Large- and very large-scale motions in open-channel flow: Spectra and structure functions
ORAL
Abstract
Large-scale motions (LSMs) and very-large-scale motions (VLSMs) in open-channel flows are coherent structures that, in premultiplied streamwise velocity spectra, are represented by two “hills” at wavelengths of λx ≈ 2-4 and λx ≈ 20-50 flow depths, respectively. The origin of VLSMs remains unclear. Two main hypotheses suggest that VLSMs originate either from alignment of LSMs or as relatively independent structures.
Based on experimental data, it is found that the spectral correlation coefficient ρuw = Cuw / (SuuSww)0.5 (C is cospectrum, S is autospectrum, and u and w are streamwise and vertical velocity components) increases monotonically with scale, from LSMs to VLSMs, indicating greater coherence and efficiency in momentum delivery to the wall by the VLSMs compared to the LSMs. Furthermore, the negative sign of Cuw at the VLSM wavelength indicates energy extraction from the mean flow.
LSMs and VLSMs are also assessed via the streamwise second-order structure function (Duu). In particular, we used the derivative of Duu multiplied by the streamwise spatial separation rx (i.e., rx ∂Duu / ∂rx), which, similar to premultiplied spectra, represents energy distribution as a function of rx. Analysis of the third-order structure function (Duuu) indicates an energy flux from VLSMs towards LSMs and smaller scales.
The results are consistent with the hypothesis of VLSMs as independent structures, whereas the “LSM alignment” seems to be incompatible with the distributions of ρuw and Duuu.
Based on experimental data, it is found that the spectral correlation coefficient ρuw = Cuw / (SuuSww)0.5 (C is cospectrum, S is autospectrum, and u and w are streamwise and vertical velocity components) increases monotonically with scale, from LSMs to VLSMs, indicating greater coherence and efficiency in momentum delivery to the wall by the VLSMs compared to the LSMs. Furthermore, the negative sign of Cuw at the VLSM wavelength indicates energy extraction from the mean flow.
LSMs and VLSMs are also assessed via the streamwise second-order structure function (Duu). In particular, we used the derivative of Duu multiplied by the streamwise spatial separation rx (i.e., rx ∂Duu / ∂rx), which, similar to premultiplied spectra, represents energy distribution as a function of rx. Analysis of the third-order structure function (Duuu) indicates an energy flux from VLSMs towards LSMs and smaller scales.
The results are consistent with the hypothesis of VLSMs as independent structures, whereas the “LSM alignment” seems to be incompatible with the distributions of ρuw and Duuu.
*This work was supported by the Engineering and Physical Sciences Research Council/UK grant “Secondary currents in turbulent flows over rough walls” (EP/V002414/1). The Ph.D. thesis of B.C. was funded by the Riverly Research Unit and Aqua Department of INRAE. The visit of B.C. to Aberdeen was funded by the Doctoral School MEGA.
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Publication: Zampiron, A., Cerino, B., Berni, C., Proust, S., & Nikora, V. (2024). Very-large-scale motions in open-channel flow: Insights from velocity spectra, correlations, and structure functions. Physics of Fluids, 36(4), https://doi.org/10.1063/5.0205033.
Presenters
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Andrea Zampiron
- Università degli Studi di Padova