Measuring the probability distribution of the relative velocities in grid-generated turbulence

Abstract

Homodyne photon correlation spectroscopy (HCS) and laser Doppler velocimetry (LDV) were used to study the probability density function of velocity differences \ensuremath{\delta}v(l) between points in the fluid separated by a distance l. The two measuring schemes yield different results for the probability density, P(\ensuremath{\delta}v(l))d\ensuremath{\delta}v(l). HCS probes the spatial fluctuations directly, whereas LDV records temporal fluctuations in velocity and relates them to the spatial fluctuations through the Taylor hypothesis. The measurements therefore imply the failure of this hypothesis in the Reynolds number range where we have applied it.