Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T14:54:03.608Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  13 March 2013

Mohammad Omidyeganeh  and
Ugo Piomelli
Mohammad Omidyeganeh*
Affiliation:
Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canada K7L 3N6
Ugo Piomelli
Affiliation:
Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canada K7L 3N6
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: River dynamics Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 721 , 25 April 2013 , pp. 454 - 483
Copyright
©2013 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, J. R. L. 1968 Current Ripples: Their Relation to Patterns of Water and Sediment Motion. North-Holland.Google Scholar
Armenio, V. & Piomelli, U. 2000 A Lagrangian mixed subgrid-scale model in generalized coordinates. Flow Turbul. Combust. 65, 51–81.CrossRefGoogle Scholar
Ashley, G. M. 1990 Classification of large-scale subaqueous bedforms: a new look at an old problem. J. Sedim. Petrol. 60 (1), 160–172.Google Scholar
Baas, J. H. 1994 A flume study on the development and equilibrium morphology of current ripples in very fine sand. Sedimentology 41, 185–209.Google Scholar
Baas, J. H. 1999 An empirical model for the development and equilibrium morphology of current ripples in fine sands. Sedimentology 46, 123–138.Google Scholar
Baas, J. H., Oost, A. P., Sztano, O. K., de Boer, P. L. & Postma, G. 1993 Time as an independent variable for current ripples developing towards linguoid equilibrium morphology. Terra Nova 5, 29–35.Google Scholar
Babakaiff, S. C. & Hickin, E. 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. 321–342. Wiley.Google Scholar
Balachandar, R. & Patel, V. C. 2008 Flow over a fixed rough dune. Can. J. Civ. Eng. 35, 511–520.Google Scholar
Balachandar, R., Yun, B.-S. & Patel, V. C. 2007 Effect of depth on flow over a fixed dune. Can. J. Civ. Eng. 43, 1587–1599.Google Scholar
Bennett, S. J. & Best, J. L. 1995 Mean flow and turbulence structure over fixed, two-dimensional dunes: implications for sediment transport and bedform stability. Sedimentology 42, 491–514.CrossRefGoogle Scholar
Bennett, S. J. & Best, J. 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. 281–304. Wiley.Google Scholar
Best, J. L. 2005 The fluid dynamics of river dunes: a review and some future research directions. J. Geophys. Res. 119 (F04S02), 1–21.Google Scholar
Best, J. L., Kostaschuk, R. A. & Villard, P. 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), 373–381.CrossRefGoogle Scholar
Carling, P. A., Gölz, E., Orr, H. G. & Radeki-Pawlik, A. 2000 The morphodynamics of fluvial sand dunes in the River Rhine, near Mainz, Germany. I. Sedimentology and morphology. Sedimentology 47, 227–252.Google Scholar
Chapman, G. T. & Yates, L. A. 1991 Topology of flow separation on three-dimensional bodies. Appl. Mech. Rev. 44 (7), 329–345.Google Scholar
Flemming, B. W. 1978 Underwater sand dunes along the southeast african continental margin – observations and implications. Mar. Geol. 28, 177–198.Google Scholar
Gabel, S. L. 1993 Geometry and kinematics of dunes during steady and unsteady flows in the Calamus River, Nebraska, USA. Sedimentology 40, 237–269.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765.Google Scholar
Grigoriadis, D. G. E., Balaras, E. & Dimas, A. A. 2009 Large-eddy simulations of unidirectional water flow over dunes. J. Geophys. Res. 114.Google Scholar
Hyun, B. S., Balachandar, R., Yu, K. & Patel, V. C. 2003 Assessment of PIV to measure mean velocity and turbulence in open-channel flow. Exp. Fluids 35, 262–267.Google Scholar
Jackson, R. G. 1976 Sedimentological and fluid-dynamic implications of the turbulent bursting phenomenon in geophysical flows. J. Fluid Mech. 77, 531–560.Google Scholar
Jordan, S. A. 1999 A large-eddy simulation methodology in generalized curvilinear coordinates. J. Comput. Phys. 148 (2), 322–340.Google Scholar
Kadota, A. & Nezu, I. 1999 Three-dimensional structure of space-time correlation on coherent vortices generated behind dune crests. J. Hydr. Res. 37 (1), 59–80.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
Kostaschuk, R. & Villard, P. 1996 Flow and sediment transport over large subaqueous dunes: Fraser River, Canada. Sedimentology 43, 849–863.Google Scholar
Kostaschuk, R. A. 2000 A field study of turbulence and sediment dynamics over subaqueous dunes with flow separation. Sedimentology 47 (3), 519–531.Google Scholar
Kostaschuk, R. A. & Church, M. A. 1993 Macroturbulence generated by dunes: Fraser River, Canada. Sedim. Geol. 85 (1–4), 25–37.Google Scholar
Le, H., Moin, P. & Kim, J. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374.Google Scholar
Leonard, A. 1974 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18A, 237–248.Google Scholar
Maddux, T. B., McLean, S. R. & Nelson, J. M. 2003a Turbulent flow over three-dimensional dunes: 2. Fluid and bed stresses. J. Geophys. Res. 108(F1), 6010.Google Scholar
Maddux, T. B., Nelson, J. M. & McLean, S. R. 2003b Turbulent flow over three-dimensional dunes: 1. Free surface and flow response. J. Geophys. Res. 108(F1), 6009.Google Scholar
