In ideal turbulence where energy-containing motions
are random and independent, the Fourier coefficients tend to Gaussian and
independent of each other. Velocity fluctuations accordingly tend to Gaussian.
However, if energy-containing motions are intermittent or contaminated with
bounded-amplitude motions such as wavy wakes, the Fourier coefficients tend to
non-Gaussian and dependent of each other. Velocity fluctuations accordingly
tend to non-Gaussian. These situations are found in our experiment of a
rough-wall boundary layer.
