Relative velocity fluctuations in turbulent flows at moderate Reynolds numbers. I. Experimental

Abstract

Turbulent pipe flow and grid flow have been explored by the scattering of light from small particles suspended in a fluid. Laser Doppler velocimetry and visual observation were used to characterize the gross features of the flows. However, novel information came from the homodyne correlation function g(t), which was measured as a function of the Reynolds number, the photon momentum transfer, and the size of the scattering volume. In terms of these control variables, g(t) was found to be of scaling form. Using such measurements one can deduce from the probability distribution function, P(V,R), that two particles, separated by a distance R, have velocity difference V(R,t). For small‐velocity fluctuations, the scaling behavior of g(t) implies that P(V,R) has the form Q[V/ū(R)]/ū(R). This self‐similarity in P(V,R) is seen only when Re exceeds a transition Reynolds number Re_c. The measured scaling velocity ū(R) has the form ū(R)∼R^ζ, with ζ increasing from 0 at Re=Re_c to ∼ (1)/(3) at the maximum attainable levels of turbulence. This scaling behavior was seen in both the grid and pipe flows. By measuring g(t) at very small t, one can also obtain information about the large‐velocity fluctuations. It is found that P(V,R) is well approximated by the product of a Lorentzian and a Gaussian function with characteristic velocities ū(R) and u(R), respectively. Here u(R) identifies the large‐velocity fluctuations.