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

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.

30 pages, 11 figures

References in corpus (9)

• The multifractal nature of turbulent energy dissipation
• The turbulent cascade in five dimensions
• Persistence Problem in Two-Dimensional Fluid Turbulence
• "Clusterization" and intermittency of temperature fluctuations in turbulent convection
• On the mixing length eddies and logarithmic mean velocity profile in wall turbulence
• Direct Measurement of the Solar-Wind Taylor Microscale using MMS Turbulence Campaign Data
• Life-cycle of streaks in the buffer layer of wall-bounded turbulence
• Persistence analysis of velocity and temperature fluctuations in convective surface layer turbulence
• Effect of finite Reynolds number on self-similar crossing statistics and fractal measurements in turbulence

Cited by in corpus (3)

• Turbulence organization and mean profile shapes in the stably stratified boundary layer: zones of uniform momentum and air temperature
• Self-similarity and vanishing diffusion in fluvial landscapes
• On the wall-normal velocity variance in canonical wall-bounded turbulence