Spatial and Temporal Growth of Perturbations in Open-Channel Viscous Transverse Shear Flow
Publication: Journal of Hydraulic Engineering
Volume 142, Issue 12
Abstract
The comparison between spatial and temporal growth of perturbations in a shear layer is revisited for the case of a viscous open-channel flow with velocity inflection. Turbulence is characterized by two distinct scales: a subdepth turbulence associated with the bed shear stress and a large-scale turbulence associated with the large horizontal eddies that develop in the shear layer. Temporal and spatial linear stability analyses are performed. The base flow is assumed to be affected only by the subdepth scale turbulence. Therefore, the base flow represents not the average flow but the flow completely free of the effect of the instability of the shear layer. Temporal and spatial approaches present less discrepancy in the viscous than in the previously analyzed in-viscous case. In particular, the phase velocity was found to be strongly correlated to the frequency in both the temporal and spatial approaches.
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References
Carnie, R., Tonina, D., McKean, J. A., and Isaak, D. (2015). “Habitat connectivity as a metric for aquatic microhabitat quality: Application to Chinook salmon spawning habitat.” Ecohydrology, in press.
Chen, D., and Jirka, G. H. (1997). “Absolute and convective instabilities of plane turbulent wakes in a shallow water layer.” J. Fluid Mech., 338, 157–172.
Chu, V. H., Wu, J.-H., and Khayat, R. E. (1991). “Stability of transverse shear flows in shallow open channels.” J. Hydraul. Eng., 1370–1388.
Fischer, H. B., List, E. J., Koh, R. C. J., Imberger, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic, New York.
Freymuth, P. (1965). “Diss. Technische Universität Berlin (as cited in Michalke, 1965).” (in German).
Freymuth, P. (1966). “On transition in a separated laminar boundary layer.” J. Fluid Mech., 25(4), 683–704.
Gaster, M. (1962). “A note on the relation between the temporally-increasing and spatially-increasing disturbances in hydrodynamic instability.” J. Fluid Mech., 14(2), 222–224.
Ghidaoui, M. S., and Kolyshkin, A. A. (1999). “Linear stability analysis of lateral motions in compound open channel.” J. Hydraul. Eng., 871–880.
Ho, C.-M., and Huerre, P. (1984). “Perturbed free shear layers.” Ann. Rev. Fluid Mech., 16(1), 365–422.
Ikeda, S., Izumi, N., and Itoh, R. (1991). “Effects of pile dikes on flow retardation and sediment transport.” J. Hydraul. Eng., 1459–1478.
Ikeda, S., Ohta, K., and Hasegawa, H. (1994). “Instability-induced horizontal vortices in shallow open-channel flows with an inflection point in skewed velocity profile.” J. Hydrosci. Hydraul. Eng., 12(2), 69–84.
Kitamura, T., Jia, Y., Tsujimoto, T., and Wang, S. (1998). “Sediment transport capacity in channels with vegetation zone.” Water resource engineering ‘98, S. R. Abt, J. Youngpezeshk, and C. C. Watson, eds., ASCE, Baltimore.
Kolyshkin, A. A., and Ghidaoui, M. S. (2002). “Gravitational and shear instabilities in compound and composite channels.” J. Hydraul. Eng., 1076–1086.
Lima, A. C., and Izumi, N. (2014a). “Linear stability analysis of open-channel shear flow generated by vegetation.” J. Hydraul. Eng., 231–240.
Lima, A. C., and Izumi, N. (2014b). “On the nonlinear development of shear layers in partially vegetated channels.” Phys. Fluids, 26(8), 084109-1–084109-22.
Michalke, A. (1964). “On the inviscid instability of hyperbolic tangent velocity profile.” J. Fluid Mech., 19(4), 543–556.
Michalke, A. (1965). “On spatially growing disturbances in an inviscid shear layer.” J. Fluid Mech., 23(3), 521–544.
Monkewitz, P. A., and Huerre, P. (1982). “Influence of the velocity ratio on the spatial instability of mixing layers.” Phys. Fluids, 25(7), 1137–1143.
Nadaoka, K., and Yagi, H. (1998). “Shallow-water turbulence modeling and horizontal large-eddy computation of river flow.” J. Hydraul. Eng., 493–500.
Prooijen, B. C., and Uijttewaal, W. S. J. (2002). “A linear approach for the evolution of coherent structures in shallow mixing layers.” Phys. Fluids, 14(12), 4105–4114.
Schmid, P. J., and Henningson, D. S. (2001). Stability and transition in shear flows, Springer, Berlin.
Su, X., and Li, C. W. (2002). “Large eddy simulation of free surface turbulent flow in partially vegetated open channels.” Int. J. Numer. Methods Fluids, 39(10), 919–937.
Tamai, N., Asaeda, T., and Ikeda, H. (1986). “Study on generation of periodical large surface eddies in a composite channel flow.” Water Resour. Res., 22(7), 1129–1138.
Tsujimoto, T. (1991). “Open channel flow with bank vegetation.” KHL Commun., 2, 41–54.
Tsujimoto, T., and Kitamura, T. (1995). “Lateral bed-load transport and sand-ridge formation near vegetation zone in an open channel.” J. Hydrosci. Hydraul. Eng., 13(1), 35–45.
Uijttewaal, W. S. J., and Booij, R. (2000). “Effects of shallowness on the development of free-surface mixing layers.” Phys. Fluids, 12(2), 392–4402.
White, B. L., and Nepf, H. M. (2007). “Shear instability and coherent structures in shallow flow adjacent to a porous layer.” J. Fluid Mech., 593, 1–32.
White, B. L., and Nepf, H. M. (2008). “A vortex-based model of velocity and shear stress in a partially vegetated shallow channel.” Water Resour. Res., 44(1), W01412.
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Published In
Journal of Hydraulic Engineering
Volume 142 • Issue 12 • December 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 12, 2015
Accepted: Jun 8, 2016
Published online: Aug 1, 2016
Published in print: Dec 1, 2016
Discussion open until: Jan 1, 2017
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