Relative velocity fluctuations in turbulent flows at moderate Reynolds number. II. Model calculation

Abstract

A model calculation is presented to study turbulence at moderate Reynolds number, Re. In conformity with recent measurements, it is proposed that in the energy cascade the fractional volume occupied by eddies of various sizes depends on Re. By introducing a Re‐dependent parameter in the random beta model, it is shown that the scaling behavior of the small‐velocity fluctuations at moderate Re can be characterized by a single Re‐dependent scaling exponent α₀. The calculated Re dependence of α₀ is consistent with the experimental data. Corrections to this scaling are calculated using the multifractal concept. The Reynolds number dependence of other multifractal properties in turbulent flows is also calculated.