Skip to main content Accessibility help

Numerical simulation of sand waves in a turbulent open channel flow

  • Ali Khosronejad (a1) and Fotis Sotiropoulos (a1)


We develop a coupled hydro-morphodynamic numerical model for carrying out large-eddy simulation of stratified, turbulent flow over a mobile sand bed. The method is based on the curvilinear immersed boundary approach of Khosronejad et al. (Adv. Water Resour., vol. 34, 2011, pp. 829–843). We apply this method to simulate sand wave initiation, growth and evolution in a mobile bed laboratory open channel, which was studied experimentally by Venditti & Church (J. Geophys. Res., vol. 110, 2005, F01009). We show that all the major characteristics of the computed sand waves, from the early cross-hatch and chevron patterns to fully grown three-dimensional bedforms, are in good agreement with the experimental data both qualitatively and quantitatively. Our simulations capture the measured temporal evolution of sand wave amplitude, wavelength and celerity with good accuracy and also yield three-dimensional topologies that are strikingly similar to what was observed in the laboratory. We show that near-bed sweeps are responsible for initiating the instability of the initially flat sand bed. Stratification effects, which arise due to increased concentration of suspended sediment in the flow, also become important at later stages of the bed evolution and need to be taken into account for accurate simulations. As bedforms grow in amplitude and wavelength, they give rise to energetic coherent structures in the form of horseshoe vortices, which transport low-momentum near-bed fluid and suspended sediment away from the bed, giving rise to characteristic ‘boil’ events at the water surface. Flow separation off the bedform crestlines is shown to trap sediment in the lee side of the crestlines, which, coupled with sediment erosion from the accelerating flow over the stoss side, provides the mechanism for continuous bedform migration and crestline rearrangement. The statistical and spectral properties of the computed sand waves are calculated and shown to be similar to what has been observed in nature and previous numerical simulations. Furthermore, and in agreement with recent experimental findings (Singh et al., Water Resour. Res., vol. 46, 2010, pp. 1–10), the spectra of the resolved velocity fluctuations above the bed exhibit a distinct spectral gap whose width increases with distance from the bed. The spectral gap delineates the spectrum of turbulence from the low-frequency range associated with very slowly evolving, albeit energetic, coherent structures induced by the migrating sand waves. Overall the numerical simulations reproduce the laboratory observations with good accuracy and elucidate the physical phenomena governing the interaction between the turbulent flow and the developing mobile bed.


Corresponding author

Email address for correspondence:


Hide All
Allen, J. R. L. 1968 Current Ripples: Their Relation to Patterns of Water and Sediment Motion. p. 433. North-Holland.
Allen, J. R. L. 1971 Bed forms due to mass transfer in turbulent flows: a kaleidoscope of phenomena. J. Fluid Mech. 49, 4963.
Andreotti, B., Claudin, P., Devauchelle, O., Durán, O. & Fourrière, A. 2011 Bedforms in a turbulent stream: ripples, chevrons and antidunes. J. Fluid Mech. 690, 94128.
Andreotti, B., Claudin, P. & Douady, S. 2002 Selection of dune shapes and velocities, Part 1: Dynamics of sand, wind and barchans. Eur. Phys. J. B 28, 321329.
Angelis, V. D., Lombardi, P. & Banerjee, S. 1997 Direct numerical simulation of turbulent flow over a wavy wall. Phys. Fluids 9, 24292442.
Ashley, G. M. 1990 Classification of large-scale subaqueous bedforms: a new look at an old problem. J. Sedim. Petrol. 60, 160172.
Barabási, A. L. & Stanley, H. E. 1995 Fractal Concepts in Surface Growth. Cambridge University Press.
Barr, B. C., Slinn, D., Piero, T. & Winters, K. 2004 Numerical simulation of turbulent, oscillatory flow over sand ripples. J. Geophys. Res. 109, C09009.
Besio, G., Blondeaux, P. & Vittori, G. 2006 On the formation of sand waves and sand banks. J. Fluid Mech. 557, 127.
Best, J. 2005 The fluid dynamics of river dunes: a review and some future research directions. J. Geophys. Res. 119, 121.
Best, J. & Kostaschuk, R. A. 2002 An experimental study of turbulent flow over a low-angle dune. J. Geophys. Res. 107 (C9), 3135.
