Abstract
Based on the Reynolds-averaged Navier–Stokes equations and the Shiono and Knight method, this paper describes the development of an analytical model to predict the lateral distribution of depth-averaged velocities in steady uniform flows in rectangular ice-covered channels, including the effect of river bed resistance, ice sheet resistance, eddy viscosity, and secondary flows. The analytical model has three working conditions: full ice cover, symmetrical shore ice, and asymmetrical shore ice. The modeled results agreed well with the available experimental data, thereby indicating that the proposed model can accurately predict the lateral distribution of depth-averaged velocity in rectangular ice-covered channels. The application of dimensionless eddy viscosity, resistance coefficient, and secondary flow coefficient was analyzed. Results illustrate that the calculation method for the dimensionless eddy viscosity and resistance coefficient in open channels is also applicable to ice-covered channels. The study shows that secondary flow, which has a close relationship with flow depth, plays an important role in ice-covered channels. In the application of the model, ignoring the secondary flow will lead to a large computational error.
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Acknowledgments
This work was financially supported by the Natural Science Foundation of China (Grant Nos. 51439007, 11672213, and 11872285). Special thanks to the chief editor, associate editor, and anonymous reviewers for their very helpful comments and suggestions on this paper.
References
Abril, J. B., and D. W. Knight. 2004. “Stage-discharge prediction for rivers in flood applying a depth-averaged model.” J. Hydraul. Res. 42 (6): 616–629. https://doi.org/10.1080/00221686.2004.9628315.
Alawadi, W., W. Al-Rekabi, and A. H. Al-Aboodi. 2018. “Application of the Shiono and Knight method in asymmetric compound channels with different side slopes of the internal wall.” Appl. Water Sci. 8 (1): 4. https://doi.org/10.1007/s13201-018-0663-4.
Attar, S., and S. S. Li. 2012. “Data-fitted velocity profiles for ice-covered channels.” Can. J. Civ. Eng. 39 (3): 334–338. https://doi.org/10.1139/l2012-001.
Attar, S., and S. S. Li. 2013. “Momentum, energy and drag coefficients for ice-covered channels.” River Res. Appl. 29 (10): 1267–1276. https://doi.org/10.1002/rra.v29.10.
Bonakdari, H. 2012. “Establishment of relationship between mean and maximum velocities in narrow sewers.” J. Environ. Manage. 113 (1): 474–480. https://doi.org/10.1016/j.jenvman.2012.10.016.
Chen, G., S. Gu, W. Huai, and Y. Zhang. 2015. “Boundary shear stress in rectangular ice-covered channels.” J. Hydraul. Eng. 141 (6): 06015005. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001004.
Chen, G., W. X. Huai, J. Han, and M. D. Zhao. 2010. “Flow structure in partially vegetated rectangular channels.” J. Hydrodyn. 22 (4): 590–597. https://doi.org/10.1016/S1001-6058(09)60092-5.
Chen, Y., Z. Wang, D. Zhu, and Z. Liu. 2016. “Longitudinal dispersion coefficient in ice-covered rivers.” J. Hydraul. Res. 54 (5): 558–566. https://doi.org/10.1080/00221686.2016.1175519.
Cox, R. G. 1973. Effective hydraulic roughness for channels having bed roughness different from bank roughness. Vicksburg, MS: US Army Corps of Engineers Waterways Experiment Station.
Einstein, H. A. 1942. “Formulas for the transportation of bed-load.” Trans. ASCE 107 (2140): 561–597.
Einstein, H. A., and R. B. Banks. 1950. “Fluid resistance of composite roughness.” Trans. Am. Geophys. Union 31 (4): 603–610. https://doi.org/10.1029/TR031i004p00603.
Ervine, D. A., K. Babaeyan-Koopaei, and R. H. J. Sellin. 2000. “Two-dimensional solution for straight and meandering overbank flows.” J. Hydraul. Eng. 126 (9): 653–669. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:9(653).
Goring, D. G., and V. I. Nikora. 2002. “Despiking acoustic Doppler velocimeter data.” J. Hydraul. Eng. 128 (1): 117–126. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:1(117).
