Submerged flexible vegetation impact on open channel flow velocity distribution: An analytical modelling study on drag and friction
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摘要
In this paper,an analytical model that represents the stream wise velocity distribution for open channel flow with submerged flexible vegetation is studied.In the present vegetated flow modelling,the whole flow field has been separated into two layers vertically:a vegetated layer and a non-vegetated free-water layer.Within the vegetated layer,an analysis of the mechanisms affecting water flow through flexible vegetation has been conducted.In the non-vegetated layer,a modified log-law equation that represents the velocity profile varying with vegetation height has been investigated.Based on the studied analytical model,a sensitivity analysis has been conducted to assess the influences of the drag(C_D)and friction(C_f)coefficients on the flow velocity.The investigated ranges of C_D and Cf have also been compared to published values.The findings suggest that the C_D and Cf values are non-constant at different depths and vegetation densities,unlike the constant values commonly suggested in literature.This phenomenon is particularly clear for flows with flexible vegetation,which is characterised by large deflection.
In this paper,an analytical model that represents the stream wise velocity distribution for open channel flow with submerged flexible vegetation is studied.In the present vegetated flow modelling,the whole flow field has been separated into two layers vertically:a vegetated layer and a non-vegetated free-water layer.Within the vegetated layer,an analysis of the mechanisms affecting water flow through flexible vegetation has been conducted.In the non-vegetated layer,a modified log-law equation that represents the velocity profile varying with vegetation height has been investigated.Based on the studied analytical model,a sensitivity analysis has been conducted to assess the influences of the drag(C_D)and friction(C_f)coefficients on the flow velocity.The investigated ranges of C_D and Cf have also been compared to published values.The findings suggest that the C_D and Cf values are non-constant at different depths and vegetation densities,unlike the constant values commonly suggested in literature.This phenomenon is particularly clear for flows with flexible vegetation,which is characterised by large deflection.
In this paper,an analytical model that represents the stream wise velocity distribution for open channel flow with submerged flexible vegetation is studied.In the present vegetated flow modelling,the whole flow field has been separated into two layers vertically:a vegetated layer and a non-vegetated free-water layer.Within the vegetated layer,an analysis of the mechanisms affecting water flow through flexible vegetation has been conducted.In the non-vegetated layer,a modified log-law equation that represents the velocity profile varying with vegetation height has been investigated.Based on the studied analytical model,a sensitivity analysis has been conducted to assess the influences of the drag(C_D)and friction(C_f)coefficients on the flow velocity.The investigated ranges of C_D and Cf have also been compared to published values.The findings suggest that the C_D and Cf values are non-constant at different depths and vegetation densities,unlike the constant values commonly suggested in literature.This phenomenon is particularly clear for flows with flexible vegetation,which is characterised by large deflection.
引文
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Bootle,W.J.,1971.Forces on an inclined circular cylinder in supercritical flow.AIAA J.9(3),514-516.https://doi.org/10.2514/3.6213.
Chen,L.,2010.An integral approach for large deflection cantilever beams.Int.J.Non-Linear Mech.45(3),301-305.https://doi.org/10.1016/j.ijnonlinmec.2009.12.004.
Cheng,N.,Nguyen,H.,2011.Hydraulic radius for evaluating resistance induced by simulated emergent vegetation in open-channel flows.J.Hydraul.Eng.137(9),995-1004.https://doi.org/10.1061/(ASCE)HY.1943-7900.0000377.
Coles,D.,1956.The law of the wake in the turbulent boundary layer.J.Fluid Mech.1(2),191-226.https://doi.org/10.1017/S0022112056000135.
Dijkstra,J.T.,Uittenbogaard,R.E.,2010.Modeling the interaction between flow and highly flexible aquatic vegetation.Water Resour.Res.46(12),W12547.https://doi.org/10.1029/2010WR009246.
Han,L.J.,Zeng,Y.H.,Chen,L.,Huai,W.X.,2016.Lateral velocity distribution in open channels with partially flexible submerged vegetation.Environ.Fluid Mech.16(6),1267-1282.https://doi.org/10.1007/s1065 2-016-9485-9.
Hu,Y.,Huai,W.X.,Han,J.,2013.Analytical solution for vertical profile of stream wise velocity in open-channel flow with submerged vegetation.Environ.Fluid Mech.13(4),389-402.https://doi.org/10.1007/s10652-013-9267-6.
