Single-Layer Model for Average Flow Velocity with Submerged Rigid Cylinders
Publication: Journal of Hydraulic Engineering
Volume 141, Issue 10
Abstract
A single-layer velocity model is proposed in this study to predict the cross-sectional average velocity for open channel flows with submerged rigid cylinders. This model is preferable to previous two-layer models in that it does not involve evaluations of vegetation drag coefficient and hydrodynamic height of roughness elements. In the development of the single-layer model, the concept of the hydraulic radius is applied to determine the length scale of the entire cross-section affected by the submerged vegetation. The resulting friction factor scales largely with the ratio of stem height to flow depth with exponent , and also decreases slightly with an increasing Reynolds number. Comparisons of the single-layer model with experimental data show that its performance is comparable to the previous two-layer models, and the model is also applicable to open channel flows subject to submerged flexible vegetation. However, the proposed model cannot be extended to two extreme conditions including flows over a smooth channel bed without vegetation and flows passing through emergent vegetation.
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References
Baptist, M. J., et al. (2007). “On inducing equations for vegetation resistance.” J. Hydraul. Res., 45(4), 435–450.
Cheng, N. S. (2011). “Representative roughness height of submerged vegetation.” Water Resour. Res., 47, W08517.
Cheng, N. S. (2013). “Calculation of drag coefficient for arrays of emergent circular cylinders with pseudo-fluid model.” J. Hydraul. Eng., 602–611.
Cheng, N. S., and Nguyen, H. T. (2011). “Hydraulic radius for evaluating resistance induced by simulated emergent vegetation in open-channel flows.” J. Hydraul. Eng., 995–1004.
Cheng, N. S., Nguyen, H. T., Tan, S. K., and Shao, S. D. (2012). “Scaling of velocity profiles for depth-limited open channel flows over simulated rigid vegetation.” J. Hydraul. Eng., 673–683.
Dunn, C., Lopez, F., and Garcia, M. (1996). “Mean flow and turbulence in a laboratory channel with simulated vegetation.” Hydrosystem Lab., Univ. of Illinois, Urbana, IL.
Ghisalberti, M., and Nepf, H. (2004). “The limited growth of vegetated shear layers.” Water Resour. Res., 40, W07502.
Huthoff, F., Augustijn, D. C. M., and Hulscher, S. J. M. H. (2007). “Analytical solution of the depth-averaged flow velocity in case of submerged rigid cylindrical vegetation.” Water Resour. Res., 43, W06413.
Ishikawa, Y., Mizuhara, K., and Ashida, S. (2000). “Effect of density of trees on drag exerted on trees in river channels.” J. Forest Res., 5(4), 271–279.
James, C. S., Birkhead, A. L., Jordanova, A. A., and O’Sullivan, J. J. (2004). “Flow resistance of emergent vegetation.” J. Hydraul. Res., 42(4), 390–398.
Järvelä, J. (2003). “Influence of vegetation on flow structure in floodplains and wetlands.” Proc., 3rd IAHR Symp. on River, Coastal and Estuarine Morphodynamics (RCEM 2003), International Association for Hydro-Environment Engineering and Research (IAHR), 845–856.
Kothyari, U. C., Hayashi, K., and Hashimoto, H. (2009). “Drag coefficient of unsubmerged rigid vegetation stems in open channel flows.” J. Hydraul. Res., 47(6), 691–699.
Kouwen, N., Unny, T. E., and Hill, H. M. (1969). “Flow retardance in vegetated channels.” J. Irrig. Drain. Div., 95(IR2), 329–342.
Kubrak, E., Kubrak, J., and Rowinski, P. M. (2008). “Vertical velocity distributions through and above submerged, flexible vegetation.” Hydrol. Sci. J., 53(4), 905–920.
Liu, D., Diplas, P., Fairbanks, J. D., and Hodges, C. C. (2008). “An experimental study of flow through rigid vegetation.” J. Geophys. Res.-Earth Surf., 113(F04015), 1–16.
Meijer, D. G., and van Velzen, E. H. (1999). “Prototype-scale flume experiments on hydraulic roughness of submerged vegetation.” XXVIII IAHR Conf., Institute for Hydraulics and Hydrology, Technische Universität Graz, Graz, Austria.
Murphy, E., Ghisalberti, M., and Nepf, H. (2007). “Model and laboratory study of dispersion in flows with submerged vegetation.” Water Resour. Res., 43(5), W05438.
Nepf, H. M., and Vivoni, E. R. (2000). “Flow structure in depth-limited, vegetated flow.” J. Geophys. Res.-Oceans, 105(C12), 28547–28557.
Nezu, I., and Sanjou, M. (2008). “Turburence structure and coherent motion in vegetated canopy open-channel flows.” J. Hydro-Environ. Res., 2(2), 62–90.
Okamoto, T., and Nezu, I. (2010). “Flow resistance law in open-channel flows with rigid and flexible vegetation.” River flow 2010, A. Dittrich, K. Koll, J. Aberle, and P. Geisenhainer, eds., Bundesanstalt für Wasserbau, Karlsruhe, Germany, 261–268.
Okamoto, T. A., and Nezu, I. (2009). “Turbulence structure and ‘Monami’ phenomena in flexible vegetated open-channel flows.” J. Hydraul. Res., 47(6), 798–810.
Poggi, D., Krug, C., and Katul, G. G. (2009). “Hydraulic resistance of submerged rigid vegetation derived from first-order closure models.” Water Resour. Res., 45(10), W10442.
Raupach, M. R., Finnigan, J. J., and Brunet, Y. (1996). “Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy.” Boundary-Layer Meteorol., 78(3–4), 351–382.
Shimizu, Y., Tsujimoto, T., Nakagawa, H., and Kitamura, T. (1991). “Experimental study on flow over rigid vegetation simulated by cylindrical with equi-spacing.” Jpn. Soc. Civ. Eng., 31–40 (in Japanese).
Stone, B. M., and Shen, H. T. (2002). “Hydraulic resistance of flow in channels with cylindrical roughness.” J. Hydraul. Eng., 500–506.
Tanino, Y., and Nepf, H. M. (2008). “Laboratory investigation of mean drag in a random array of rigid, emergent cylinders.” J. Hydraul. Eng., 34–41.
Yan, J. (2008). “Experimental study of flow resistance and turbulence characteristics of open channel flow with vegetation.” Ph.D. thesis, Hohai Univ., China.
Yang, W. (2008). “Experimental study of turbulent open-channel flows with submerged vegetation.” Ph.D. thesis, Yonsei Univ., Korea.
Yang, W., and Choi, S. U. (2010). “A two-layer approach for depth-limited open-channel flows with submerged vegetation.” J. Hydraul. Res., 48(4), 466–475.
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Published In
Journal of Hydraulic Engineering
Volume 141 • Issue 10 • October 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Apr 24, 2014
Accepted: Mar 19, 2015
Published online: Jun 1, 2015
Published in print: Oct 1, 2015
Discussion open until: Nov 1, 2015
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