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Formation of sediment patterns in channel flow: minimal unstable systems and their temporal evolution

Published online by Cambridge University Press:  06 April 2017

Aman G. Kidanemariam Open the ORCID record for Aman G. Kidanemariam [Opens in a new window]  and
Markus Uhlmann Open the ORCID record for Markus Uhlmann [Opens in a new window]
Aman G. Kidanemariam*
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
Markus Uhlmann
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
*
†Email address for correspondence: aman.kidanemariam@kit.edu
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Abstract

The phenomenon of sediment pattern formation in a channel flow is numerically investigated by performing simulations which resolve all the relevant length and time scales of the problem. The numerical approach employed and the flow configuration considered is identical to our previous study (Kidanemariam & Uhlmann J. Fluid Mech., vol. 750, 2014, R2), the only difference being the length of the computational domain. The latter was systematically varied in order to investigate its influence on the initiation and evolution aspects. By successively reducing the streamwise length, the minimum box dimension which accommodates an unstable sediment bed is revealed, thus determining the lower threshold of the unstable modes. For the considered parameter point, the cutoff length for pattern formation lies in the range 75–100 times the particle diameter (3–4 times the clear fluid height). We also simulate the flow in a very long streamwise box with a size of 48 times the clear fluid height (featuring well over one million particles), accommodating approximately 11 initial ripple units with a wavelength in the range of 100–110 particle diameters. The evolution of the amplitude of the patterns exhibits two regimes of growth: an initial exponential regime, with a growth rate independent of the chosen domain size, and a subsequent nonlinear regime which is strongly constrained by the domain length. In the small domain cases, after the initial exponential regime, the ripples evolve steadily, maintaining their shape and migration velocity, at a mean wavelength equal to the length of the domain. The asymmetric ripple shape is characterized by a spectrum which exhibits a power-law decay over the first few dominant non-dispersive modes propagating at the mean dune migration velocity. The rate of particle transport and the mean interface shear stress exhibited an increase with increasing ripple dimensions. Nevertheless, the relationship between the two was observed to be approximately described by the empirical power-law formula for sediment transport by Wong & Parker (J. Hydraul. Engng, vol. 132, 2006, pp. 1159–1168).

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Geophysical and Geological Flows: Sediment transport Turbulent Flows: Turbulent Flows
Type
Papers
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Journal of Fluid Mechanics , Volume 818 , 10 May 2017 , pp. 716 - 743
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© 2017 Cambridge University Press 

