Abstract
A model is presented of particle advection near groynes in an open channel. Open channel hydrodynamics is modelled using the shallow water equations, obtained as the depth-averaged form of Reynolds-averaged continuity and Navier-Stokes momentum equations. A Lagrangian particle-tracking model is used to predict trajectories of tracer particles advected by the flow field, with bilinear interpolation representing the continuous flow field. The particle-tracking model is verified for chaotic advection in an alternating flow field of a pair of blinking vortices. The combined shallow flow and Lagrangian particle-tracking model is applied to the simulation of tracer advection in flow past a pair of side-wall cavities separated by a groyne, and in an open rectangular channel containing a pair of parallel groynes oriented normal to the channel wall. The study is potentially useful in understanding mixing processes in shallow flow fields near hydraulic structures in wide rivers.
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References
Rutherford J. C. Handbook on mixing in rivers [M]. Wellington, New Zealand: Water and Soil Miscellaneous Publication, 1981, 60.
Aref H. Stirring by chaotic advection [J]. Journal of Fluid Mechanics, 1984, 143: 1–21.
Kranenburg C. Wind-driven chaotic advection in a shallow model lake [J]. Journal of Hydraulic Research, 1992, 30 (1): 29–46.
Pearson R. V., Barber R. W. Modelling depth-integrated coastal pollution using a Lagrangian particle technique [J]. Transactions on Ecology and the Environment, 1998, 17: 233–240.
Weitbrecht V., Uijttewaal W. S. J., Jirka G. H. 2-D Particle tracking to determine transport characteristics in rivers with dead zones [C]. The 4th International Symposium on Shallow Flows, Delft, The Netherlands, 2003, 1–8.
Zsugyel M., Tél T., Józsa J. Numerical investigation of chaotic advection past a groyne based on laboratory flow experiment [J]. Advances in Water Resources, 2014, 71: 81–92.
Jalali M. M. Curvilinear shallow flow and particle tracking model for a groyned river bend [D]. Doctoral Thesis, Edinburgh, UK: The University of the Edinburgh, 2016, 1–184.
Falconer R. A. (Abbott M. B., Price W. A. Coastal, estuarial and harbour engineer’s reference book). An introduction to nearly-horizontal flows [M]. London, UK: Chapman and Hall, 1993, 27–36.
Abbott M. B. Computational hydraulics: Elements of the theory of free surface flows [M]. London, UK: Pitman Advanced Publishing Program, 1979, 324.
Fletcher C. Computational techniques for fluid dynamics 1, Fundamental and general techniques [M]. 2nd Edition, Berlin Heidelberg, Germany: Springer-Verlag 1998, 401.
Abbott M. B., Basco D. R. Computational fluid dynamics-an introduction for engineers [M]. Harlow, UK: Longman Scientific and Technical/New York, USA: John Wiley and Sons, 1989, 439.
Khakhar D. V., Ottino J. M. Fluid mixing (stretching) by time periodic sequences for weak flows [J]. Physics of Fluids, 1986, 29 (11): 3503–3505.
Khakhar D. V., Rising H., Ottino J. M. Analysis of chaotic mixing in two model systems [J]. Journal of Fluid Mechanics, 1986, 172: 419–451.
Tuna B. A., Rockwell D. Self-sustained oscillations of shallow flow past sequential cavities [J]. Journal of Fluid Mechanics, 2014, 758: 655–685.
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The first author is grateful to the University of Edinburgh which partly funded this research.
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Jalali, M.M., Borthwick, A.G.L. Tracer advection in a pair of adjacent side-wall cavities, and in a rectangular channel containing two groynes in series. J Hydrodyn 30, 564–572 (2018). https://doi.org/10.1007/s42241-018-0064-z
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DOI: https://doi.org/10.1007/s42241-018-0064-z