Counting Methods and Equipment for Mean-Value Measurements in Turbulence Research

Abstract

This report deals with methods of measuring the probability distributions and mean values of random functions as encountered in turbulence research. Applications to the measurement of probability distributions of the axial velocity fluctuation u(t) and its derivative du/dt in isotropic turbulence are shown. The assumption of independent probabilities of u(t) and du/dt, which has been used as an approximation in the application of zero counts to the measurement of the microscale of turbulence [lambda], is investigated. The results indicate that the assmuption is satisfied within a few percent and that there is, so far, no evidence that the systematic difference between [lambda] measured from zero counts and [lambda] measured independently can be traced entirely to the statistical dependence of u and du/dt. The chronological development of apparatus is described, concluding with the present 10-channel statistical analyzer based upon a system of pulse amplitude modulation followed by an amplitude discriminator and a counter. A discussion of the relative merits of various systems is included to indicate the reasons for this choice.