Fractal Aspect of Iso-velocity Set in a Turbulent Boundary Layer

Abstract

In this work, we report on the fractal aspect of an iso-velocity set in a turbulent boundary layer. The iso-velocity set is a one-dimensional point set defined by an instantaneous velocity signal. We use both a box-counting algorithm and a method based on the probability distribution function. The analysis is carried out carefully with clarification of the region of scale similarity. The iso-velocity set clearly indicates fractal features, except for near the local mean velocity, and their dimension is less than 0. 4 in space. Scale similarity extends from the Kolmogorov scale to the largest eddy scale. The instantaneous turbulent energy field also shows fractal features and has a close connection with the iso-velocity set.