Blondeaux, P. 2001 Mechanics of coastal forms. Annu. Rev. Fluid Mech. 33, 339370.
Blondeaux, P. & Vittori, G. 1991 Vorticity dynamics in an oscillatory flow over a rippled bed. J. Fluid Mech. 226, 257289.
Borazjani, I., Ge, L. & Sotiropoulos, F. 2008 Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J. Comput. Phys. 227, 75877620.
Bucher, W. H. 1919 On ripples and related sedimentary surface forms and their paleogeographic interpretation. Am. J. Sci. 47, 149210.
Celik, I. & Rodi, W. 1988 Modeling suspended sediment transport in non-equilibrium situations. J. Hydraul. Engng ASCE 114 (10), 11571191.
Chang, Y. S. & Scotti, A. 2003 Entrainment and suspension of sediments into a turbulent flow over ripples. J. Turbul. 4 (19), 122.
Chang, Y. S. & Scotti, A. 2004 Modeling unsteady turbulent flows over ripples: Reynolds-averaged Navier–Stokes equations (RANS) versus large-eddy simulation (LES). J. Geophys. Res. 109, C09012.
Charru, F., Andreotti, B. & Claudin, P. 2013 Sand ripples and dunes. Annu. Rev. Fluid Mech. 45, 469493.
Chau, L. & Bhaganagar, K. 2012 Understanding turbulent flow over ripple-shaped random roughness in a channel. Phys. Fluids 24, 115102.
Chou, Y. J. & Fringer, O. B. 2008 Modeling dilute sediment suspension using large-eddy simulation with a dynamic mixed model. Phys. Fluids 20, 115103.
Chou, Y. J. & Fringer, O. B. 2010 A model for the simulation of coupled flow–bed form evolution in turbulent flows. J. Geophys. Res. 115, C10041.
Chrisohoides, A. & Sotiropoulos, F. 2003 Experimental visualization of Lagrangian coherent structures in aperiodic flows. Phys. Fluids 15, L25L28.
Coco, G., Murray, A. B., Green, M. O., Thieler, E. R. & Hume, T. M. 2007 Sorted bed forms as self-organized patterns: 1. Model development. J. Geophys. Res. 112, F03015.
Coleman, S. E. & Fenton, J. D. 2000 Potential-flow instability theory and alluvial stream bed forms. J. Fluid Mech. 418, 101117.
Coleman, S. E. & Melville, B. W. 1994 Bed form development. J. Hydraul. Engng 120, 544560.
Coleman, S. E. & Nikora, V. I. 2008 A unifying framework for particle entrainment. Water Resour. Res. 44, W04415.
Coleman, S. E. & Nikora, V. I. 2009 Exner equation: a continuum approximation of a discrete granular system. Water Resour. Res. 45, W09421.
Coleman, S. E., Nikora, V. I., McLean, S. R., Clunie, T. M., Schlicke, T. & Melville, B. W. 2006 Equilibrium hydrodynamics concept for developing dunes. Phys. Fluids 18, 105104.
Colombini, R. M. 2004 Revisiting the linear theory of sand dune formation. J. Fluid Mech. 502, 116.
Colombini, M. & Stocchino, A. 2012 Three-dimensional river bed forms. J. Fluid Mech. 695, 6380.
Dargahi, B. 1989 The turbulent flow field around a circular cylinder. Exp. Fluids 8, 112.
Dargahi, B. 1990 Controlling mechanism of local scouring. J. Hydraul. Engng 116 (10), 11971214.
Diplas, P., Dancey, C. L., Celik, A. O., Valyrakis, M., Greer, K. & Akar, T. 2008 The role of impulse on the initiation of particle movement under turbulent flow conditions. Science 322 (5902), 717720.
Dreano, J., Valance, A., Lague, D. & Cassar, C. 2010 Experimental study on transient and steady-state dynamics of bedforms in supply limited configuration. Earth Surf. Process. Landf. 35 (14), 17301743.
Escauriaza, C. & Sotiropoulos, F. 2011a Initial stages of erosion and bed-form development in turbulent flow past a bridge pier. J. Geophys. Res. 116, F03007.
