Skip to main content
SpringerLink
Log in

Propagating characteristics of waves on a thin layer of mud

  • Article
  • Published:
Journal of Hydrodynamics Aims and scope Submit manuscript

Abstract

The propagating characteristics of the water and muddy waves are one of the concerns of theoretical studies because of the following facts: (1) With the development of the economy in the estuaries, local residents and government paid increasing attention to the ecological environment of the estuarine beaches The propagating characteristics of the water and muddy waves are closely related to the ecological environment, the concern of the government and the residents. (2) The propagating characteristics of the mud are the bottleneck of the study of the coastal and beach dynamics because of the complicated constitutive relation of the mud. The different constitutive models may lead to different explanations of its mechanism. Hence, the proper selection of the model is one of the keys to reveal the true kinematic properties of the mud in the estuaries. This paper first establishes a power law model of the constitutive relation of the mud. Based on this model, a gravity wave theory is proposed. According to the mechanism of the mud wave transportation, the coupled mud-water wave field can be divided into two layers. The upper layer is described as the viscous Newtonian fluid, whereas the lower high-concentration mud layer is described as the power law fluid. Next, the equations of the proposed model are discretized and the calculations are made by using the difference method. Then, the propagating characteristics are discussed, and the dispersion relations of the water and mud waves are analyzed in detail.

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.

Similar content being viewed by others

References

  1. Fang H. W., He G. J., Huang L. et al. Progresses and challenges in the study of Eco-fluvial Dynamics [J]. Journal of Hydraulic Engineering, 2018, 50(1): 75–87, 96(in Chinese).

    Google Scholar 

  2. Gade H. G. Effects of a non-rigid impermeable bottom on plane surface waves in shallow water [J]. Journal of Marine Research, 1958, 16(3): 61–82.

    Google Scholar 

  3. Cueva I. P. On the response of a muddy bottom to surface water waves [J]. Journal of Hydraulic Research, 1993, 31(5): 681–696.

    Article  Google Scholar 

  4. Su X. L., Xu W. X., Chen W. Numerical study for laminar flow of non-Newtonian fluid based on fractal derivative [J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1020–1028.

    Google Scholar 

  5. Nava G., Tie Y., Vitali V. et al. Newtonian to non-Newtonian fluid transition of a model transient network [J]. Soft Matter, 2018, 14(17): 3288–3295.

    Article  Google Scholar 

  6. Pantokratoras A. Flow past a rotating sphere in a non-Newtonian, power-law fluid, up to a Reynolds number of 10000 [J]. Chemical Engineering Science, 2018, 181(18): 311–314.

    Article  Google Scholar 

  7. Charu D., Gwynn J. E. Dynamics and rheology of particles in shear-thinning fluids [J]. Journal of Non-Newtonian Fluid Mechanics, 2018, 262: 107–114.

    Article  MathSciNet  Google Scholar 

  8. Xu H., Bai Y., Li C. Hydro-instability characteristics of Bingham fluid flow as in the Yellow River [J]. Journal of Hydro-environment Research, 2018, 20: 22–30.

    Article  Google Scholar 

  9. Niu X. J., Yu X. P. A numerical method for flows of fluids with complex viscoelasticity [J]. Chinese Journal of Hydrodynamics, 2008, 23(3): 331–337(in Chinese).

    MathSciNet  Google Scholar 

  10. Zhang X. Y., Ng C. O. Mud-wave interaction: A viscoelastic model [J]. China Ocean Engineering, 2006, 20(1): 15–26.

    Google Scholar 

  11. Xia Y. Z., Zhu K. Q. A study of wave attenuation over a Maxwell model of a muddy bottom [J]. Wave Motion, 2010, 47(8): 601–615.

    Article  MathSciNet  Google Scholar 

  12. Niu X. J., Yu X. P. Visco-elastic-plastic model for muddy seabeds [J]. Journal of Tsinghua University (Science and Technology), 2008, 48(9): 1417–1421.

    Google Scholar 

  13. Rosti M. E., Izbassarov D., Tammisola O. et al. Turbulent channel flow of an elastoviscoplastic fluid [J]. Journal of Fluid Mechanics, 2018, 853: 488–514.