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References

Andreotti, B. & Claudin, P. 2013 Aeolian and subaqueous bedforms in shear flows. Phil. Trans. A Math. Phys. Engng Sci. 371 (2004), 20120364.Google Scholar
Andreotti, B., Claudin, P., Devauchelle, O., Durán, O. & Fourrière, A. 2011 Bedforms in a turbulent stream: ripples, chevrons and antidunes. J. Fluid Mech. 690, 94–128.CrossRefGoogle Scholar
Bagnold, R. A. 1941 The Physics of Blown Sand and Desert Dunes. Chapman and Hall.Google Scholar
Best, J. 2005 The fluid dynamics of river dunes: a review and some future research directions. J. Geophys. Res. 110 (F4), F04S02.CrossRefGoogle Scholar
Betat, A., Kruelle, C. A., Frette, V. & Rehberg, I. 2002 Long-time behavior of sand ripples induced by water shear flow. Eur. Phys. J. E. 8 (5), 465–476.CrossRefGoogle ScholarPubMed
Blondeaux, P. 1990 Sand ripples under sea waves part 1. Ripple formation. J. Fluid Mech. 218, 1–17.CrossRefGoogle Scholar
Blondeaux, P., Foti, E. & Vittori, G. 2015 A theoretical model of asymmetric wave ripples. Phil. Trans. R. Soc. Lond. A 373, 20140112.Google Scholar
Bridge, J. S. & Best, J. L. 1988 Flow, sediment transport and bedform dynamics over the transition from dunes to upper-stage plane beds: implications for the formation of planar laminae. Sedimentology 35, 753–763.Google Scholar
Cardona Florez, J. E. & Franklin, E. M. 2016 The formation and migration of sand ripples in closed conduits: experiments with turbulent water flows. Exp. Therm. Fluid Sci. 71, 95–102.Google Scholar
Chan-Braun, C., García-Villalba, M. & Uhlmann, M. 2011 Force and torque acting on particles in a transitionally rough open-channel flow. J. Fluid Mech. 684, 441–474.CrossRefGoogle Scholar
Charru, F. 2006 Selection of the ripple length on a granular bed sheared by a liquid flow. Phys. Fluids 18 (12), 121508.Google Scholar
Charru, F., Andreotti, B. & Claudin, P. 2013 Sand ripples and dunes. Annu. Rev. Fluid Mech. 45 (1), 469–493.Google Scholar
Chou, Y. & Fringer, O. B. 2010 A model for the simulation of coupled flow-bed form evolution in turbulent flows. J. Geophys. Res. 115 (C10), C10041.CrossRefGoogle Scholar
Claudin, P. & Andreotti, B. 2006 A scaling law for aeolian dunes on Mars, Venus, Earth, and for subaqueous ripples. Earth Planet. Sci. Lett. 252 (1–2), 30–44.CrossRefGoogle Scholar
Coleman, S. E., Fedele, J. J. & Garca, M. H. 2003 Closed-conduit bed-form initiation and development. J. Hydraul. Engng 129 (12), 956–965.Google Scholar
Coleman, S. E. & Melville, B. W. 1994 Bed-form development. J. Hydraul. Engng 120 (5), 544–560.Google Scholar
Coleman, S. E. & Nikora, V. I. 2009a Bed and flow dynamics leading to sediment-wave initiation. Water Resour. Res. 45 (4), W04402.CrossRefGoogle Scholar
Coleman, S. E. & Nikora, V. I. 2009b Exner equation: a continuum approximation of a discrete granular system. Water Resour. Res. 45 (9), 1–8.Google Scholar
Coleman, S. E. & Nikora, V. I. 2011 Fluvial dunes: initiation, characterization, flow structure. Earth Surf. Process. Landf. 36 (1), 39–57.CrossRefGoogle Scholar
Colombini, M. 2014 A decade’s investigation of the stability of erodible stream beds. J. Fluid Mech. 756, 1–4.Google Scholar
Colombini, M. & Stocchino, A. 2008 Finite-amplitude river dunes. J. Fluid Mech. 611, 283–306.Google Scholar
Derksen, J. J. 2015 Simulations of granular bed erosion due to a mildly turbulent shear flow. J. Hydraul. Res. 53 (5), 622–632.Google Scholar
Durań, O., Andreotti, B. & Claudin, P. 2012 Numerical simulation of turbulent sediment transport, from bed load to saltation. Phys. Fluids 24 (10), 103306.CrossRefGoogle Scholar
Duran, O., Claudin, P. & Andreotti, B. 2014 Direct numerical simulations of aeolian sand ripples. Proc. Natl Acad. Sci. USA 111 (44), 15665–15668.CrossRefGoogle ScholarPubMed
Engelund, F. & Fredsoe, J. 1982 Sediment ripples and dunes. Annu. Rev. Fluid Mech. 14 (1), 13–37.CrossRefGoogle Scholar
Fourrière, A., Claudin, P. & Andreotti, B. 2010 Bedforms in a turbulent stream: formation of ripples by primary linear instability and of dunes by nonlinear pattern coarsening. J. Fluid Mech. 649, 287–328.Google Scholar
Franklin, E. M. & Charru, F. 2011 Subaqueous barchan dunes in turbulent shear flow. Part 1. Dune motion. J. Fluid Mech. 675 (1988), 199–222.Google Scholar
