Skip to main content
×
Home
    • Aa
    • Aa

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 1. Turbulence statistics

  • Mohammad Omidyeganeh (a1) and Ugo Piomelli (a1)
Abstract
Abstract

We performed large-eddy simulations of flow over a series of three-dimensional dunes at laboratory scale (Reynolds number based on the average channel depth and streamwise velocity was 18 900) using the Lagrangian dynamic eddy-viscosity subgrid-scale model. The bedform three-dimensionality was imposed by shifting a standard two-dimensional dune shape in the streamwise direction according to a sine wave. The statistics of the flow are discussed in 10 cases with in-phase and staggered crestlines, different deformation amplitudes and wavelengths. The results are validated qualitatively against experiments. The three-dimensional separation of flow at the crestline alters the distribution of wall pressure, which in turn may cause secondary flow across the stream, which directs low-momentum fluid, near the bed, toward the lobe (the most downstream point on the crestline) and high-momentum fluid, near the top surface, toward the saddle (the most upstream point on the crestline). The mean flow is characterized by a pair of counter-rotating streamwise vortices, with core radius of the order of the flow depth. However, for wavelengths smaller than the flow depth, the secondary flow exists only near the bed and the mean flow away from the bed resembles the two-dimensional case. Staggering the crestlines alters the secondary motion; the fastest flow occurs between the lobe and the saddle planes, and two pairs of streamwise vortices appear (a strong one, centred about the lobe, and a weaker one, coming from the previous dune, centred around the saddle). The distribution of the wall stress and the focal points of separation and attachment on the bed are discussed. The sensitivity of the average reattachment length, depends on the induced secondary flow, the streamwise and spanwise components of the channel resistance (the skin friction and the form drag), and the contribution of the form drag to the total resistance are also studied. Three-dimensionality of the bed increases the drag in the channel; the form drag contributes more than in the two-dimensional case to the resistance, except for the staggered-crest case. Turbulent-kinetic energy is increased in the separated shear layer by the introduction of three-dimensionality, but its value normalized by the plane-averaged wall stress is lower than in the corresponding two-dimensional dunes. The upward flow on the stoss side and higher deceleration of flow on the lee side over the lobe plane lift and broaden the separated shear layer, respectively, affecting the turbulent kinetic energy.