Escauriaza, C. & Sotiropoulos, F. 2011b Lagrangian dynamics of bedload transport in turbulent junction flows. J. Fluid Mech. 666, 3676.
Fredsoe, J. 1974 On the development of dunes in erodible channels. J. Fluid Mech. 60, 116.
Ge, L. & Sotiropoulos, F. 2007 A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries. J. Comput. Phys. 225, 17821809.
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 17601765.
Gilmanov, A. & Sotiropoulos, F. 2005 A hybrid Cartesian/immersed boundary method for simulating flows with three-dimesional, geometrically complex, moving bodies. J. Comput. Phys. 207 (2), 457492.
Giri, S. & Shimizu, Y. 2006 Numerical computation of sand dune migration with free surface. Water Resour. Res. 42 (10), W10422.
Giri, S. & Shimizu, Y. 2007 Validation of a numerical model for flow and bedform dynamics. Annu. J. Hydraul. Engng, Jpn. Soc. Civ. Engng 51, 139144.
Grass, A. J. 1970 Initial instability of fine bed sand. J. Hydraul. Div. ASCE HY3, 619632.
Grass, A. J. 1971 Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233255.
Gyr, A. & Schmid, A. 1989 The different ripple formation mechanism. J. Hydraul. Res. 27, 6174.
Hansen, J., van Hecke, M., Haaning, A., Ellegaard, C., Andersen, K., Bohr, T. & Sams, T. 2001 Pattern formation: instabilities in sand ripples. Nature 410, 324.
Hayashi, T. 1970 Formation of dunes and antidunes in open channels. J. Hydraul. Engng 96, 357366.
Henn, D. & Sykes, R. I. 1999 Large-eddy simulation of flow over wavy surfaces. J. Fluid Mech. 383, 75112.
Hino, M. 1968 Equilibrium-range spectra of sand waves formed by flowing water. J. Fluid Mech. 34, 565573.
Van Der Hoven, I. 1957 Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. J. Meteorol. 14, 160194.
Jackson, R. G. 1976 Sedimentological and fluid-dynamic implications of the turbulence bursting phenomenon in geophysical flows. J. Fluid Mech. 77, 531560.
Jain, S. C. & Kennedy, J. F. 1974 The spectral evolution of sedimentary bed forms. J. Fluid Mech. 63, 301314.
Jerolmack, D. J. & Mohrig, D. 2005a A unified model for subaqueous bedform dynamics. Water Resour. Res. 41, W12421.
Jerolmack, D. J. & Mohrig, D. 2005b Formation of Precambrian sediment ripples. Nature 433, 123127.
Jerolmack, D. J. & Mohrig, D. 2005c Interactions between bed forms: topography, turbulence and transport. J. Geophys. Res. 110, F02014.
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202228.
de Jong, B. 1989 Bed waves generated by internal waves in alluvial channels. J. Hydraul. Engng 115, 801817.
Kang, S., Lightbody, A., Hill, C. & Sotiropoulos, F. 2011 High-resolution numerical simulation of turbulence in natural waterways. Adv. Water Resour. 34 (1), 98113.
Kang, S. & Sotiropoulos, F. 2011 Flow phenomena and mechanisms in a field-scale experimental meandering channel with a pool–riffle sequence: insights gained via numerical simulation. J. Geophys. Res. 116, F03011.
Kang, S. & Sotiropoulos, F. 2012 Assessing the predictive capabilities of isotropic, eddy-viscosity Reynolds-averaged turbulence models in a natural-like meandering channel. Water Resour. Res. 48, W06505.
von Kármán, T. 1947 Sand ripples in the desert. Technion Yearbook 6, 5254.
Kennedy, J. F. 1969 The formation of sediment ripples, dunes and antidunes. Annu. Rev. Fluid Mech. 1, 147168.
Khelifa, A. & Ouellet, Y. 2000 Prediction of sand ripple geometry under waves and currents ASCE. J. Waterway Port Coast. Ocean Engng 126 (1), 1422.
Khosronejad, A.2006 Three-dimensional numerical simulation of turbulent flow and sediment transport in dam reservoirs. PhD thesis, Tarbiat Modares University, Iran.
Khosronejad, A., Hill, C., Kang, S. & Sotiropoulos, F. 2013 Computational and experimental investigation of scour past laboratory models of stream restoration rock structures. Adv. Water Resour. 54, 191207.
