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Inflows/outflows driven particle dynamics in an idealised lake

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Abstract

This paper considers fluid mixing driven by inflows connected to a circular shallow lake using a numerical framework consisting of a shallow water hydrodynamic model and a passive particle-tracking model. With the flow field driven by alternate inflows predicted by a shallow water model, particle trajectories are traced out using a particle tracking model. The horizontal fluid mixing dynamics are then interpreted using dynamics system analysis approaches including finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS). From the simulation results, it is confirmed that periodic inflows are able to create a weak dynamic system in an idealised circular lake, with the particle dynamics controlled by a single dimensionless parameter associated with the inflow duration. The mixing and transport property of the lake changes from regular to chaotic as the value of the dimensionless parameter increases until global chaotic particle dynamics is achieved. By further analysing the advection of particles injected continuously to the inflows (freshwater), the fate of “freshwater” particles in a “polluted” lake is tracked and revealed. The results provide useful guidance for engineering applications, i.e., transferring freshwater from rivers to improve the water quality in polluted water bodies such as lakes. The presented approach will be able to facilitate the design of ‘optimised’ schemes for such engineering implementation.

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References

  1. Liu X. B., Peng W. Q., He G. J. et al. A coupled model of hydrodynamics and water quality for Yuqiao reservoir in Haihe river basin [J]. Journal of Hydrodynamics, 2008, 20(5): 574–582.

    Article  Google Scholar 

  2. Liang D., Wu X. A random walk simulation of scalar mixing in flows through submerged vegetations [J]. Journal of Hydrodynamics, 2014, 26(3): 343–350.

    Article  MathSciNet  Google Scholar 

  3. Zhang C., Gao X., Wang L. et al. Analysis of agricultural pollution by flood flow impact on water quality in a reservoir using a three-dimensional water quality model [J]. Journal of Hydroinformatics, 2013, 15(4): 1061–1072.

    Article  Google Scholar 

  4. Kranenburg C. Wind-driven chaotic advection in a shallow model lake [J]. Journal of Hydraulic Research, 1992, 30(1): 29–46.

    Article  Google Scholar 

  5. Liang Q., Borthwick A. G. L., Taylor P. H. Wind-induced chaotic advection in shallow flow geometries. Part I: Circular basins [J]. Journal of Hydraulic Research, 2006, 44(2): 170–179.

    Article  Google Scholar 

  6. Liang Q., Borthwick A. G. L., Taylor P. H. Wind-induced chaotic advection in shallow flow geometries. Part II: Non-circular basins [J]. Journal of Hydraulic Research, 2006, 44(2): 180–188.

    Article  Google Scholar 

  7. Károlyi G., Pattantyús-Ábrahám M., Krámer T. et al. Finite-size Lyapunov exponents: A new tool for lake dynamics [J]. ICE-Engineering and Computational Mechanics, 2010, 163(4): 251–259.

    Google Scholar 

  8. Lee W. K., Borthwick A. G. L., Taylor P. H. Wind-induced chaotic mixing in a two-layer density-stratified shallow flow [J]. Journal of Hydraulic Research, 2014, 52(2): 219–227.

    Article  Google Scholar 

  9. García-Garrido V. J., Ramos A., Mancho A. M. et al. A dynamical systems perspective for a real-time response to a marine oil spill [J]. Marine pollution bulletin, 2016, 112(1–2): 201–210.

    Article  Google Scholar 

  10. Liao S. J. On the clean numerical simulation (CNS) of chaotic dynamic systems [J]. Journal of Hydrodynamics, 2017, 29(5): 729–747.

    Article  Google Scholar 

  11. Aref H. Stirring by chaotic advection [J]. Journal of Fluid Mechanics, 1984, 143: 1–21.

    Article  MathSciNet  Google Scholar 

  12. Benson D. A., Pankavich S., Bolster D. On the separate treatment of mixing and spreading by the reactive-particle-tracking algorithm: An example of accurate upscaling of reactive Poiseuille flow [J]. Advances in Water Resources, 2019, 123: 40–53.

    Article  Google Scholar 

  13. Xie T., Xu C. Numerical and experimental investigations of chaotic mixing behavior in an oscillating feedback micromixer [J]. Chemical Engineering Science, 2017, 171: 303–317.

