Self-similar geometries within the inertial subrange of scales in boundary layer turbulence

TL;DR

This study links the self-similar geometric properties of velocity isosurfaces in boundary layer turbulence to the inertial subrange, revealing fractal characteristics and power law behaviors that reflect the physical structure of turbulence.

Contribution

It demonstrates that velocity isosurfaces exhibit self-similar fractal geometry within the inertial subrange, connecting geometric features to turbulence statistics and power laws.

Findings

Fractal dimension of isosurfaces is constant in the inertial subrange.

Power law trends in structure functions are explained by isosurface self-similarity.

Transition to production range involves confinement of large-scale wrinkles.

Abstract

The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions - both in theory and from observations. Despite promising findings on the topic of fractal geometries in turbulence, there is no accepted image for the physical flow features corresponding to this statistical signature in the inertial subrange. The present study uses boundary layer turbulence measurements to evaluate the self-similar geometric properties of velocity isosurfaces and investigate their influence on statistics for the velocity signal. The fractal dimension of streamwise velocity isosurfaces, indicating statistical self-similarity in the size of "wrinkles" along each isosurface, is shown to be constant only within the inertial subrange of scales. For the transition between the inertial subrange and production range, it is inferred that the largest wrinkles become increasingly confined by the overall size of large-scale coherent velocity regions such as uniform momentum zones. The self-similarity of isosurfaces yields power law trends in subsequent one-dimensional statistics. For instance, the theoretical 2/3 power law exponent for the structure function can be recovered by considering the collective behavior of numerous isosurface level sets. The results suggest that the physical presence of inertial subrange eddies is manifested in the self-similar wrinkles of isosurfaces.