Huai,W.X.,Gao,M.,Zeng,Y.H.,Li,D.,2009.Two-dimensional analytical solution for compound channel flows with vegetated floodplains.Appl.Math.Mech.30(9),1121-1130.https://doi.org/10.1007/s10483-009-0906-z.
Huai,W.X.,Wang,W.J.,Zeng,Y.H.,2013.Two-layer model for open channel flow with submerged flexible vegetation.J.Hydraul.Res.5 1(6),708-7 1 8.https://doi.org/10.1080/00221686.2013.8185 85.
Ishikawa,Y.,Mizuhara,K.,Ashida,S.,2000.Effect of density of trees on drag exerted on trees in river channels.J.For.Res.5(4),271-279.https://doi.org/10.1007/BF02767121.
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Keulegan,G.H.,1938.Laws of turbulent flow in open channels.J.Res.Natl.Bur.Stand.21,707-741.
Kothyari,U.,Hayashi,K.,Hashimoto,H.,2009.Drag coefficient of unsubmerged rigid vegetation stems in open channel flows.J.Hydraul.Res.47(6),691-699.https://doi.org/10.3 826/jhr.2009.3283.
Kouwen,N.,Fathi-Moghadam,M.,2000.Friction factors for coniferous trees along rivers.J.Hydraul.Eng.126(10),732-740.https://doi.org/10.1061/(ASCE)0733-9429(2000)126:10(73 2).
Kubrak,E.,Kubrak,J.,Rowinski,P.M.,2008.Vertical velocity distributions through and above submerged,flexible vegetation.Hydrol.Sci.J.53(4),905-920.https://doi.Org/10.1623/hy sj.53.4.905.
Lassabatere,L.,Pu,J.H.,Bonakdari,H.,Joannis,C.,Larrarte,F.,2013.Analytical model for streamwise velocity profile in open channels.J.Hydraul.Eng.139(1),37-43.https://doi.org/10.1061/(ASCE)HY.1943-7900.0000609.
Liu,Z.W.,Chen,Y.C.,Zhu,D.J.,Hui,E.Q.,Jiang,C.B.,2012.Analytical model for vertical velocity profiles in flows with submerged shrub-like vegetation.Environ.Fluid Mech.12(4),341-346.https://doi.org/10.1007/s10652-012-9243-6.
Liu,Z.W.,Chen,Y.C.,Wu,Y.Y.,Wang,W.Y.,Li,L.,2017.Simulation of exchange flow between open water and floating vegetation using a modified RNG k-εturbulence model.Environ.Fluid Mech.17(2),355-372.https://doi.org/10.1007/s1065 2-016-9489-5.
Nepf,H.M.,Vivoni,E.R.,1999.Turbulence structure in depth-limited vegetated flow:transition between emergent and submerged regimes.In:Proceedings of the 28th International IAHR Conference.IAHR,Graz.
Nezu,I.,Nakagawa,H.,1993.Turbulent Open-Channel Flows,IAHR Monograph Series.IAHR,Rotterdam.
Pope,S.B.,2000.Turbulent Flows.Cambridge University Press,New York.
Pu,J.H.,2013.Universal velocity distribution for smooth and rough open channel flows.J.Appl.Fluid Mech.6(3),413-423.
Pu,J.H.,Hussain,K.,Shao,S.,Huang,Y.,2014a.Shallow sediment transport flow computation using time-varying sediment adaptation length.Int.J.Sediment Res.29(2),171-183.https://doi.org/10.1016/S1001-6279(14)60033-0.
Pu,J.H.,Lim,S.Y.,2014.Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment.Environ.Fluid Mech.14(1),69-86.https://doi.org/10.1007/s10652-013-9286-3.
Pu,J.H.,Shao,S.,Huang,Y.,2014b.Numerical and experimental turbulence studies on shallow open channel flows.J.Hydro-Environ.Res.8(1),9-19.https://doi.org/10.101 6/j.j her.2012.12.001.
Pu,J.H.,2015.Turbulence modelling of shallow water flows using Kolmogorov approach.Comput.Fluid 115,66-74.https://doi.org/10.1016/j.compfluid.2015.03.010.
Pu,J.H.,Wei,J.,Huang,Y.,2017.Velocity distribution and 3D turbulence characteristic analysis for flow over water-worked rough bed.Water 9(9),668.https://doi.org/10.3 3 90/w9090668.