Khosronejad, A., Kang, S., Borazjani, I. & Sotiropoulos, F. 2011 Curvilinear immersed boundary method for simulating coupled flow and bed morphodynamic interactions due to sediment transport phenomena. Adv. Water Resour. 34 (7), 829843.
Khosronejad, A., Kang, S. & Sotiropoulos, F. 2012 Experimental and computational investigation of local scour around bridge piers. Adv. Water Resour. 37, 7385.
Khosronejad, A., Kozarek, J. L. & Sotiropoulos, F. 2014 Simulation-based approach for stream restoration structure design: model development and validation. J. Hydraul. Engng 140 (7), 116.
Khosronejad, A., Rennie, C., Salehi, A. & Townsend, R. 2007 3D numerical modeling of flow and sediment transport in laboratory channel bends. J. Hydraul. Engng 133 (10), 11231134.
Khosronejad, A., Salehi, A. A. & Rennie, C. 2008 Three dimensional numerical modeling of sediment release in a water reservoir. J. Hydraul. Res. 46 (2), 209223.
Kidanemariam, A. G. & Uhlmann, M. 2014 Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, 113.
Kostaschuk, R. A. 2000 A field study of turbulence and sediment dynamics over subaqueous dunes with flow separation. Sedimentology 47, 519531.
Kraft, S., Wang, Y. & Oberlack, M. 2011 Large eddy simulation of sediment deformation in a turbulent flow by means of level-set method. J. Hydraul. Engng 137 (11), 13941405.
Lacy, J. R., Rubin, D. M., Ikeda, H., Mokudai, K. & Hanes, D. M. 2007 Bed forms created by simulated waves and currents in a large flume. J. Geophys. Res. 112, C10018.
Liu, H. K. 1957 Mechanics of sediment-ripple formation. J. Hydraul. Engng 83, 123.
MacVicar, B. J., Parrott, L. & Roy, A. G. 2006 A two-dimensional discrete particle model of gravel bed river systems. J. Geophys. Res. 111, F03009.
Mazumder, B., Pal, D., Ghoshal, K. & Ojha, S. 2009 Turbulence statistics of flow over isolated scalene and isosceles triangular-shaped bed forms. J. Hydraul. Res. 47 (5), 626637.
de Moraes Franklin, E. 2013 Three-dimensional sand ripples as the product of vortex instability. Appl. Math. Model. 37, 31933199.
Muller, A. & Gyr, A. 1986 On the vortex formation in the mixing layer behind dunes. J. Hydraul Res. 24, 359375.
Nabi, M., de Vriend, H. J., Mosselman, E., Sloff, J. & Shimizu, Y. 2012 Detailed simulation of morphodynamics: 1. Hydrodynamic model. Water Resour. Res. 48, W12523.
Nezu, L. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows, IAHR Monograph. Balkema.
Niemann, S. L., Fredsøe, J. & Jacobsen, N. G. 2011 Sand dunes in steady flow at low Froude numbers: dune height evolution and flow resistance. J. Hydraul. Engng 137 (1), 514.
Nishimori, H. & Ouchi, N. 1993 Formation of ripple patterns and dunes by wind-blown sand. Phys. Rev. Lett. 71, 197200.
Nittrouer, J. A., Allison, M. A. & Campanella, R. 2008 Bedload transport rates for the lowermost Mississippi River. J. Geophys. Res. 113, F03004.
Nittrouer, J. A., Mohrig, D. & Allison, M. A. 2011 Punctuated sand transport in the lowermost Mississippi River. J. Geophys. Res. 116, F04025.
Omidyeganeh, M. & Piomelli, U. 2013a Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 1. Turbulence statistics. J. Fluid Mech. 721, 454483.
Omidyeganeh, M. & Piomelli, U. 2013b Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures. J. Fluid Mech. 734, 509534.
Palmsten, M. L., Kozarek, J. L., Calantoni, J., Kooney, T. & Holland, K.2011 Spatial and temporal evolution of stream bedforms. AGU Fall Meeting Abstracts, p. I1315.
Paola, C. & Voller, V. R. 2005 A generalized Exner equation for sediment mass balance. J. Geophys. Res. 110, F04014.
