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Sediment transport in ice-covered channel under non-equilibrium condition

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Abstract

Many rivers and lakes located at high altitudes in different parts of the world experience ice conditions during the winter for prolonged period and an ice cover on the top causes a transition from an open flow state to a closed underflow one. The distribution of the suspended sediment concentration is presented under such condition where the concentration is a function of spatial coordinates along with time. Existing expressions of eddy viscosity and settling velocity are used that contain the combined effects of both the lower channel bed and the upper ice cover boundary. The flow is considered sediment free initially and assumes a uniform inlet condition. No mass transfer is taken on the ice cover surface and a constant reference concentration is assumed at the reference level. Numerical method (ADI method) has been utilized for the solution of the PDE in conjunction with the given initial and boundary conditions. It is found that with increasing time and downstream distance, concentration values first increase along a vertical and then reach a stable value. Following this, the solution is compared with the available experimental data at large time under far-field conditions. At the end, the concentration profiles are analysed by varying different parameters. It is seen that as the dimensionless correction coefficient present in the settling velocity expression increases, the concentration values also increase. An opposite result is found when the dimensionless proportionality constant present in the eddy viscosity expression is varied and in comparison to lower times, the amount of concentration change occurs rapidly with higher times.

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References

  • Bai Y, Duan Y (2021) The vertical distribution of suspended sediment and phosphorus in a channel with ice cover. Environ Sci Pollut Res 28:37953–37962

    Article  CAS  Google Scholar 

  • Beldowska M, Jedruch A, Sienska D, Chwialkowski W, Magnuszewski A, Kornijow R (2021) The impact of sediment, fresh and marine water on the concentration of chemical elements in water of the ice-covered lagoon. Environ Sci Pollut Res 28(43):61189–61200

    Article  CAS  Google Scholar 

  • Bolla Pittaluga M, Seminara G (2003) Depth-integrated modeling of suspended sediment transport. Water Resour Res. https://doi.org/10.1029/2002WR001306

    Article  Google Scholar 

  • Bueche T, Hamilton DP, Vetter M (2017) Using the general lake model (GLM) to simulate water temperatures and ice cover of a medium-sized lake: a case study of lake Ammersee, Germany. Environ Earth Sci 76:1–14

    Article  Google Scholar 

  • Buendia C, Vericat D, Batalla RJ, Gibbins CN (2016) Temporal dynamics of sediment transport and transient in-channel storage in a highly erodible catchment. Land Degrad Dev 27(4):1045–1063

    Article  Google Scholar 

  • Chen Y, Wang Z, Zhu D, Liu Z (2016) Longitudinal dispersion coefficient in ice-covered rivers. J Hydraul Res 54(5):558–566

    Article  Google Scholar 

  • Douglas J, Rachford HH (1956) On the numerical solution of heat conduction problems in two and three space variables. Trans Am Math Soc 82(2):421–439

    Article  Google Scholar 

  • Duguay CR, Prowse TD, Bonsal BR, Brown RD, Lacroix MP, Ménard P (2006) Recent trends in Canadian lake ice cover. Hydrol Process Int J 20(4):781–801

    Article  Google Scholar 

  • Ettema R (2002) Review of alluvial-channel responses to river ice. J Cold Reg Eng 16(4):191–217

    Article  Google Scholar 

  • Galappatti G, Vreugdenhil C (1985) A depth-integrated model for suspended sediment transport. J Hydraul Res 23(4):359–377

    Article  Google Scholar 

  • Ghoshal K, Jain P, Absi R (2022) Nonlinear partial differential equation for unsteady vertical distribution of suspended sediments in open channel flows: effects of hindered settling and concentration-dependent mixing length. J Eng Mech 148(1):04021123

    Article  Google Scholar 

  • Guo J, Shan H, Xu H, Bai Y, Zhang J (2017) Exact solution for asymmetric turbulent channel flow with applications in ice-covered rivers. J Hydraul Eng 143(10):04017041

    Article  Google Scholar 

  • Harun MA, Safari MJS, Gul E, Ab Ghani A (2021) Regression models for sediment transport in tropical rivers. Environ Sci Pollut Res 28(38):53097–53115

