2D numerical contributions for the study of non-cohesive sediment transport beneath tidal bores

Yoga Satria Putra; Anthony Beaudoin; Germain Rousseaux; Lionel Thomas; Serge Huberson

doi:10.1016/j.crme.2018.11.004

2D numerical contributions for the study of non-cohesive sediment transport beneath tidal bores

Yoga Satria Putra ¹; Anthony Beaudoin ¹ ; Germain Rousseaux ¹; Lionel Thomas ¹; Serge Huberson ¹

¹ Department of Fluids, Thermal and Combustion Sciences, Pprime Institute, UPR 3346, CNRS, University of Poitiers, ISAE ENSMA, TSA 51124, 86073 Poitiers cedex 9, France

Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 166-180.

Abstract

2D numerical simulations of tidal bores were obtained using the OpenFOAM CFD software to solve the Navier–Stokes equations by means of the Finite Volume Method by applying a LES turbulence model. The trajectories of non-cohesive sediment particles beneath tidal bores were estimated using a tracker method. Using the fourth order Runge–Kutta scheme, the tracker method solves the Maxey and Riley equations, which requires the knowledge of the velocity field at time t. From 2D numerical simulations of tidal bores, we proposed a classification of tidal bores with respect to the Froude number Fr (or r the ratio of water depths). For a Froude number $1 < F r < 1.43$ ( $1 < r < 1.57$ ), the tidal bore is undular. For a Froude number $1.43 < F r < 1.57$ ( $1.57 < r < 1.75$ ), the tidal bore is partially breaking, which is similar to the transitional tidal bore defined by Furgerot (2014). And for a Froude number $F r > 1.57$ ( $r > 1.75$ ), the tidal bore is totally breaking. The numerical results of trajectories of non-cohesive sediment particles are similar to the type of trajectories given by the analytical model proposed by Chen et al. (2012) with some modifications to take into account the effects of gravity, elevation, and attenuation. The parameters of modified Chen's model, $β_{1}$ , $β_{2}$ and $β_{3}$ , are linearly proportional to the Froude number Fr. This is because the level of turbulence for undular tidal bores is low. The flow induced by an undular tidal bore is not complex. This physical phenomenon is quasi linear. The parameter $β_{1}$ , related to the front celerity of the undular tidal bore, decreases when the Froude number Fr increases. The parameter $β_{2}$ , related to the elevation, increases when the Froude number Fr increases. And the parameter $β_{3}$ , related to the attenuation of the secondary waves, increases when the Froude number Fr increases.

Received: 2018-07-28
Accepted: 2018-11-15
Published online: 2019-01-10

DOI: 10.1016/j.crme.2018.11.004

Keywords: Sediment transport, Maxey–Riley equations, Tracker method, Tidal bore, Froude number, Ratio of water depths, OpenFoam

Author's affiliations:

Yoga Satria Putra ¹; Anthony Beaudoin ¹; Germain Rousseaux ¹; Lionel Thomas ¹; Serge Huberson ¹

¹ Department of Fluids, Thermal and Combustion Sciences, Pprime Institute, UPR 3346, CNRS, University of Poitiers, ISAE ENSMA, TSA 51124, 86073 Poitiers cedex 9, France

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     author = {Yoga Satria Putra and Anthony Beaudoin and Germain Rousseaux and Lionel Thomas and Serge Huberson},
     title = {2D numerical contributions for the study of non-cohesive sediment transport beneath tidal bores},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {166--180},
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Yoga Satria Putra; Anthony Beaudoin; Germain Rousseaux; Lionel Thomas; Serge Huberson. 2D numerical contributions for the study of non-cohesive sediment transport beneath tidal bores. Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 166-180. doi : 10.1016/j.crme.2018.11.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.11.004/

References
Cited by

[1] C. Donnelly; H. Chanson Environmental impact of undular tidal bores in tropical rivers, Environ. Fluid Mech., Volume 5 (2005), pp. 481-494

[2] H. Chanson Tidal Bores, Aegir, Eagre, Mascaret, Pororoca: Theory and Observations, World Scientific, Singapore, 2011

[3] L. Furgerot; D. Mouaze; B. Tessier; L. Perez; S. Haquin Sediment transport induced by tidal bores. An estimation from suspended matter measurements in the Sée River (Mont Saint-Michel Bay, northwestern France), C. R. Geoscience, Volume 348 (2016), pp. 432-441

