Alternative to R_lambda-scaling of Small-Scale Turbulence Statistics

Abstract

Traditionally, trends of universal turbulence statistics are presented versus R-lambda, which is the Reynolds number based on Taylor's scale, lambda, and the root-mean-squared (rms) velocity component, u'. Taylor's scale and u', and hence R-lambda, do not have the attribute of universality. The ratio of rms fluid-particle acceleration to rms viscous acceleration is an alternative to R-lambda which has the advantage of being determined by the small scales of turbulence. This ratio, denoted R-a, has the following attributes: it is a Reynolds number, it is composed of statistics of the small scales of turbulence, it can be evaluated with single-wire hot-wire anemometry, and like R-lambda, can be partially evaluated by means of flow similarity. For isotropic turbulence the relationship between R-a and R-lambda is shown. Velocity derivative flatness measured between counter-rotating blades appears monotonic when graphed versus R-a, unlike when graphed versus R-lambda.