Copyright
Corresponding author
Email address for correspondence: omidyeganeh@me.queensu.ca
References
Hide All
AllenJ. R. L. 1968 Current Ripples: Their Relation to Patterns of Water and Sediment Motion. North-Holland.
ArmenioV. & PiomelliU. 2000 A Lagrangian mixed subgrid-scale model in generalized coordinates. Flow Turbul. Combust. 65, 5181.
AshleyG. M. 1990 Classification of large-scale subaqueous bedforms: a new look at an old problem. J. Sedim. Petrol. 60 (1), 160172.
BaasJ. H. 1994 A flume study on the development and equilibrium morphology of current ripples in very fine sand. Sedimentology 41, 185209.
BaasJ. H. 1999 An empirical model for the development and equilibrium morphology of current ripples in fine sands. Sedimentology 46, 123138.
BaasJ. H., OostA. P., SztanoO. K., de BoerP. L. & PostmaG. 1993 Time as an independent variable for current ripples developing towards linguoid equilibrium morphology. Terra Nova 5, 2935.
BabakaiffS. C. & HickinE. J. 1996 Coherent flow structures in Squamish River Estuary, British Columbia, Canada. In Coherent Flow Structures in Open Channels (ed. Ashworth P., Bennett S.J., Best J.L. & McLelland S.J.). pp. 321342. Wiley.
BalachandarR. & PatelV. C. 2008 Flow over a fixed rough dune. Can. J. Civ. Eng. 35, 511520.
BalachandarR., YunB.-S. & PatelV. C. 2007 Effect of depth on flow over a fixed dune. Can. J. Civ. Eng. 43, 15871599.
BennettS. J. & BestJ. L. 1995 Mean flow and turbulence structure over fixed, two-dimensional dunes: implications for sediment transport and bedform stability. Sedimentology 42, 491514.
BennettS. J. & BestJ. L. 1996 Mean flow and turbulence structure over fixed ripples and the ripple dune transition. In Coherent Flow Structures in Open Channels (ed. Ashworth P., Bennett S.J., Best J.L. & McLelland S. J.), pp. 281304. Wiley.
BestJ. L. 2005 The fluid dynamics of river dunes: a review and some future research directions. J. Geophys. Res. 119 (F04S02), 121.
BestJ. L., KostaschukR. A. & VillardP. V. 2001 Quantitative visualization of flow fields associated with alluvial sand dunes: results from the laboratory and field using ultrasonic and acoustic Doppler anemometry. J. Vis. 4 (4), 373381.
CarlingP. A., GölzE., OrrH. G. & Radeki-PawlikA. 2000 The morphodynamics of fluvial sand dunes in the River Rhine, near Mainz, Germany. I. Sedimentology and morphology. Sedimentology 47, 227252.
ChapmanG. T. & YatesL. A. 1991 Topology of flow separation on three-dimensional bodies. Appl. Mech. Rev. 44 (7), 329345.
FlemmingB. W. 1978 Underwater sand dunes along the southeast african continental margin – observations and implications. Mar. Geol. 28, 177198.
GabelS. L. 1993 Geometry and kinematics of dunes during steady and unsteady flows in the Calamus River, Nebraska, USA. Sedimentology 40, 237269.
GermanoM., PiomelliU., MoinP. & CabotW. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 17601765.
GrigoriadisD. G. E., BalarasE. & DimasA. A. 2009 Large-eddy simulations of unidirectional water flow over dunes. J. Geophys. Res. 114.
HyunB. S., BalachandarR., YuK. & PatelV. C. 2003 Assessment of PIV to measure mean velocity and turbulence in open-channel flow. Exp. Fluids 35, 262267.
JacksonR. G. 1976 Sedimentological and fluid-dynamic implications of the turbulent bursting phenomenon in geophysical flows. J. Fluid Mech. 77, 531560.
JordanS. A. 1999 A large-eddy simulation methodology in generalized curvilinear coordinates. J. Comput. Phys. 148 (2), 322340.
KadotaA. & NezuI. 1999 Three-dimensional structure of space-time correlation on coherent vortices generated behind dune crests. J. Hydr. Res. 37 (1), 5980.
KimJ. & MoinP. 1985 Application of a fractional step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.
KostaschukR. & VillardP. 1996 Flow and sediment transport over large subaqueous dunes: Fraser River, Canada. Sedimentology 43, 849863.
KostaschukR. A. 2000 A field study of turbulence and sediment dynamics over subaqueous dunes with flow separation. Sedimentology 47 (3), 519531.
KostaschukR. A. & ChurchM. A. 1993 Macroturbulence generated by dunes: Fraser River, Canada. Sedim. Geol. 85 (1–4), 2537.
LeH., MoinP. & KimJ. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349374.
LeonardA. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18A, 237248.
MadduxT. B., McLeanS. R. & NelsonJ. M. 2003a Turbulent flow over three-dimensional dunes: 2. Fluid and bed stresses. J. Geophys. Res. 108(F1), 6010.
MadduxT. B., NelsonJ. M. & McLeanS. R. 2003b Turbulent flow over three-dimensional dunes: 1. Free surface and flow response. J. Geophys. Res. 108(F1), 6009.
MatthesG. H. 1947 Macroturbulence in natural stream flow. Trans. American Ceophys. Union 28 (2), 255265.
