Linear Stability Analysis of Open-Channel Shear Flow Generated by Vegetation
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 3
Abstract
A linear stability analysis of flow in an open-channel partially covered with vegetation was performed. The differential drag between vegetated zones and adjacent nonvegetated zones is known to induce a lateral gradient of the streamwise velocity. The velocity gradient may result in flow instability in the shear layer around the edge of the vegetated zone causing the generation of discrete horizontal vortices. We assume that the base state flow field before the occurrence of instability is characterized by turbulence with a smaller length scale than the flow depth, which is mainly generated by the bottom friction. By introducing perturbations to the flow depth as well as the streamwise and transverse velocities in the base state, the conditions required for perturbations to grow in time were studied over a wide range of (1) Froude number, (2) normalized nonvegetated zone width, and three other dimensionless parameters that represent the relative effect of (3) bed friction, (4) vegetation drag, and (5) subdepth eddy viscosity. All parameters were found to have positive and negative growth rates of perturbations within their respective evaluated ranges. The characteristic vortex shedding frequencies associated with the maximum growth rate was compared with those observed in experiments. Although the analysis that employs a base state set without the large scale lateral motions was shown to be capable of predicting the order of magnitude of the frequencies, there is a systematic discrepancy between the predicted and observed frequencies, which may be due to the limitation of linear stability analysis.
Get full access to this article
View all available purchase options and get full access to this article.
References
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.
Ghidaoui, M. S., and Kolyshkin, A. A. (1999). “Linear stability analysis of lateral motions in compound open channel.” J. Hydraul. Eng., 871–880.
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.
Kolyshkin, A. A., and Ghidaoui, M. S. (2002). “Gravitational and shear instabilities in compound and composite channels.” J. Hydraul. Eng., 1076–1086.
Michalke, A. (1964). “On the inviscid instability of hyperbolic tangent velocity profile.” J. Fluid Mech., 19(4), 543–556.
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, 4105–4114.
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 Communication, 2, Dept. of Civil Engineering, Kanazawa Univ., Kanazawa, Japan, 41–54 (in Japanese).
Tsujimoto, T., and Kitamura, T. (1992). “Experimental study on open-channel flow with vegetated zone along side wall.” KHL Progressive Rep. 92, Hydraulics Laboratory, Kanazawa Univ., Kanazawa, Japan, 29–35 (in Japanese).
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.
Xiaohui, S., and Li, C. W. (2002). “Large eddy simulation of free surface turbulent flow in partially vegetated open channels.” Int. J. Numer. Meth. Fluids, 39, 919–937.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 3 • March 2014
Pages: 231 - 240
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Oct 9, 2012
Accepted: Sep 5, 2013
Published online: Sep 7, 2013
Discussion open until: Feb 7, 2014
Published in print: Mar 1, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.