Pu,J.H.,Tait,S.,Guo,Y.,Huang,Y.,Hanmaiahgari,P.R.,2018.Dominant features in three-dimensional turbulence structure:Comparison of nonuniform accelerating and decelerating flows.Environ.Fluid Mech.18(2),395-416.https://doi.org/10.1007/s10652-017-9557-5.
Tanino,Y.,Nepf,H.M.,2008.Lateral dispersion in random cylinder arrays at high Reynolds number.J.Fluid Mech.600,339-371.https://doi.org/10.1017/S0022112008000505.
Tsujimoto,T.,Kitamura,T.,1990.Velocity profile of flow in vegetated-bed channels.In:KHL Progressive Report 1.Kazavava University,pp.43-55.
Wu,F.C.,Shen,H.W.,Chou,Y.J.,1999.Variation of roughness coefficients for unsubmerged and submerged vegetation.J.Hydraul.Eng.125(9),934-942.https://doi.org/10.1061/(ASCE)0733-9429(1999)125:9(934).
Yang,W.,Choi,S.U.,2010.A two-layer approach for depth-limited openchannel flows with submerged vegetation.J.Hydraul.Res.48(4),466-475.https://doi.org/10.108 0/00221686.2010.491649.
Bootle,W.J.,1971.Forces on an inclined circular cylinder in supercritical flow.AIAA J.9(3),514-516.https://doi.org/10.2514/3.6213.
Chen,L.,2010.An integral approach for large deflection cantilever beams.Int.J.Non-Linear Mech.45(3),301-305.https://doi.org/10.1016/j.ijnonlinmec.2009.12.004.
Cheng,N.,Nguyen,H.,2011.Hydraulic radius for evaluating resistance induced by simulated emergent vegetation in open-channel flows.J.Hydraul.Eng.137(9),995-1004.https://doi.org/10.1061/(ASCE)HY.1943-7900.0000377.
Coles,D.,1956.The law of the wake in the turbulent boundary layer.J.Fluid Mech.1(2),191-226.https://doi.org/10.1017/S0022112056000135.
Dijkstra,J.T.,Uittenbogaard,R.E.,2010.Modeling the interaction between flow and highly flexible aquatic vegetation.Water Resour.Res.46(12),W12547.https://doi.org/10.1029/2010WR009246.
Han,L.J.,Zeng,Y.H.,Chen,L.,Huai,W.X.,2016.Lateral velocity distribution in open channels with partially flexible submerged vegetation.Environ.Fluid Mech.16(6),1267-1282.https://doi.org/10.1007/s1065 2-016-9485-9.
Hu,Y.,Huai,W.X.,Han,J.,2013.Analytical solution for vertical profile of stream wise velocity in open-channel flow with submerged vegetation.Environ.Fluid Mech.13(4),389-402.https://doi.org/10.1007/s10652-013-9267-6.
Huai,W.X.,Gao,M.,Zeng,Y.H.,Li,D.,2009.Two-dimensional analytical solution for compound channel flows with vegetated floodplains.Appl.Math.Mech.30(9),1121-1130.https://doi.org/10.1007/s10483-009-0906-z.
Huai,W.X.,Wang,W.J.,Zeng,Y.H.,2013.Two-layer model for open channel flow with submerged flexible vegetation.J.Hydraul.Res.5 1(6),708-7 1 8.https://doi.org/10.1080/00221686.2013.8185 85.
Ishikawa,Y.,Mizuhara,K.,Ashida,S.,2000.Effect of density of trees on drag exerted on trees in river channels.J.For.Res.5(4),271-279.https://doi.org/10.1007/BF02767121.
Jarvela,J.,2004.Determination of flow resistance caused by non-submerged woody vegetation.Int.J.River Basin Manag.2(1),61-70.https://doi.org/10.1080/15 715124.2004.963 5 222.
Keulegan,G.H.,1938.Laws of turbulent flow in open channels.J.Res.Natl.Bur.Stand.21,707-741.
Kothyari,U.,Hayashi,K.,Hashimoto,H.,2009.Drag coefficient of unsubmerged rigid vegetation stems in open channel flows.J.Hydraul.Res.47(6),691-699.https://doi.org/10.3 826/jhr.2009.3283.