    Article  Google Scholar 

  • Hjelmfelt A, Lenau C (1970) Nonequilibrium transport of suspended sediment. J Hydraul Div 96(7):1567–1586

    Article  Google Scholar 

  • Huang F (2014) A numerical model study on river ice and sediment dynamics. Ph.D. thesis, Clarkson University, Potsdam, NY

  • Hunt J (1954) The turbulent transport of suspended sediment in open channels. Proc R Soc Lond Ser A Math Phys Sci 224(1158):322–335

    CAS  Google Scholar 

  • Ionita M, Badaluta CA, Scholz P, Chelcea S (2018) Vanishing river ice cover in the lower part of the Danube basin-signs of a changing climate. Sci Rep 8(1):7948

    Article  CAS  Google Scholar 

  • Kirillin G, Leppäranta M, Terzhevik A, Granin N, Bernhardt J, Engelhardt C, Efremova T, Golosov S, Palshin N, Sherstyankin P et al (2012) Physics of seasonally ice-covered lakes: a review. Aquat Sci 74:659–682

    Article  Google Scholar 

  • Knack IM (2011) Mathematical modeling of river dynamics with thermal-ice-sediment processes. Ph. D. thesis, Clarkson University, Potsdam, NY

  • Knack I, Shen HT (2015) Sediment transport in ice-covered channels. Int J Sedim Res 30(1):63–67

    Article  Google Scholar 

  • Krishnappan BG (1983) Suspended sediment profile for ice-covered flows. J Hydraul Eng 109(3):385–399

    Article  Google Scholar 

  • Lau YL, Krishnappan BG (1985) Sediment transport under ice cover. J Hydraul Eng 111(6):934–950

    Article  Google Scholar 

  • Lawler D (1993) Needle ice processes and sediment mobilization on river banks: the river Ilston, West Glamorgan, UK. J Hydrol 150(1):81–114

    Article  Google Scholar 

  • Liu X (2016) Analytical solutions for steady two-dimensional suspended sediment transport in channels with arbitrary advection velocity and eddy diffusivity distributions. J Hydraul Res 54(4):389–398

    Article  Google Scholar 

  • Liu X, Nayamatullah M (2014) Semianalytical solutions for one-dimensional unsteady nonequilibrium suspended sediment transport in channels with arbitrary eddy viscosity distributions and realistic boundary conditions. J Hydraul Eng 140(5):04014011

    Article  Google Scholar 

  • Lorentz HA (1907) Ein allgemeiner satz, die bewegung einer reibenden flüssigkeit betreffend, nebst einigen anwendungen desselben. Abh Theor Phys 1:23

    Google Scholar 

  • Lotsari E, Kasvi E, Kamari M, Alho P (2017) The effects of ice cover on flow characteristics in a subarctic meandering river. Earth Surf Proc Land 42(8):1195–1212

    Article  Google Scholar 

  • Magnuson JJ, Robertson DM, Benson BJ, Wynne RH, Livingstone DM, Arai T, Assel RA, Barry RG, Card V, Kuusisto E et al (2000) Historical trends in lake and river ice cover in the northern hemisphere. Science 289(5485):1743–1746

    Article  CAS  Google Scholar 

  • Mazumder BS, Ghoshal K (2006) Velocity and concentration profiles in uniform sediment-laden flow. Appl Math Model 30(2):164–176

    Article  Google Scholar 

  • Mei CC (1969) Nonuniform diffusion of suspended sediment. J Hydraul Div 95(1):581–584

    Article  Google Scholar 

  • Merritt WS, Letcher RA, Jakeman AJ (2003) A review of erosion and sediment transport models. Environ Model Softw 18(8–9):761–799

    Article  Google Scholar 

  • Muste M, Braileanu F, Ettema R (2000) Flow and sediment transport measurements in a simulated ice-covered channel. Water Resour Res 36(9):2711–2720

    Article  Google Scholar 

  • Peaceman DW, Rachford HH (1955) The numerical solution of parabolic and elliptic differential equations. J Soc Ind Appl Math 3(1):28–41