McLeanS. R., NelsonJ. M. & WolfeS. R. 1994 Turbulence structure over two-dimensional bedforms: implications for sediment transport. J. Geophys. Res. 99, 1272912747.
McLeanS. R. & SmithJ. D. 1986 A model for flow over two-dimensional bed forms. J. Hydr. Engng 112 (4), 300317.
McLeanS. R., WolfeS. R. & NelsonJ. M. 1999 Predicting boundary shear stress and sediment transport over bed forms. J. Hydr. Engng 125 (7), 725736.
MeneveauC., LundT. S. & CabotW. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353385.
MüllerA. & GyrA. 1986 On the vortex formation in the mixing layer behind dunes. J. Hydr. Res. 24, 359375.
NelsonJ. M., McLeanS. R. & WolfeS. R. 1993 Mean flow and turbulence fields over two-dimensional bed forms. Water Resour. Res. 29 (12), 39353953.
NelsonJ. M. & SmithJ. D. 1989 Mechanics of flow over ripples and dunes. J. Geophys. Res. 94 (C6), 81468162.
NezuI. & NakagawaH. 1993 Turbulence in Open-Channel Flows. Balkema.
OmidyeganehM. & PiomelliU. 2011 Large-eddy simulation of two-dimensional dunes in a steady, unidirectional flow. J. Turbul. 12 (42), 131.
ParsonsD. R., BestJ. L., OrfeoO., HardyR. J., KostaschukR. & LaneS. N. 2005 Morphology and flow fields of three-dimensional dunes, Rio Paraná, Argentina: results from simultaneous multibeam echo sounding and acoustic doppler current profiling. J. Geophys. Res. 110, F04S03.
PolatelC., MusteM., PatelV. C. & StoesserT. 2006 Free-surface response to large-scale bed roughness. In The 7th Int. Conf. on Hydroscience and Engineering, pp. 111. Drexel University, College of Engineering.
RadhakrishnanS., PiomelliU. & KeatingA. 2008 Wall-modelled large-eddy simulations of flows with curvature and mild separation. ASME J. Fluids Engng. 130, 101203.
RadhakrishnanS., PiomelliU., KeatingA. & Silva LopesA. 2006 Reynolds-averaged and large-eddy simulations of turbulent non-equilibrium flows. J. Turbul. 7 (63), 130.
RhieC. M. & ChowW. L. 1983 Numerical study of the turbulent flow past an aerofoil with trailing edge separation. AIAA J. 21, 15251532.
van RijnL. C. 1984 Sediment transport, part III: Bed forms and alluvial roughness. J. Hydr. Engng 110 (12), 17331754.
RobertA. & UhlmanW. 2001 An experimental study on the ripple dune transition. Earth Surf. Process. Landf. 26, 615629.
RodenJ. E. 1998 The sedimentology and dynamics of mega-dunes, Jamuna River, Bangladesh. PhD thesis, Univ. Leeds, Leeds, U.K.
SchindlerR. J. & RobertA. 2005 Flow and turbulence structure across the ripple–dune transition: an experiment under mobile bed conditions. Sedimentology 52, 627649.
SchmeeckleM. W., ShimizuY., BabaH. & IkezakiS. 1999 Numerical and experimental investigation of turbulence over dunes in open-channel flow. Monthly Rep. Civ. Eng. Res. Inst. 551, 215.
Silva LopesA. & PalmaJ. M. L. M. 2002 Simulations of isotropic turbulence using a non-orthogonal grid system. J. Comput. Phys. 175 (2), 713738.
Silva LopesA., PiomelliU. & PalmaJ. M. L. M. 2006 Large-eddy simulation of the flow in an S-duct. J. Turbul. 7 (11), 124.
SirovichL. & KarlssonS. 1997 Turbulent drag reduction by passive mechanisms. Nature 388, 753755.
SpalartP. R. & WatmuffJ. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337371.
StoesserT., BraunC., García-VillalbaM. & RodiW. 2008 Turbulence structures in flow over two-dimensional dunes. J. Hydr. Engng 134 (1), 4255.
VendittiJ. G. 2007 Turbulent flow and drag over fixed two- and three-dimensional dunes. J. Geophys. Res. 112, F04008.
VendittiJ. G. & BauerB. O. 2005 Turbulent flow over a dune: Green River, Colorado. Earth Surf. Process. Landf. 30, 289304.
VendittiJ. G. & BennettS. J. 2000 Spectral analysis of turbulent flow and suspended sediment transport over dunes. J. Geophys. Res. 105, 2203522047.
VendittiJ. G., ChurchM. & BennetS. J. 2005 On the transition between 2D and 3D dunes. Sedimentology 52, 13431359.
YalinM. S. 1964 Geometrical properties of sand waves. J. Hydr. Div. ASCE 90 (HY5), 105119.
YoonJ. Y. & PatelV. C. 1996 Numerical model of turbulent flow over sand dune. J. Hydr. Engng 122 (1), 1018.
YueW., LinC. L. & PatelV. C. 2005 Large eddy simulation of turbulent open-channel flow with free surface simulated by level set method. Phys. Fluids 17, 025108.
YueW., LinC.-L. & PatelV. C. 2006 Large-eddy simulation of turbulent flow over a fixed two-dimensional dune. J. Hydr. Engng 132 (7), 643651.
ZedlerE. A. & StreetR. L. 2001 Large-eddy simulation of sediment transport: current over ripples. J. Hydr. Res. 127, 444452.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 55 *
Loading metrics...

Abstract views

Total abstract views: 178 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd October 2017. This data will be updated every 24 hours.