Kouwen,N.,Fathi-Moghadam,M.,2000.Friction factors for coniferous trees along rivers.J.Hydraul.Eng.126(10),732-740.https://doi.org/10.1061/(ASCE)0733-9429(2000)126:10(73 2).
Kubrak,E.,Kubrak,J.,Rowinski,P.M.,2008.Vertical velocity distributions through and above submerged,flexible vegetation.Hydrol.Sci.J.53(4),905-920.https://doi.Org/10.1623/hy sj.53.4.905.
Lassabatere,L.,Pu,J.H.,Bonakdari,H.,Joannis,C.,Larrarte,F.,2013.Analytical model for streamwise velocity profile in open channels.J.Hydraul.Eng.139(1),37-43.https://doi.org/10.1061/(ASCE)HY.1943-7900.0000609.
Liu,Z.W.,Chen,Y.C.,Zhu,D.J.,Hui,E.Q.,Jiang,C.B.,2012.Analytical model for vertical velocity profiles in flows with submerged shrub-like vegetation.Environ.Fluid Mech.12(4),341-346.https://doi.org/10.1007/s10652-012-9243-6.
Liu,Z.W.,Chen,Y.C.,Wu,Y.Y.,Wang,W.Y.,Li,L.,2017.Simulation of exchange flow between open water and floating vegetation using a modified RNG k-εturbulence model.Environ.Fluid Mech.17(2),355-372.https://doi.org/10.1007/s1065 2-016-9489-5.
Nepf,H.M.,Vivoni,E.R.,1999.Turbulence structure in depth-limited vegetated flow:transition between emergent and submerged regimes.In:Proceedings of the 28th International IAHR Conference.IAHR,Graz.
Nezu,I.,Nakagawa,H.,1993.Turbulent Open-Channel Flows,IAHR Monograph Series.IAHR,Rotterdam.
Pope,S.B.,2000.Turbulent Flows.Cambridge University Press,New York.
Pu,J.H.,2013.Universal velocity distribution for smooth and rough open channel flows.J.Appl.Fluid Mech.6(3),413-423.
Pu,J.H.,Hussain,K.,Shao,S.,Huang,Y.,2014a.Shallow sediment transport flow computation using time-varying sediment adaptation length.Int.J.Sediment Res.29(2),171-183.https://doi.org/10.1016/S1001-6279(14)60033-0.
Pu,J.H.,Lim,S.Y.,2014.Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment.Environ.Fluid Mech.14(1),69-86.https://doi.org/10.1007/s10652-013-9286-3.
Pu,J.H.,Shao,S.,Huang,Y.,2014b.Numerical and experimental turbulence studies on shallow open channel flows.J.Hydro-Environ.Res.8(1),9-19.https://doi.org/10.101 6/j.j her.2012.12.001.
Pu,J.H.,2015.Turbulence modelling of shallow water flows using Kolmogorov approach.Comput.Fluid 115,66-74.https://doi.org/10.1016/j.compfluid.2015.03.010.
Pu,J.H.,Wei,J.,Huang,Y.,2017.Velocity distribution and 3D turbulence characteristic analysis for flow over water-worked rough bed.Water 9(9),668.https://doi.org/10.3 3 90/w9090668.
Pu,J.H.,Tait,S.,Guo,Y.,Huang,Y.,Hanmaiahgari,P.R.,2018.Dominant features in three-dimensional turbulence structure:Comparison of nonuniform accelerating and decelerating flows.Environ.Fluid Mech.18(2),395-416.https://doi.org/10.1007/s10652-017-9557-5.
Tanino,Y.,Nepf,H.M.,2008.Lateral dispersion in random cylinder arrays at high Reynolds number.J.Fluid Mech.600,339-371.https://doi.org/10.1017/S0022112008000505.
Tsujimoto,T.,Kitamura,T.,1990.Velocity profile of flow in vegetated-bed channels.In:KHL Progressive Report 1.Kazavava University,pp.43-55.
Wu,F.C.,Shen,H.W.,Chou,Y.J.,1999.Variation of roughness coefficients for unsubmerged and submerged vegetation.J.Hydraul.Eng.125(9),934-942.https://doi.org/10.1061/(ASCE)0733-9429(1999)125:9(934).
Yang,W.,Choi,S.U.,2010.A two-layer approach for depth-limited openchannel flows with submerged vegetation.J.Hydraul.Res.48(4),466-475.https://doi.org/10.108 0/00221686.2010.491649.