    Article  Google Scholar 

  • Rao L, Qian J, Ao Yh (2014) Influence of artificial ecological floating beds on river hydraulic characteristics. J Hydrodyn 26(3):474–481

    Article  Google Scholar 

  • Rijn LCV (1984) Sediment transport, part II: suspended load transport. J Hydraul Eng 110(11):1613–1641

    Article  Google Scholar 

  • Rouse H (1937) Modern conceptions of the mechanics of fluid turbulence. Trans Am Soc Civ Eng 102(1):463–505

    Article  Google Scholar 

  • Sayre WW, Song G (1979) Effects of ice covers on alluvial channel flow and sediment transport processes. Technical report, Iowa institute of Hydraulic Research Iowa city

  • Sen S, Kundu S, Absi R, Ghoshal K (2023) A model for coupled fluid velocity and suspended sediment concentration in an unsteady stratified turbulent flow through an open channel. J Eng Mech 149(1):04022088

    Article  Google Scholar 

  • Teal MJ, Ettema R, Walker JF (1994) Estimation of mean flow velocity in ice-covered channels. J Hydraul Eng 120(12):1385–1400

    Article  Google Scholar 

  • Tsai WF, Ettema R (1994) Modified eddy viscosity model in fully developed asymmetric channel flows. J Eng Mech 120(4):720–732

    Article  Google Scholar 

  • Turcotte B, Morse B, Bergeron NE, Roy AG (2011) Sediment transport in ice-affected rivers. J Hydrol 409(1–2):561–577

    Article  Google Scholar 

  • Umeyaina M (1992) Vertical distribution of suspended sediment in uniform open-channel flow. J Hydraul Eng 118(6):936–941

    Article  Google Scholar 

  • Uzuner MS (1975) The composite roughness of ice covered streams. J Hydraul Res 13(1):79–102

    Article  Google Scholar 

  • Wang Z (1992) Theoretical analysis on depth-integrated modelling of suspended sediment transport. J Hydraul Res 30(3):403–421

    Article  Google Scholar 

  • Wang F, Huai W, Liu M, Fu X (2020) Modeling depth-averaged streamwise velocity in straight trapezoidal compound channels with ice cover. J Hydrol 585:124336

    Article  Google Scholar 

  • Wang F, Huai W, Guo Y (2021a) Analytical model for the suspended sediment concentration in the ice-covered alluvial channels. J Hydrol 597:126338

    Article  Google Scholar 

  • Wang F, Huai W, Guo Y, Liu M (2021b) Turbulence structure and momentum exchange in compound channel flows with shore ice covered on the floodplains. Water Resour Res 57(4):e2020WR028621

    Article  Google Scholar 

  • Wang F, Li Z, Zhang Y, Guo J (2023) Fractional derivative modeling for sediment suspension in ice-covered channels. Environ Sci Pollut Res 30(5):12508–12520

    Article  Google Scholar 

  • Zhang R, Xie J, Wang M, Huang J (1998) River sediment dynamics. China Water and Power Press, Beijing

    Google Scholar 

Download references

Funding

The Council of Scientific and Industrial Research (CSIR) provides financial assistance.

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Authors and Affiliations

  1. Department of Mathematics, IIT Kharagpur, Kharagpur, West Bengal, 721302, India

    Sweta Narayan Sahu, Sourav Hossain, Sumit Sen & Koeli Ghoshal

Authors
  1. Sweta Narayan Sahu
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  2. Sourav Hossain
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  3. Sumit Sen
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  4. Koeli Ghoshal
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Contributions

All authors contributed to the study conception and design, where the idea came from Koeli Ghoshal. Material preparation, data collection and analysis were performed by Sweta Narayan Sahu, Sourav Hossain, Sumit Sen and Koeli Ghoshal. The first draft of the manuscript was written by Sweta Narayan Sahu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Koeli Ghoshal.

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Sahu, S.N., Hossain, S., Sen, S. et al. Sediment transport in ice-covered channel under non-equilibrium condition. Environ Earth Sci 83, 315 (2024). https://doi.org/10.1007/s12665-024-11642-x

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