Guo, J., H. Shan, H. Xu, Y. Bai, and J. Zhang. 2017. “Exact solution for asymmetric turbulent channel flow with applications in ice-covered rivers.” J. Hydraul. Eng. 143 (10): 04017041. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001360.
Islam, M. R., and D. Z. Zhu. 2013. “Kernel density-based algorithm for despiking ADV data.” J. Hydraul. Eng. 139 (7): 785–793. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000734.
Larsen, P. A. 1969. “Head losses caused by an ice cover on open channels.” J. Boston Soc. Civ. Eng. 56 (1): 45–67.
Lau, Y. L., and B. G. Krishnappan. 1981. “Ice cover effects on stream flows and mixing.” J. Am. Soc. Civ. Eng. Hydraul. Div. 107 (10): 1225–1242.
Liao, H., and D. W. Knight. 2007. “Analytic stage-discharge formulae for flow in straight trapezoidal open channels.” Adv. Water Resour. 30 (11): 2283–2295. https://doi.org/10.1016/j.advwatres.2007.05.002.
Liu, C., X. Luo, X. Liu, and K. Yang. 2013. “Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation.” Adv. Water Resour. 60 (8): 148–159. https://doi.org/10.1016/j.advwatres.2013.08.002.
Liu, C., N. Wright, X. Liu, and K. Yang. 2014. “An analytical model for lateral depth-averaged velocity distributions along a meander in curved compound channels.” Adv. Water Resour. 74 (12): 26–43. https://doi.org/10.1016/j.advwatres.2014.08.003.
Lotter, G. K. 1933. “Considerations on hydraulic design of channels with different roughness of walls.” Trans. All-Union Sci. Res. Inst. Hydraul. Eng. Leningrad 9: 238–241.
Morse, B., and F. Hicks. 2005. “Advances in river ice hydrology 1999–2003.” Hydrol. Processes 19 (1): 247–263. https://doi.org/10.1002/(ISSN)1099-1085.
Muste, M., F. Braileanu, and R. Ettema. 2000. “Flow and sediment transport measurements in a simulated ice-covered channel.” Water Resour. Res. 36 (9): 2711–2720. https://doi.org/10.1029/2000WR900168.
Parthasarathy, R. N., and M. Muste. 1994. “Velocity measurements in asymmetric turbulent channel flows.” J. Hydraul. Eng. 120 (9): 1000–1020. https://doi.org/10.1061/(ASCE)0733-9429(1994)120:9(1000).
Pavlovskii, N. N. 1931. “On a design formula for uniform flow in channels with non-homogeneous walls.” Trans. All-Union Sci. Res. Inst. Hydraul. Eng. Leningrad 3: 157–164.
Peltier, Y., N. Rivière, S. Proust, E. Mignot, A. Paquier, and K. Shiono. 2013. “Estimation of the error on the mean velocity and on the Reynolds stress due to a misoriented ADV probe in the horizontal plane: Case of experiments in a compound open-channel.” Flow Meas. Instrum. 34: 34–41. https://doi.org/10.1016/j.flowmeasinst.2013.08.002.
Peters, M., K. Dow, S. Clark, J. Malenchak, and D. Danielson. 2017. “Experimental investigation of the flow characteristics beneath partial ice covers.” Cold Reg. Sci. Technol. 142 (10): 69–78. https://doi.org/10.1016/j.coldregions.2017.07.007.
Robert, A., and T. Tran. 2012. “Mean and turbulent flow fields in a simulated ice-covered channel with a gravel bed: Some laboratory observations.” Earth Surf. Processes Landforms 37 (9): 951–956. https://doi.org/10.1002/esp.v37.9.
Shen, H. T., and T. O. Harden. 1978. “The effects of ice cover on vertical transfer streamwise channels.” J. Am. Water Resour. Assoc. 14 (6): 1429–1439. https://doi.org/10.1111/jawr.1978.14.issue-6.