Raudkivi, A. J. 1966 Bed forms in alluvial channels. J. Fluid Mech. 26, 507514.
Raudkivi, A. J. 2007 Transition from ripples to dunes. J. Hydraul. Engng 132, 13161320.
Richards, K. J. 1980 The formation of ripples and dunes on an erodible bed. J. Fluid Mech. 99, 597618.
van Rijn, L. C. 1984 Sediment transport, Part III: Bed forms and alluvial roughness. J. Hydraul. Engng 110 (12), 17331754.
van Rijn, L. C. 1993 Principles of Sediment Transport in Rivers, Estuaries, and Coastal Seas. Aqua Publications.
Roulund, A., Sumer, B. M., Fredsoe, J. & Michelsen, J. 2005 Numerical and experimental investigation of flow and scour around a circular pile. J. Fluid Mech. 534, 351401.
Sagaut, P. 1988 Large Eddy Simulation for Incompressible Flows. Springer.
Sarkar, S. & Dey, S. 2010 Double-averaging turbulence characteristics in flows over a gravel-bed. J. Hydraul. Res. 48, 801809.
Scandura, P. G., Vittori, G. & Blondeaux, P. 2000 Three-dimensional oscillatory flow over steep ripples. J. Fluid Mech. 412, 335378.
Schindler, R. J. & Robert, A. 2004 Suspended sediment concentration and the ripple–dune transition. Hydrol. Process. 18, 32153227.
Seminara, G., Colombini, M. & Parker, G. 1996 Nearly pure sorting waves and formation of bedload sheets. J. Fluid Mech. 312, 253278.
Singh, A., Porté-Agel, F. & Foufoula-Georgiou, E. 2010 On the influence of gravel bed dynamics on velocity power spectra. Water Resour. Res. 46, 110.
Smagorinsky, J. S. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99164.
Tjerry, S. & Fredsøe, J. 2005 Calculation of dune morphology. J. Geophys. Res. 110, F04013.
Venditti, J. G. & Bauer, B. O. 2005 Turbulent flow over a dune: Green River, Colorado. Earth Surf. Process. Landf. 30, 289304.
Venditti, J. G. & Bennett, S. J. 2000 Spectral analysis of turbulent flow and suspended sediment transport over fixed dunes. J. Geophys. Res. 105, 2203522047.
Venditti, J. G. & Church, M. A. 2005 Bed form initiation from a flat sand bed. J. Geophys. Res. 110, F01009.
Venditti, J. G., Church, M. A. & Bennett, S. J. 2005a Morphodynamics of small-scale superimposed sand waves over migrating dune bed forms. Water Resour. Res. 41, W10423.
Venditti, J. G., Church, M. A. & Bennett, S. J. 2005b On the transition between 2D and 3D dunes. Sedimentology 52, 13431359.
Venditti, J. G., Church, M. A. & Bennett, S. J. 2006 On interfacial instability as a cause of transverse subcritical bed forms. Water Resour. Res. 42, W07423.
Venugopal, V., Porté Agel, F., Foufoula-Georgiou, E. & Carper, M. 2003 Multiscale interactions between surface shear stress and velocity in turbulent boundary layers. J. Geophys. Res. 108 (D19), 4613.
Wu, W., Rodi, W. & Wenka, T. 2000 3D numerical modeling of flow and sediment transport in open channels. J. Hydraul. Engng 126 (1), 415.
Yalin, M. S. 1992 River Mechanics. Elsevier.
Yue, W., Lin, C. L. & Patel, V. C. 2005 Coherent structures in open-channel flows over a fixed dune. Trans. ASME: J. Fluids Engng 127 (5), 858864.
Zedler, E. A. & Street, R. L. 2001 Large-eddy simulation of sediment transport: currents over ripples. J. Hydraul. Engng 127 (6), 444452.
Zedler, E. A. & Street, R. L. 2006 Sediment transport over ripples in oscillatory flow. J. Hydraul. Engng 132 (2), 114.
Zou, L. Y., Liu, N. S. & Lu, X. Y. 2006 An investigation of pulsating turbulent open channel flow by large eddy simulation. Comput. Fluids 35 (1), 74102.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Numerical simulation of sand waves in a turbulent open channel flow

  • Ali Khosronejad (a1) and Fotis Sotiropoulos (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.