Gaeuman, D. & Jacobson, R. B. 2007 Field assessment of alternative bed-load transport estimators. J. Hydraul. Engng 133 (12), 1319–1328.CrossRefGoogle Scholar
García, M. H.(Ed.) 2008 Sedimentation Engineering. Processes, Measurments, Modeling and Practice. American Society of Civil Engineers.Google Scholar
Hersen, P., Douady, S. & Andreotti, B. 2002 Relevant length scale of barchan dunes. Phys. Rev. Lett. 89 (26), 264301.Google Scholar
Hino, M. 1968 Equilibrium-range spectra of sand waves formed by flowing water. J. Fluid Mech. 34 (03), 565–573.Google Scholar
Jain, S. C. & Kennedy, J. F. 1974 The spectral evolution of sedimentary bed forms. J. Fluid Mech. 63 (02), 301.Google Scholar
Jenny, M., Dušek, J. & Bouchet, G. 2004 Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid. J. Fluid Mech. 508, 201–239.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Julien, P. Y. 1998 Erosion and Sedimentation. Cambridge University Press.Google Scholar
Khosronejad, A. & Sotiropoulos, F. 2014 Numerical simulation of sand waves in a turbulent open channel flow. J. Fluid Mech. 753, 150–216.Google Scholar
Kidanemariam, A. G.2015 The formation of patterns in subaqueous sediment. PhD thesis, Karlsruhe Institute of Technology.Google Scholar
Kidanemariam, A. G., Chan-Braun, C., Doychev, T. & Uhlmann, M. 2013 Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys. 15 (2), 025031.Google Scholar
Kidanemariam, A. G. & Uhlmann, M. 2014a Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2.CrossRefGoogle Scholar
Kidanemariam, A. G. & Uhlmann, M. 2014b Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar channel flow. Intl J. Multiphase Flow 1–27.Google Scholar
Langlois, V. & Valance, A. 2007 Initiation and evolution of current ripples on a flat sand bed under turbulent water flow. Eur. Phys. J. E. 22 (3), 201–208.Google Scholar
Maurin, R., Chauchat, J., Chareyre, B. & Frey, P. 2015 A minimal coupled fluid-discrete element model for bedload transport. Phys. Fluids 27 (11), 113302.Google Scholar
Meyer-Peter, E. & Müller, R. 1948 Formulas for bed-load transport. In Proceedings of 2nd Meeting, Stockholm, Sweden, pp. 39–64. IAHR.Google Scholar
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. & Walters, R. 2007 Double-averaging concept for rough-bed open-channel and overland flows: theoretical background. J. Hydraul. Engng 133 (8), 873–883.Google Scholar
Nikora, V. I., Sukhodolov, A. N. & Rowinski, P. M. 1997 Statistical sand wave dynamics in one-directional water flows. J. Fluid Mech. 351, 17–19.CrossRefGoogle Scholar
Ouriemi, M., Aussillous, P. & Guazzelli, É. 2009 Sediment dynamics. Part 2. Dune formation in pipe flow. J. Fluid Mech. 636, 295–319.Google Scholar
Raudkivi, A. J. 1997 Ripples on stream bed. J. Hydraul. Engng 123 (1), 58–64.Google Scholar
Sauermann, G., Kroy, K. & Herrmann, H. 2001 Continuum saltation model for sand dunes. Phys. Rev. E 64 (3), 031305.Google Scholar
Schmeeckle, M. W. 2014 Numerical simulation of turbulence and sediment transport of medium sand. J. Geophys. Res. Earth Surf. 119 (6), 1240–1262.Google Scholar
Seminara, G. 2010 Fluvial sedimentary patterns. Annu. Rev. Fluid Mech. 42 (1), 43–66.Google Scholar
Sleath, J. F. A. 1976 On rolling-grain ripples. J. Hydraul. Res. 14 (1), 69–81.Google Scholar
Soulsby, R. L. & Whitehouse, R. J. S. 1997 Threshold of sediment motion in coastal environments. In Proceedings of the 13th Australasian Coastal and Ocean Engineering Conference, pp. 149–154. Centre for Advanced Engineering, University of Canterbury.Google Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209 (2), 448–476.Google Scholar
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20 (5), 053305.CrossRefGoogle Scholar
Vittori, G. & Blondeaux, P. 1990 Sand ripples under sea waves part 2. Finite-amplitude development. J. Fluid Mech. 218, 19–39.Google Scholar
Vowinckel, B., Kempe, T. & Fröhlich, J. 2014 Fluid-particle interaction in turbulent open channel flow with fully-resolved mobile beds. Adv. Water Resour. 72, 32–44.Google Scholar
Wong, M. & Parker, G. 2006 Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database. J. Hydraul. Engng 132, 1159–1168.Google Scholar
Yalin, M. S. 1977 Mechanics of Sediment Transport, 2nd edn. Pergamon.Google Scholar