Shiono, K., and T. Feng. 2003. “Turbulence measurements of dye concentration and effects of secondary flow on distribution in open channel flows.” J. Hydraul. Eng. 129 (5): 373–384. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:5(373).
Shiono, K., and D. W. Knight. 1991. “Turbulent open-channel flows with variable depth across the channel.” J. Fluid Mech. 222: 617–646. https://doi.org/10.1017/S0022112091001246.
Sui, J., J. Wang, H. E. Yun, and F. Krol. 2010. “Velocity profiles and incipient motion of frazil particles under ice cover.” Int. J. Sediment Res. 25 (1): 39–51. https://doi.org/10.1016/S1001-6279(10)60026-1.
Tang, X., and D. W. Knight. 2008. “A general model of lateral depth-averaged velocity distributions for open channel flows.” Adv. Water Resour. 31 (5): 846–857. https://doi.org/10.1016/j.advwatres.2008.02.002.
Tatinclaux, J. C., and M. Gogus. 1983. “Asymmetric plane flow with application to ice jams.” J. Hydraul. Eng. 109 (11): 1540–1554. https://doi.org/10.1061/(ASCE)0733-9429(1983)109:11(1540).
Teal, M. J., R. Ettema, and J. F. Walker. 1994. “Estimation of mean flow velocity in ice-covered channels.” J. Hydraul. Eng. 120 (12): 1385–1400. https://doi.org/10.1061/(ASCE)0733-9429(1994)120:12(1385).
Voulgaris, G., and J. H. Trowbridge. 1998. “Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements.” J. Atmos. Oceanic Technol. 15 (1): 272–289. https://doi.org/10.1175/1520-0426(1998)015%3C0272:EOTADV%3E2.0.CO;2.
Walker, J. F., and D. Wang. 1997. “Measurement of flow under ice covers in North America.” J. Hydraul. Eng. 123 (11): 1037–1040. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:11(1037).
Wang, Y., and W. Huai. 2016. “Estimating the longitudinal dispersion coefficient in straight natural rivers.” J. Hydraul. Eng. 142 (11): 04016048. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001196.
Yang, K. 2015. “Lateral distribution of depth-averaged velocities in ice-covered channels.” [In Chinese.] J. Hydraul. Eng. 46 (3): 291–297.
Yang, K., S. Cao, and D. W. Knight. 2007. “Flow patterns in compound channels with vegetated floodplains.” J. Hydraul. Eng. 133 (2): 148–159. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:2(148).
Yang, K., R. Nie, X. Liu, and S. Cao. 2013. “Modeling depth-averaged velocity and boundary shear stress in rectangular compound channels with secondary flows.” J. Hydraul. Eng. 139 (1): 76–83. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000638.
Yang, S., J. Yu, and Y. Wang. 2004. “Estimation of diffusion coefficients, lateral shear stress, and velocity in open channels with complex geometry.” Water Resour. Res. 40 (5): 312–328. https://doi.org/10.1029/2003WR002818.
Yen, B. 2002. “Open channel flow resistance.” J. Hydraul. Eng. 128 (1): 20–39. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:1(20).
Zhong, Y., W. X. Huai, Y. Wang, and G. Chen. 2018. “Estimation of longitudinal dispersion coefficient in ice-covered rivers.” J. Hydraul. Eng. 144 (6): 04018026. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001475.
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©2018 American Society of Civil Engineers.
History
Received: Jul 3, 2017
Accepted: Jul 16, 2018
Published online: Oct 27, 2018
Published in print: Jan 1, 2019
Discussion open until: Mar 27, 2019
ASCE Technical Topics:
- Channels (waterway)
- Coastal engineering
- Coastal processes
- Coasts, oceans, ports, and waterways engineering
- Cold regions engineering
- Design (by type)
- Eddy (fluid dynamics)
- Engineering fundamentals
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Fluid velocity
- Hydraulic engineering
- Hydraulic structures
- Hydrologic engineering
- Ice
- Load and resistance factor design
- Load factors
- Ocean currents
- Secondary flow
- Structural design
- Velocity distribution
- Viscosity
- Water and water resources
- Waterways
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