Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-01T02:20:48.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulations of ripples in an oscillatory flow

Published online by Cambridge University Press:  28 January 2019

Marco Mazzuoli Open the ORCID record for Marco Mazzuoli [Opens in a new window] ,
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]
Marco Mazzuoli*
Affiliation:
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
Aman G. Kidanemariam
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Markus Uhlmann
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Sea ripples are small-scale bedforms which originate from the interaction of an oscillatory flow with an erodible sand bed. The phenomenon of sea ripple formation is investigated by means of direct numerical simulation in which the sediment bed is represented by a large number of fully resolved spherical grains (i.e. the flow around each individual particle is accounted for). Two sets of parameter values (differing in the amplitude and frequency of fluid oscillations, among other quantities) are adopted which are motivated by laboratory experiments on the formation of laminar rolling-grain ripples. The knowledge of the origin of ripples is presently enriched by insights and by providing fluid- and sediment-related quantities that are difficult to obtain in the laboratory (e.g. particle forces, statistics of particle motion, bed shear stress). In particular, detailed analysis of flow and sediment bed evolution has confirmed that ripple wavelength is determined by the action of steady recirculating cells which tend to accumulate sediment grains into ripple crests. The ripple amplitude is observed to grow exponentially, consistent with established linear stability analysis theories. Particles at the bed surface exhibit two kinds of motion depending on their position with respect to the recirculating cells: particles at ripple crests are significantly faster and show larger excursions than those lying in ripple troughs. In analogy with the segregation phenomenon of polydisperse sediments, the non-uniform distribution of the velocity field promotes the formation of ripples. The wider the gap between the excursion of fast and slow particles, the larger the resulting growth rate of the ripples. Finally, it is revealed that, in the absence of turbulence, the sediment flow rate is driven by both the bed shear stress and the wave-induced pressure gradient, the dominance of each depending on the phase of the oscillation period. In phases of maximum bed shear stress, the sediment flow rate correlates more with the Shields number while the pressure gradient tends to drive sediment bed motion during phases of minimum bed shear stress.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 572 - 600
Copyright
© 2019 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.)

Footnotes

‡

Present address: Federal Waterways Engineering and Research Institute (BAW), 76152 Karlsruhe, Germany

