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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 behaviour 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.
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Scaling Laws for the Length Scale of Energy‐Containing Eddies in a Sheared and Thermally Stratified Atmospheric Surface Layer
Abstract In the atmospheric surface layer (ASL), a characteristic wavelength marking the limit between energy‐containing and inertial subrange scales can be defined from the vertical velocity spectrum. This wavelength is related to the integral length scale of turbulence, used in turbulence closure approaches for the ASL. The scaling laws describing the displacement of this wavelength with changes in atmospheric stability have eluded theoretical treatment and are considered here. Two derivations are proposed for mildly unstable to mildly stable ASL flows one that only makes use of normalizing constraints on the vertical velocity variance along with idealized spectral shapes featuring production to inertial subrange regimes, while another utilizes a co‐spectral budget with a return‐to‐isotropy closure. The expressions agree with field experiments and permit inference of the variations of the wavelength with atmospheric stability. This methodology offers a new perspective for numerical and theoretical modeling of ASL flows and for experimental design.
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- PAR ID:
- 10451679
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 47
- Issue:
- 23
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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