[4] P. Bonneton; A.G. Filippini; L. Arpaia; N. Bonneton; M. Ricchiuto Conditions for tidal bore formation in convergent alluvial estuaries, Estuar. Coast. Shelf Sci., Volume 172 (2016), pp. 121-127

[5] R. Lemoine Sur les ondes positives de translation dans les canaux et sur le ressaut ondulé de faible amplitude, Houille Blanche (1948), pp. 183-185

[6] V. Andersen Undular hydraulic jump, J. Hydraul. Div., Volume 104 (1978), pp. 1185-1188

[7] M. Berry Minimal analytical model for undular tidal bore profile; quantum and hawking effect analogies, New J. Phys., Volume 20 (2018)

[8] H. Favre Etude Théorique et Expérimentale des Ondes de Translation dans les Canaux Découverts, Dunod, Paris, 1935 (Publications du Laboratoire de recherches hydrauliques, annexé a l'École polytechnique fédérale de Zurich)

[9] A. Treske Undular bores (favre-waves) in open channels – experimental studies, J. Hydraul. Res., Volume 32 (1994), pp. 355-370

[10] H. Hornung; C. Willert; S. Turner The flow field downstream of a hydraulic jump, J. Fluid Mech., Volume 287 (1995), pp. 299-316

[11] C. Koch; H. Chanson Turbulent mixing beneath an undular bore front, J. Coast. Res., Volume 24 (2008), pp. 999-1007

[12] G. Rousseaux; J. Mougenot; L. Chatellier; L. David; D. Calluaud A novel method to generate tidal-like bores in the laboratory, Eur. J. Mech. B, Fluids, Volume 55 (2016), pp. 31-38

[13] N. Khezri Modelling Turbulent Mixing and Sediment Process Beneath Tidal Bores: Physical and Numerical Investigations, School of Civil Engineering, University of Queensland, 2013 (Ph.D. thesis)

[14] B. Simon Effects of Tidal Bores on Turbulent Mixing: a Numerical and Physical Study in Positive Surges, Université de Bordeaux and University of Queensland, 2013 (Ph.D. thesis)

[15] A. Berchet; B. Simon; A. Beaudoin; P. Lubin; G. Rousseaux; S. Huberson Flow fields and particle trajectories beneath a tidal bore: a numerical study, Int. J. Sediment Res., Volume 33 (2018) no. 3, pp. 351-370

[16] http://www.indonesia-tourism.com (lenstraffic, Bono Tidal Bore Surfing in Sumatera, Accessed 2017-10-4)

[17] L. Furgerot Propriétés hydrodynamiques du mascaret et de son influence sur la dynamique sé dimentaire. une approche couplée en canal et in situ (estuaire de la sée, baie du mont saint-michel), University of Caen, France, 2014 (Ph.D. thesis)

[18] S. Bartsch-Winkler; D.K. Lynch Catalog of Worldwide Tidal Bore Occurrences and Characteristics, USGS, 1988 (Tech. Rep. Numbered Series Ci No. 1022)

[19] Y.-Y. Chen; H.-C. Hsu; H.-H. Wung Particle trajectories beneath wave-current interaction in a two-dimensional field, Nonlinear Process. Geophys., Volume 19 (2012), pp. 185-197

[20] A. Berchet Modélisation par des méthodes lagrangiennes du transport sédimentaire induit par les mascarets, SIMMEA, Université de Poitiers, France, 2014 (Ph.D. thesis)

[21] Team, The Open Source CFD Toolbox: Programmer's Guide, v1706, 28th June 2017 Edition, OpenCFD Limited, 2017.

