Abstract

Before photon correlation spectroscopy was used in condensed matter physics, and all measurements were made in the frequency domain, it was recognized by Bourke et al.[1] that turbulence could be studied by light scattering. The frequency of light scattered by a single seed particle moving with velocity v(t) in the flowing fluid, will be Doppler shifted by an amount (k) • v(r(t)), where k is the scattering vector. If the fluid contains not one particle but two, a photodetector will register the beat frequency Ω of these two Doppler shifts, and the photocurrent will be modulated at a frequency Ω = k·δv, where δv = [v(r) –v(r + ℓ), where the two particles are separated by the ℓ. The intensity itself, will then be, within a multiplicative constant, I(t) = 1 + cosΩt. Since k is of the order of 10⁵ cm^–1. In a water tunnel one might encounter velocity differences of the order of 10 cm/sec, if ℓ is a few mm or less. In this case Ω^–1 will be of the order of 1 µsec, a characteristic time that falls in the range of present-day correlators. Of course, a seeded turbulent fluid will contain many particle pairs. If they are present at random positions in turbulent or laminar flow, the seed particles will give a pairwise contribution to I(t), and will cause the the scattered intensity to fluctuate ain time in a random fashion[2].

© 1992 Optical Society of America