Separation of scales on a broad, shallow turbulent flow

Carrasco, Alfredo; Vionnet, Carlos A.

doi:10.1080/00221686.2004.9628316

Cited by 8 publications

(3 citation statements)

References 20 publications

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“…In studying shallow free-surface flows most attention has been traditionally paid to their small-scale three-dimensional structure [2] while the importance of large-scale dynamics for transport processes and energy transfer in these flows has only lately been recognised. In a recent review of the problem, Jirka [1] suggests three key mechanisms forming large-scale coherent structures in shallow flows: (I) topographic forcing when boundary features such as islands or groynes create a strong transverse shear layer generating quasi-two-dimensional vortices [3]; (II) internal transverse shear instabilities due to lateral variations of hydrodynamic characteristics, occurring, for instance, in shallow jets or wakes [4]; and (III) secondary instabilities of the base flow which may take place as a result of internal fluctuations even in flows with negligible time-averaged transverse gradients in turbulence properties. As an example, this third mechanism may well be responsible for large-scale flow structures in wide rivers reported in Yokosi [5], Grinvald and Nikora [6], and Nikora [7].…”

Section: Introductionmentioning

confidence: 99%

Large-scale turbulent structure of uniform shallow free-surface flows

et al. 2007

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The hydrodynamics of super-and sub-critical shallow uniform free-surface flows are assessed using laboratory experiments aimed at identifying and quantifying flow structure at scales larger than the flow depth. In particular, we provide information on probability distributions of horizontal velocity components, their correlation functions, velocity spectra, and structure functions for the near-water-surface flow region. The data suggest that for the high Froude number flows the structure of the near-surface layer resembles that of two-dimensional turbulence with an inverse energy cascade. In contrast, although large-scale velocity fluctuations were also present in low Froude number flow its behaviour was different, with a direct energy cascade. Based on our results and some published data we suggest a physical explanation for the observed behaviours. The experiments support Jirka's [Jirka GH (2001) J Hydraul Res 39(6):567-573] hypothesis that secondary instabilities of the base flow may generate large-scale two-dimensional eddies, even in the absence of transverse gradients in the time-averaged flow properties.

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Section: Introductionmentioning

confidence: 99%

Large-scale turbulent structure of uniform shallow free-surface flows

et al. 2007

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“…General kinetic energy spectra are suggested by Nikora [2005]spanning micro‐ to macroturbulence to longer scales, where the low frequency‐wavenumber macroturbulence is hypothesized to be white noise scaled with depth and width associated with hydraulic phenomenon with the intermediate frequencies rolling‐off as f −1 , thought to be representative for the transition from 2D horizontal turbulence to 3D turbulence [e.g., Carrasco and Vionnet , 2004]. At the higher frequencies the energy is expected to roll off as a

\frac{5}{3}

Kolmogorov slope based on the assumption of isotropic turbulence at higher frequency.…”

Section: Discussionmentioning

confidence: 99%

“…In the frequency domain, decay in coherence is caused by either a change in amplitude or a shift in frequency relative to a background noise [ Bendant and Piersol , 2000]. Decrease in coherence can also occur in the presence of an inverse energy cascade, where energy is transferred to the low‐frequency motions from higher frequency turbulence [ Carrasco and Vionnet , 2004]; however, there is no evidence of a spectral peak in the high‐frequency range from which the energy can be transferred. In the spatial domain, coherence of vortical motions advected downstream by the mean flow can decrease owing to distortions caused by shear and accelerations of the mean flow.…”

Section: Discussionmentioning

confidence: 99%

Frequency–wavenumber velocity spectra, Taylor's hypothesis, and length scales in a natural gravel bed river

MacMahan

Reniers

Ashley

et al. 2012

Water Resources Research

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[1] Macroscale turbulent coherent flow structures in a natural fast-flowing river were examined with a combination of a novel 2 MHz Acoustic Doppler Beam (ADB) and a Maximum Likelihood Estimator (MLE) to characterize the streamwise horizontal length scales and persistence of coherent flow structures by measuring the frequency ( f )-streamwise-wavenumber (k s ) energy density velocity spectrum, E( f, k s ), for the first time in natural rivers. The ADB was deployed under a range of Froude numbers (0.1-0.6) at high Reynolds numbers ($10 6 ) based on depth and velocity conditions within a gravel bed reach of the Kootenai River, Idaho. The MLE employed on the ADB data increased our ability to describe river motions with relatively long (>10 m) length scales in $1 m water depths. The E( f, k s ) spectra fell along a ridge described by V = f/k s , where V is the mean velocity over depth, consistent with Taylor's hypothesis. New, consistent length scale measures are defined based on averaged wavelengths of the low-frequency E( f, k s ) and coherence spectra. Energetic ($50% of the total spectral energy), low-frequency (f < 0.05 Hz) streamwise motions were found. Mean length scales, L m , compared with the depth, h, are significantly larger than previously suggested for macroturbulence with L m /h $ 28-118. Although the energy appears as low-pass white noise, it is streamwise coherent along the length of the array. In fast flows with velocities > 1 m/s, L m were found to be significantly longer than their corresponding coherence lengths, suggesting that the turbulent structures evolve rapidly under these conditions. This is attributed to the stretching and concomitant deformation of preexisting macroturbulent motions by the ubiquitous bathymetry-induced spatial flow accelerations present in a natural gravel bed river.Citation: MacMahan, J., A. Reniers, W. Ashley, and E. Thornton (2012), Frequency-wavenumber velocity spectra, Taylor's hypothesis, and length scales in a natural gravel bed river, Water Resour. Res., 48, W09548,

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