    Article  Google Scholar 

  14. Aref H. The development of chaotic advection [J]. Physics of Fluids, 2002, 14(4): 1315–1325.

    Article  MathSciNet  Google Scholar 

  15. Koshel K. V., Prants S. V. Chaotic advection in the ocean [J]. Physics-Uspekhi, 2006, 49(11): 1151–1178.

    Article  Google Scholar 

  16. Liang Q., Borthwick A. G. L. Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography [J]. Computers and Fluids, 2009, 38(2): 221–234.

    Article  MathSciNet  Google Scholar 

  17. Smith S. D. Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature [J]. Journal of Geophysical Research: Oceans, 1988, 93(C12): 15467–15472.

    Article  Google Scholar 

  18. Xia X., Liang Q. A new efficient implicit scheme for discretising the stiff friction terms in the shallow water equations [J]. Advances in Water Resources, 2018, 117: 87–97.

    Article  Google Scholar 

  19. Shadden S. C., Lekien F., Marsden J. E. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows [J]. Physica D: Nonlinear Phenomena, 2005, 212(3): 271–304.

    Article  MathSciNet  Google Scholar 

  20. Haller G., Yuan G. Lagrangian coherent structures and mixing in two-dimensional turbulence [J]. Physica D: Nonlinear Phenomena, 2000, 147(3): 352–370.

    Article  MathSciNet  Google Scholar 

  21. Mancho A. M., Small D., Wiggins S. A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues [J]. Physics Reports, 2006, 437(3): 55–124.

    Article  Google Scholar 

  22. Shadden S. C., Lekien F., Paduan J. D. et al. The correlation between surface drifters and coherent structures based on high-frequency radar data in Monterey Bay [J]. Deep Sea Research Part II: Topical Studies in Oceanography, 2009, 56(3–5): 161–172.

    Article  Google Scholar 

  23. Wiggins S. Normally hyperbolic invariant manifolds in dynamical systems [M]. Now York, USA: Springer Science and Business Media, 1994.

    Book  Google Scholar 

  24. Haller G. A variational theory of hyperbolic Lagrangian coherent structures [J]. Physica D: Nonlinear Phenomena, 2011, 240(7): 574–598.

    Article  MathSciNet  Google Scholar 

  25. Liang Q., Borthwick A. G. L., Taylor P. H. Chaotic mixing in a basin due to a sinusoidal wind field [J]. International Journal for Numerical Methods in Fluids, 2005, 47(8): 871–877.

    Article  Google Scholar 

  26. Guo H., He W., Peterka T. et al. Finite-time Lyapunov exponents and Lagrangian coherent structures in uncertain unsteady flows [J]. IEEE Transactions on Visualization and Computer Graphics, 2016, 22(6): 1672–1682.

    Article  Google Scholar 

  27. Sieber M., Ostermann F., Woszidlo R. et al. Lagrangian coherent structures in the flow field of a fluidic oscillator [J]. Physical Review Fluids, 2016, 1(5): 050509.

    Article  Google Scholar 

  28. Cimatoribus A. A., Lemmin U., Barry D. A. Tracking Lagrangian transport in Lake Geneva: A 3D numerical modeling investigation [J]. Limnology and Oceanography, 2019, 64(3): 1252–1269.

    Article  Google Scholar 

  29. Li Y., Tang C., Wang C. et al. Improved Yangtze River diversions: are they helping to solve algal bloom problems in Lake Taihu, China? [J]. Ecological Engineering, 2013, 51: 104–116.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Water Conservancy and Hydropower, Hebei University of Engineering, Handan, 056021, China

    Cheng-hua Dang & Qiuhua Liang

  2. Jeremy Benn Associates Limited, Coleshill, Warwickshire, UK

    Jingchun Wang

  3. School of Architecture, Building and Civil Engineering, Loughborough University, Loughborough, UK

    Qiuhua Liang

Authors
  1. Cheng-hua Dang
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  2. Jingchun Wang
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  3. Qiuhua Liang
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Corresponding author

Correspondence to Qiuhua Liang.

Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 11371117).

Biography: Cheng-hua Dang (1967–), Female, Master, Senior Engineer

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Dang, Ch., Wang, J. & Liang, Q. Inflows/outflows driven particle dynamics in an idealised lake. J Hydrodyn 31, 873–886 (2019). https://doi.org/10.1007/s42241-019-0070-9

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  • DOI: https://doi.org/10.1007/s42241-019-0070-9

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