    Article  MathSciNet  Google Scholar 

  14. Sohbati M., Toumazou C. A two-dimensional experimental-numerical approach to investigate wave transformation over muddy beds [J]. Ocean Dynamics, 2015, 65(2): 295–310.

    Article  Google Scholar 

  15. Mei C. C., Krotov M., Huang Z. H. et al. Short and long waves over a muddy seabed [J]. Journal of Fluid Mechanics, 2010, 643: 33–58.

    Article  Google Scholar 

  16. Ng C. O., Zhang X. Y. Mass transport in water waves over a thin layer of soft viscoelastic mud [J]. Journal of Fluid Mechanics, 2007, 573: 105–130.

    Article  MathSciNet  Google Scholar 

  17. Bai Y. C., Tian Q. Interaction between mud and wave in different rheological models [J]. Journal of Tianjin University (Science and Technology), 2011, 44(3): 196–201.

    MathSciNet  Google Scholar 

  18. Liu J., Bai Y., Xu D. Mass transport in a thin layer of power-law mud under surface waves [J]. Ocean Dynamics, 2017, 67(2): 237–251.

    Article  Google Scholar 

  19. Hamid M., Usman M., Haq R. U. et al. Wavelet analysis of stagnation point flow of non-Newtonian nanofluid [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(8): 1211–1226.

    Article  MathSciNet  Google Scholar 

  20. Zhang Y. L., Smirnov M. N., Bogdanova A. I. et al. Travel time prediction with viscoelastic traffic model [J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1769–1788.

    Article  MathSciNet  Google Scholar 

  21. Cristo C. D., Iervolino M., Moramarco T. et al. Applicability of kinematic model for mud-flows: An unsteady analysis [J]. Journal of Hydrology, 2019, 577: 123967.

    Article  Google Scholar 

  22. Chesnokov A. Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane [J]. Wave Motion, 2021, 106: 102799.

    Article  MathSciNet  Google Scholar 

  23. Piedra-Cueva I. Drift velocity of spatially decaying waves in a two-layer viscous system [J]. Journal of Fluid Mechanics, 1995, 299: 217–239.

    Article  MathSciNet  Google Scholar 

  24. Bai Y. C., Ji Z. Q., Xu H. J. Hydrodynamic instability characteristics of laminar flow in a meandering channel with moving boundary [J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 274–288.

    Google Scholar 

  25. Xu H. J. Research on nonlinear theory of river weak dynamic process [D]. Doctoral Thesis, Tianjin, China: Tianjin University, 2007(in Chinese).

    Google Scholar 

  26. Zhang H., Lu D. Q. Unsteady hydro-elastic wave resistances and deflections due to two-dimensional load moving on a floating plate [J]. Chinese Journal of Hydrodynamics, 2013, 28(5): 615–625(in Chinese).

    Google Scholar 

  27. Li J. C., Wei Y. J., Wang C. et al. Water-entry cavity of heated spheres [J]. Acta Physica Sinica, 2016, 65(20): 204703(in Chinese).

    Article  Google Scholar 

  28. Liu P. L. F., Chan I. C. On long wave propagation over a fluid-mud seabed [J]. Journal of Fluid Mechanics, 2007, 579: 467–480.

    Article  MathSciNet  Google Scholar 

  29. Hu Y., Guo X., Lu X. et al. Idealized numerical simulation of breaking water wave propagating over a viscous mud layer [J]. Physics of Fluids, 2012, 24(11): 112104.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, 300072, China

    Hai-jue Xu, Jin-sen Wu & Yu-chuan Bai

  2. Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Dong-qiang Lu

  3. Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China

    Chiu-On Ng

Authors
  1. Hai-jue Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jin-sen Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu-chuan Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dong-qiang Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chiu-On Ng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu-chuan Bai.

Additional information

Projects supported by the National Natural Science Foundation of China (Grant Nos. 51979185, 51879182), the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51621092).

Biography

Hai-jue Xu (1977-), Female, Ph. D., Associate Professor, E-mail: xiaoxiaoxu_2004@163.com

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, Hj., Wu, Js., Bai, Yc. et al. Propagating characteristics of waves on a thin layer of mud. J Hydrodyn 33, 1078–1088 (2021). https://doi.org/10.1007/s42241-021-0077-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42241-021-0077-x

Key words

Search

Navigation