Matthes, G. H. 1947 Macroturbulence in natural stream flow. Trans. American Ceophys. Union 28 (2), 255–265.Google Scholar
McLean, S. R., Nelson, J. M. & Wolfe, S. R. 1994 Turbulence structure over two-dimensional bedforms: implications for sediment transport. J. Geophys. Res. 99, 12729–12747.Google Scholar
McLean, S. R. & Smith, J. D. 1986 A model for flow over two-dimensional bed forms. J. Hydr. Engng 112 (4), 300–317.Google Scholar
McLean, S. R., Wolfe, S. R. & Nelson, J. M. 1999 Predicting boundary shear stress and sediment transport over bed forms. J. Hydr. Engng 125 (7), 725–736.Google Scholar
Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.CrossRefGoogle Scholar
Müller, A. & Gyr, A. 1986 On the vortex formation in the mixing layer behind dunes. J. Hydr. Res. 24, 359–375.Google Scholar
Nelson, J. M., McLean, S. R. & Wolfe, S. R. 1993 Mean flow and turbulence fields over two-dimensional bed forms. Water Resour. Res. 29 (12), 3935–3953.Google Scholar
Nelson, J. M. & Smith, J. D. 1989 Mechanics of flow over ripples and dunes. J. Geophys. Res. 94 (C6), 8146–8162.CrossRefGoogle Scholar
Nezu, I. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows. Balkema.Google Scholar
Omidyeganeh, M. & Piomelli, U. 2011 Large-eddy simulation of two-dimensional dunes in a steady, unidirectional flow. J. Turbul. 12 (42), 1–31.Google Scholar
Parsons, D. R., Best, J. L., Orfeo, O., Hardy, R. J., Kostaschuk, R. & Lane, S. 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.Google Scholar
Polatel, C., Muste, M., Patel, V. C. & Stoesser, T. 2006 Free-surface response to large-scale bed roughness. In The 7th Int. Conf. on Hydroscience and Engineering, pp. 1–11. Drexel University, College of Engineering.Google Scholar
Radhakrishnan, S., Piomelli, U. & Keating, A. 2008 Wall-modelled large-eddy simulations of flows with curvature and mild separation. ASME J. Fluids Engng. 130, 101203.Google Scholar
Radhakrishnan, S., Piomelli, U., Keating, A. & Silva Lopes, A. 2006 Reynolds-averaged and large-eddy simulations of turbulent non-equilibrium flows. J. Turbul. 7 (63), 1–30.Google Scholar
Rhie, C. M. & Chow, W. L. 1983 Numerical study of the turbulent flow past an aerofoil with trailing edge separation. AIAA J. 21, 1525–1532.Google Scholar
van Rijn, L. C. 1984 Sediment transport, part III: Bed forms and alluvial roughness. J. Hydr. Engng 110 (12), 1733–1754.Google Scholar
Robert, A. & Uhlman, W. 2001 An experimental study on the ripple dune transition. Earth Surf. Process. Landf. 26, 615–629.Google Scholar
Roden, J. E. 1998 The sedimentology and dynamics of mega-dunes, Jamuna River, Bangladesh. PhD thesis, Univ. Leeds, Leeds, U.K.Google Scholar
Schindler, R. J. & Robert, A. 2005 Flow and turbulence structure across the ripple–dune transition: an experiment under mobile bed conditions. Sedimentology 52, 627–649.Google Scholar
Schmeeckle, M. W., Shimizu, Y., Baba, H. & Ikezaki, S. 1999 Numerical and experimental investigation of turbulence over dunes in open-channel flow. Monthly Rep. Civ. Eng. Res. Inst. 551, 2–15.Google Scholar
Silva Lopes, A. & Palma, J. M. L. M. 2002 Simulations of isotropic turbulence using a non-orthogonal grid system. J. Comput. Phys. 175 (2), 713–738.Google Scholar
Silva Lopes, A., Piomelli, U. & Palma, J. M. L. M. 2006 Large-eddy simulation of the flow in an S-duct. J. Turbul. 7 (11), 1–24.Google Scholar
Sirovich, L. & Karlsson, S. 1997 Turbulent drag reduction by passive mechanisms. Nature 388, 753–755.Google Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337–371.CrossRefGoogle Scholar
Stoesser, T., Braun, C., García-Villalba, M. & Rodi, W. 2008 Turbulence structures in flow over two-dimensional dunes. J. Hydr. Engng 134 (1), 42–55.Google Scholar
Venditti, J. G. 2007 Turbulent flow and drag over fixed two- and three-dimensional dunes. J. Geophys. Res. 112, F04008.Google Scholar
Venditti, J. G. & Bauer, B. O. 2005 Turbulent flow over a dune: Green River, Colorado. Earth Surf. Process. Landf. 30, 289–304.Google Scholar
Venditti, J. G. & Bennett, S. J. 2000 Spectral analysis of turbulent flow and suspended sediment transport over dunes. J. Geophys. Res. 105, 22035–22047.Google Scholar
Venditti, J. G., Church, M. & Bennet, S. J. 2005 On the transition between 2D and 3D dunes. Sedimentology 52, 1343–1359.Google Scholar
Yalin, M. S. 1964 Geometrical properties of sand waves. J. Hydr. Div. ASCE 90 (HY5), 105–119.Google Scholar
Yoon, J. Y. & Patel, V. C. 1996 Numerical model of turbulent flow over sand dune. J. Hydr. Engng 122 (1), 10–18.Google Scholar
Yue, W., Lin, C. L. & Patel, V. C. 2005 Large eddy simulation of turbulent open-channel flow with free surface simulated by level set method. Phys. Fluids 17, 025108.Google Scholar
Yue, W., Lin, C.-L. & Patel, V. C. 2006 Large-eddy simulation of turbulent flow over a fixed two-dimensional dune. J. Hydr. Engng 132 (7), 643–651.Google Scholar
Zedler, E. A. & Street, R. L. 2001 Large-eddy simulation of sediment transport: current over ripples. J. Hydr. Res. 127, 444–452.Google Scholar