Abstract
The article summarizes previous studies on the flow in open channels with rigid vegetation, and constructs a mathematical model for submerged and emerged rigid vegetation. The model involves the forces balance in the control volume in one-dimensional steady uniform flow. For submerged vegetation, the whole flow is divided into four regions: external region, upper vegetated region, transition region and viscous region. According to the Karman similarity theory, the article improves the mixing length expression, and then gives an analytical solution to predict the vertical distribution of stream-wise velocity in the external region. For emerged vegetation, the flow is divided into two region: outer region and viscous region. In the two circumstances, the thicknesses of each region are determined respectively. The comparison between the calculated results and our experimental data and other researchers’ data proves that the proposed model is effective.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
COWNA W. L. Estimating hydraulic roughness coef-ficients[J]. Agriculture Engineering, 1956, 37(7): 473–475.
KOUWEN N., UNNY T. E. Flexible roughness in open channels[J]. Journal of Hydraulics Division, 1973, 99(5): 713–728.
NAOT D., NEZU I. and NAKAGAWA H. Hydro-dynamic behavior of partly vegetated open channels[J]. Journal of Hydraulic Engineering, ASCE, 1996, 122(11): 625–633.
LOPEZ F., GARCIA M. H. Mean flow and turbulence structure of open-channel flow through non-emergent vegetation[J]. Journal of Hydraulic Engineering, 2001, 127(5): 392–402.
STOESSER T., LIANG C. and RODI W. et al. Large eddy simulation of fully-developed turbulent flow through submerged vegetation[C]. International Conference on Fluvial Hydraulics, SEP06-08. Lisbon, Portugal, 2006, 1: 227–234.
SU Xiao-hui, LI C. W. and CHEN Bi-hong. Three-dimensional large eddy simulation of free surface turbulent flow in open channel within submerged vegetation domain[J]. Journal of Hydrodynamics, Ser. B, 2003, 15(3): 35–43.
HUANG Ben-sheng, LAI Guan-wen and QIU Jing et al. Hydraulics of compound channel with vegetated flood-plains[J]. Journal of Hydrodynamics, Ser. A, 2002, 14(1): 23–28(in Chinese).
HUAI W. X., ZENG Y. H. and XU Z. G. Three-layer model for vertical velocity distribution in open channel flow with submerged rigid vegetation[J]. Advances in Water Resources, 2009, 32(4): 487–492.
WANG Chao, YU Ji-yu and WANG Pei-fang et al. Flow structure of partly vegetated open-channel flows with eelagrass[J]. Journal of Hydrodynamics, 2009, 21(3): 301–307.
KUBRAK E., KUBRAK J. and ROWIŃSKI P. M. Vertical velocity distributions through and above submerged, flexible vegetation[J]. Hydrological Sciences Journal, 2008, 53(4): 905–920.
HSIEH Ping-Cheng, SHIU Yu-sheng. Analytical solutions for water flow passing over a vegetal area[J]. Advances in Water Resources, 2006, 29(9): 1257–1266.
GHISALBERTI M., NEPF H. M. The limited growth of vegetated shear layers[J]. Water Resources Research, 2004, 40(7): 1–12.
NEPF H., GHISALBERTI M. Flow and transport in channels with submerged vegetation[J]. Acta Geophysica, 2008, 56(3): 753–777.
NEPF H. M. Drag, turbulence and diffusion in flow through emergent vegetation[J]. Water Resources Research, 1999, 35(2): 479–489.
ROWIŃSKI P. M., KUBRAK J. A mixing-length model for predicting vertical velocity distribution in flows through emergent vegetation[J]. Hydrological Sciences Journal, 2002, 47(6): 893–904.
WU Fu-sheng. Characteristics of flow resistance in open channels with non-submerged rigid vegetation[J]. Journal of Hydrodynamics, 2008, 20(2): 239–245.
SCHLICHTING H., KESTIN J. Boundary layer theory[M]. 7th Edition, New York: McGraw-Hill, 1979.
VELASCO D., BATEMAN A. and MEDINA V. A new integrated, hydro-mechanical model applied to flexible vegetation in riverbeds[J]. Journal of Hydraulic Research, 2008, 46(5): 579–597.
CAROLLO F. G., FERRO V. and TERMINI D. Flow velocity measurements in vegetated channels[J]. Journal of Hydraulic Engineering, 2002, 128(7): 664–673.
NAZARENKO S. Exact solutions for near-wall turbulence theory[J]. Physics Letters A, 2000, 264: 444–448.
HUAI Wen-xin, HAN Jie and ZENG Yu-hong et al. velocity distribution of flow with submerged flexible vegetations based on mixing-length approach[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(3): 343–351.
FINNIGAN J. Turbulence in plant canopies[J]. Annual Review of Fluid Mechanics, 2000, 32(1): 519–571.
WINANT C., BROWAND F. Vortex pairing: The mechanism of turbulent mixing-layer growth, at moderate Reynolds number[J]. Journal of Fluid Mechanics, 1974, 63(2): 237–255.
NEPF H. M., VIVONI E. R. Flow structure in depth-limited, vegetated flow[J]. Journal of Geophysical Research, 2000, 105(C12): 28547–28557.
NEZU I., RODI W. Open-channel flow measurements with a laser Doppler anemometer[J]. Journal of Hydraulic Engineering, ASCE, 1986, 112(5): 335–355.
SHIMIZU Y., TSUJIMOTO T. Numerical analysis of turbulent open-channel flow over a vegetation layer using a k-ε turbulence model[J]. Journal of Hydroscience and Hydraulic Engineering, 1994, 11(2): 57–67.
Author information
Authors and Affiliations
Additional information
Project support by the National Natural Science Foundation of China (Grant Nos.50679061, 50709025 and 10972163).
Biography: Huai Wen-xin (1963-), Male, Ph. D., Professer
Rights and permissions
About this article
Cite this article
Huai, Wx., Chen, Zb., Han, J. et al. Mathematical Model for the Flow with Submerged and Emerged Rigid Vegetation. J Hydrodyn 21, 722–729 (2009). https://doi.org/10.1016/S1001-6058(08)60205-X
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1001-6058(08)60205-X