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Stochastically generated instantaneous velocity profiles are used to reproduce the outer region of rough-wall turbulent boundary layers in a range of Reynolds numbers extending from the wind tunnel to field conditions. Each profile consists in a sequence of steps, defined by the modal velocities and representing uniform momentum zones (UMZs), separated by velocity jumps representing the internal shear layers. Height-dependent UMZ is described by a minimal set of attributes: thickness, mid-height elevation, and streamwise (modal) and vertical velocities. These are informed by experimental observations and reproducing the statistical behaviour of rough-wall turbulence and attached eddy scaling, consistent with the corresponding experimental datasets. Sets of independently generated profiles are reorganized in the streamwise direction to form a spatially consistent modal velocity field, starting from any randomly selected profile. The operation allows one to stretch or compress the velocity field in space, increases the size of the domain and adjusts the size of the largest emerging structures to the Reynolds number of the simulated flow. By imposing the autocorrelation function of the modal velocity field to be anchored on the experimental measurements, we obtain a physically based spatial resolution, which is employed in the computation of the velocity spectrum, and second-order structure functions. The results reproduce the Kolmogorov inertial range extending from the UMZ and their attached-eddy vertical organization to the very-large-scale motions (VLSMs) introduced with the reordering process. The dynamic role of VLSM is confirmed in the$$-u^{\prime }w^{\prime }$$co-spectra and in their vertical derivative, representing a scale-dependent pressure gradient contribution.
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Perturbative model for the second order velocity structure function tensor in turbulent shear flows
A model for the structure function tensor is proposed, incorporating the e↵ect of anisotropy as a linear perturbation to the standard isotropic form. The analysis extends the spectral approach of Ishihara et al. (2002) to physical space based on Kolmogorov’s theory and is valid in the inertial range of turbulence. Previous results for velocity co-spectra are used to obtain estimates of the model coe"cients. Structure functions measured from direct numerical simulations of channel flow and from experimental measurements in turbulent boundary layers are compared with predicted behaviour and reasonable agreement is found. We note that power-law scaling is more evident in the co-spectra than for the mixed structure functions. New observations are made about countergradient correlation between Fourier modes of wall normal and streamwise velocity components for wavenumbers approaching the Kolmogorov scale.
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- Award ID(s):
- 2103874
- PAR ID:
- 10331091
- Date Published:
- Journal Name:
- Physical review fluids
- ISSN:
- 2469-9918
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevFluids.7.064601
