Skip to main content
SpringerLink
Log in

A random displacement model of sediment transport in ice-covered alluvial channel flows

  • Research Article
  • Published:
Environmental Science and Pollution Research Aims and scope Submit manuscript

Abstract

There is a need for developing efficient models to simulate the sediment transport phenomenon in ice-covered alluvial channel flows, which is essential in enriching the theory of riverbed evolution. This study establishes a random displacement model parameterized with the time-averaged streamwise velocity U(z), the sediment settling velocity ωs(z), and the turbulent diffusion coefficient Dz(z) to calculate the suspended sediment concentration and the longitudinal dispersion coefficient for ice-covered alluvial channels. The proposed model is first validated to determine if it could be used to predict the sediment concentration profiles by comparing to limited experiments published in the literature. Results show that the simulations agree well with the measurements except for the underestimated concentration near the ice cover boundary. Once validated, the random displacement model is applied to explore the variation law of the suspended sediment concentration and the longitudinal dispersion with different sediment particle release modes. The sediment concentration and the stable value of the longitudinal dispersion coefficient for a given flow condition in the dynamic equilibrium state are not affected by the change of the particle release mode. The Fickian time required for the longitudinal dispersion coefficient converging to a constant, however, has a close relationship with the particle release mode and increases as the water depth increases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data availability

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

C :

Suspended sediment concentration (mg/l)

C a :

Reference sediment concentration at the vertical level z = a from the channel bed bottom (mg/l)

D :

Median diameter of the sediment particle (mm)

D L :

Longitudinal dispersion coefficient (m2/s)

D z :

Vertical turbulent diffusion coefficient (m2/s)

g :

Gravitational acceleration (m/s2)

H :

Water depth (m)

n b :

The Manning’s roughness coefficients of the channel bed (-)

n i :

The Manning’s roughness coefficients of the ice cover (-)

q :

Flow discharge per unit width (m2/s)

R :

Independent random variable that obeys the normal distribution (-)

S :

Channel bed slope (-)

T :

Temperature of clear water (°C)

T act :

Fickian time simulated by the RDM (s)

T theo :

Theoretical Fickian time (s)

\({u}_{\ast_b}\) :

Shear velocity resulted from the shear stress of channel bed boundary (m/s)

\({u}_{\ast_i}\) :

Shear velocity resulted from the shear stress of ice cover boundary (m/s)

U :

Time-averaged streamwise velocity (m/s)

U bulk :

Bulk mean velocity (m/s)

U max :

Maximum value of the streamwise velocity U (m/s)

\(\overline{x}\) :

Centroid position of discrete particles (m)

x :

Longitudinal coordinate (m)

z :

Vertical coordinate (m)

α, β :

Intermediate parameters (-)

γ s :

Specific weight of the sediment particle (N/m3)

γ w :

Specific weight of the clear water (N/m3)

Δt :

Time step (s)

Δx :

Longitudinal displacement (m)

Δz :

Vertical displacement (m)

κ :

von Kármán constant, and κ = 0.40 (-)

λ :

Dimensionless parameter, and \(\lambda ={u}_{\ast_i}/{u}_{\ast_b}\) (-)

ν t :

Eddy viscosity (m2/s)

ξ :

Dimensionless parameter, and ξ = z/H (-)

ξ c :

Key position of the eddy viscosity (-)

ξ D :

Dimensionless parameter, and ξD = D/H (-)

ξ max :

Dimensionless parameter, and ξmax = 1/(1 + λ2) (-)

σ :

Proportionality constant (-)

σ x 2(t):

Spatial variance at time t (m2)

v :

Kinematic viscosity coefficient of clear water (m2/s)

φ :

Dimensionless correction coefficient of sediment settling velocity (-)

ω s :

Sediment settling velocity (m/s)

ω' :

Turbulent transport velocity (m/s)

Ф:

Velocity distribution function (m/s)

References

Download references

Funding

This work was supported by the National Natural Science Foundation of China [Grant numbers 52020105006 and 11872285].

Author information

Authors and Affiliations

  1. School of Water Conservancy and Engineering, Zhengzhou University, Zhengzhou, 450001, China

    Feifei Wang & Zhiwei Li

  2. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, China

    Feifei Wang & Wenxin Huai

Authors
  1. Feifei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhiwei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenxin Huai
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Feifei Wang contributed to all aspects of this study, including conceptualization, methodology, software, investigation, data curation, visualization, and writing—original draft preparation. Zhiwei Li validated the results and reviewed the original draft of this paper. Wenxin Huai was involved in important aspects of this study, such as conceptualization, leadership, and supervision. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Wenxin Huai.

Ethics declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Additional information

Responsible Editor: Marcus Schulz

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, F., Li, Z. & Huai, W. A random displacement model of sediment transport in ice-covered alluvial channel flows. Environ Sci Pollut Res 29, 70099–70113 (2022). https://doi.org/10.1007/s11356-022-20833-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11356-022-20833-7

Keywords

Search

Navigation