[22] M. Maxey; J. Riley Equation of motion for a small rigid sphere in a nonuniform flow, Phys. Fluids, Volume 26 (1983), pp. 883-889

[23] https://www.openfoam.com/ (About OpenFOAM, Accessed 2018-2-13)

[24] H. Weller Derivation Modelling and Solution of the Conditionally Averaged Two-Phase Flow Equations, Nabla Ltd, 2002 (Technical Report tr/hgw/02 Edition)

[25] C. Hirt; B. Nichols Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., Volume 39 (1981), pp. 201-225

[26] S. Popinet Numerical models of surface tension, Annu. Rev. Fluid Mech., Volume 50 (2018), pp. 49-75

[27] D. Cassidy; J. Edwards; M. Tian An investigation of interface-sharpening schemes for multi-phase mixture flows, J. Comput. Phys., Volume 228 (2009), pp. 5629-5649

[28] Y. Tsui; S. Lin; T. Cheng; T. Wu Flux-blending schemes for interface capture in two-fluid flows, Int. J. Heat Mass Transf., Volume 52 (2009), pp. 5547-5556

[29] M. Raessi; J. Mostaghimi; M. Bussmann A volume-of-fluid interfacial flow solver with advected normals, Comput. Fluids, Volume 39 (2010), pp. 1401-1410

[30] J. Heyns; O. Oxtoby Modelling surface tension dominated multiphase flows using the VOF approach, 6th European Conference on Computational Fluid Dynamics, 2014

[31] M. Sussman; E. Puckett A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comput. Phys., Volume 162 (2000), pp. 301-337

[32] H. Versteeg; W. Malalasekera An Introduction to Computational Fluid Dynamics: the Finite Volume Method, Pearson Education Ltd, 2007

[33] S.-I. Furuyama; H. Chanson (Hydraul. Model Ser.), Volume vol. CH66/08, School of Civil Engineering, The University of Queensland, Australia (2008), p. 88

[34] S.-I. Furuyama; H. Chanson A numerical study of a tidal bore flow, Coast. Eng. J., Volume 52 (2010) no. 3, pp. 215-234

[35] P. Lubin; S. Glockner; H. Chanson Numerical simulation of a weak breaking tidal bore, Mech. Res. Commun., Volume 37 (2010), pp. 119-121

[36] P. Lubin; H. Chanson; S. Glockner Large eddy simulation of turbulence generated by a weak breaking tidal bore, Environ. Fluid Mech., Volume 10 (2010), pp. 587-602

[37] X. Leng; B. Simon; N. Khezri; P. Lubin; H. Chanson CFD modeling of tidal bores: development and validation challenges, Coast. Eng. J. (2018), pp. 1-14

[38] Y. Gong; F. Tanner Comparison of RANS and LES models in the laminar limit for a flow over a backward-facing step using OpenFOAM, Detroit, Michigan (2009)

[39] H. Chanson The Hydraulics of Open Channel Flow: an Introduction, Elsevier Butterworth–Heinemann, 2004

[40] X. Xu; X. Deng An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids, Comput. Phys. Commun., Volume 201 (2016), pp. 43-62

[41] H. Chanson; J. Montes Characteristics of undular hydraulic jumps: experimental apparatus and flow patterns, J. Hydraul. Eng., Volume 121 (1995), pp. 129-144

[42] F. Benet; J.A. Cunge Analysis of experiments on secondary undulations caused by surge waves in trapezoidal channels, J. Hydraul. Res., Volume 9 (1971) no. 1, pp. 11-33

[43] C. Koch; H. Chanson An Experimental Study of Tidal Bores and Positive Surges: Hydrodynamics and Turbulence of the Bore Front, Department of Civil Engineering, University of Queensland, Australia, 2005 (Tech. Rep.)

[44] H. Chanson Flow field in a tidal bore: a physical model, Proc. 29th IAHR Congress, Beijing, Theme E, Tsinghua University, 2001, pp. 365-373

[45] M. Tissier étude numérique de la transformation des vagues en zone littorale, de la zone de levée aux zones de surf et de jet de river, University of Bordeaux, France, 2011 (Ph.D. thesis)

[46] C. Koch; H. Chanson Turbulence measurements in positive surges and bores, J. Hydraul. Res., Volume 47 (2009), pp. 29-40

[47] H. Chanson Tidal Bores, Aegir and Pororoca: the Geophysical Wonders, IAHR-APD, Auckland, New Zealand, 2010 (Tech. Rep., Congress of IAHR Asia and Pacific Division)

[48] N. Docherty; H. Chanson Physical modeling of unsteady turbulence in breaking tidal bores, J. Hydraul. Eng., Volume 138 (2012), pp. 412-419

[49] J. Simpson; N. Fisher; P. Wiles Reynolds stress and TKE production in an estuary with a tidal bore, Estuar. Coast. Shelf Sci., Volume 60 (2004), pp. 619-627

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