References

Aussillous, P., Chauchat, J., Pailha, M., Médale, M. & Guazzelli, É. 2013 Investigation of the mobile granular layer in bedload transport by laminar shearing flows. J. Fluid Mech. 736, 594–615.10.1017/jfm.2013.546Google Scholar
Blondeaux, P. 1990 Sand ripples under sea waves. Part 1. Ripple formation. J. Fluid Mech. 218, 1–17.10.1017/S0022112090000908Google Scholar
Blondeaux, P., Sleath, J. F. A. & Vittori, G.1988 Experimental data on sand ripples in an oscillatory flow. Rep. 01/88. Hydraulics University of Genoa.Google Scholar
Coleman, S. E. & Nikora, V. I. 2011 Fluvial dunes: initiation, characterization, flow structure. Earth Surf. Process. Landf. 36 (1), 39–57.10.1002/esp.2096Google Scholar
Davies, A. G., Ribberink, J. S., Temperville, A. & Zyserman, J. A. 1997 Comparisons between sediment transport models and observations made in wave and current flows above plane beds. Coast. Engng 31 (1–4), 163–198.10.1016/S0378-3839(97)00005-7Google Scholar
Foster, D. L., Bowen, A. J., Holman, R. A. & Natoo, P. 2006 Field evidence of pressure gradient induced incipient motion. J. Geophys. Res. 111 (C5), C05004.10.1029/2004JC002863Google Scholar
Frank, D., Foster, D., Sou, I. M., Calantoni, J. & Chou, P. 2015 Lagrangian measurements of incipient motion in oscillatory flows. J. Geophys. Res. 120 (1), 244–256.10.1002/2014JC010183Google Scholar
Hino, M. 1968 Equilibrium-range spectra of sand waves formed by flowing water. J. Fluid Mech. 34 (3), 565–573.10.1017/S0022112068002089Google Scholar
Hwang, K., Hwung, H. & Huang, P. 2008 Particle motions on a plane floor under waves. In 8th Int. Conf. Hydrodynamics, ICHD2008, 30 Sept.–3 Oct. 2008, Nantes, France, pp. 211–218.Google Scholar
Jain, S. C. & Kennedy, J. F. 1974 The spectral evolution of sedimentary bed forms. J. Fluid Mech. 63 (2), 301–314.10.1017/S0022112074001157Google Scholar
Kidanemariam, A. G. & Uhlmann, M. 2014a Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2.10.1017/jfm.2014.284Google 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 67, 174–188.10.1016/j.ijmultiphaseflow.2014.08.008Google Scholar
Kidanemariam, A. G. & Uhlmann, M. 2017 Formation of sediment patterns in channel flow: minimal unstable systems and their temporal evolution. J. Fluid Mech. 818, 716–743.10.1017/jfm.2017.147Google Scholar
Lyne, W. H. 1971 Unsteady viscous flow over a wavy wall. J. Fluid Mech. 50 (01), 33–48.10.1017/S0022112071002441Google Scholar
Mazzuoli, M., Blondeaux, P., Simeonov, J. & Calantoni, J. 2017 Direct numerical simulation of oscillatory flow over a wavy, rough, and permeable bottom. J. Geophys. Res. 123 (3), 1595–1611.10.1002/2017JC013447Google Scholar
Mazzuoli, M., Kidanemariam, A. G., Blondeaux, P., Vittori, G. & Uhlmann, M. 2016 On the formation of sediment chains in an oscillatory boundary layer. J. Fluid Mech. 789, 461–480.10.1017/jfm.2015.732Google Scholar
Mazzuoli, M. & Uhlmann, M. 2017 Direct numerical simulation of open-channel flow over a fully rough wall at moderate relative submergence. J. Fluid Mech. 824, 722–765.10.1017/jfm.2017.371Google Scholar
Moon, S. J., Swift, J. B. & Swinney, H. L. 2004 Role of friction in pattern formation in oscillated granular layers. Phys. Rev. E 69 (3), 031301.Google Scholar
Nielsen, P. 1992 Coastal Bottom Boundary Layers and Sediment Transport. World Scientific.10.1142/1269Google Scholar
Nikora, V. I., Sukhodolov, A. N. & Rowinski, P. M. 1997 Statistical sand wave dynamics in one-directional water flows. J. Fluid Mech. 351, 17–39.10.1017/S0022112097006708Google Scholar
Pedocchi, F. & García, M. H. 2009 Ripple morphology under oscillatory flow: 2. Experiments. J. Geophys. Res. 114 (C12), C12015.Google Scholar
Rousseaux, G., Stegner, A. & Wesfreid, J. E. 2004a Wavelength selection of rolling-grain ripples in the laboratory. Phys. Rev. E 69 (3), 031307.Google Scholar
Rousseaux, G., Yoshikawa, H., Stegner, A. & Wesfreid, J. E. 2004b Dynamics of transient eddy above rolling-grain ripples. Phys. Fluids 16 (4), 1049–1058.10.1063/1.1651482Google Scholar
Scandura, P., Vittori, G. & Blondeaux, P. 2000 Three-dimensional oscillatory flow over steep ripples. J. Fluid Mech. 412, 355–378.10.1017/S0022112000008430Google Scholar
Sleath, J. F. A. 1976 On rolling-grain ripples. J. Hydraul. Res. 14 (1), 69–81.10.1080/00221687609499689Google Scholar
Sleath, J. F. A. 1984 Sea Bed Mechanics. Wiley.Google Scholar
Stegner, A. & Wesfreid, J. E. 1999 Dynamical evolution of sand ripples under water. Phys. Rev. E 60 (4), R3487.Google Scholar
Thibodeaux, L. J. & Boyle, J. D. 1987 Bedform-generated convective transport in bottom sediment. Nature 325 (6102), 341–343.10.1038/325341a0Google Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209 (2), 448–476.10.1016/j.jcp.2005.03.017Google Scholar
Uhlmann, M. & Chouippe, A. 2017 Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence. J. Fluid Mech. 812, 991–1023.10.1017/jfm.2016.826Google Scholar
Vittori, G. & Blondeaux, P. 1990 Sand ripples under sea waves. Part 2. Finite-amplitude development. J. Fluid Mech. 218, 19–39.10.1017/S002211209000091XGoogle Scholar
Vittori, G. & Blondeaux, P. 1992 Sand ripples under sea waves. Part 3. Brick-pattern ripple formation. J. Fluid Mech. 239, 23–45.10.1017/S0022112092004300Google 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 (11), 1159–1168.10.1061/(ASCE)0733-9429(2006)132:11(1159)Google Scholar

Mazzuoli et al. supplementary movie 1

Top view of the bed: particles are coloured according to their distance form the wall (increasing blue to red). Small panels indicate the time development of the particle flow rate (left panel) and of the free-stream velocity (right panel). PART 1.

Download Mazzuoli et al. supplementary movie 1(Video)
Video 9.5 MB

Mazzuoli et al. supplementary movie 2

Top view of the bed: particles are coloured according to their distance form the wall (increasing blue to red). Small panels indicate the time development of the particle flow rate (left panel) and of the free-stream velocity (right panel). PART 2.

Download Mazzuoli et al. supplementary movie 2(Video)
Video 9.4 MB

Mazzuoli et al. supplementary movie 3

Top view of the bed: particles are coloured according to their distance form the wall (increasing blue to red). Small panels indicate the time development of the particle flow rate (left panel) and of the free-stream velocity (right panel). PART 3.

Download Mazzuoli et al. supplementary movie 3(Video)
Video 10.1 MB

Mazzuoli et al. supplementary movie 4

Top view of the bed: particles are coloured according to their distance form the wall (increasing blue to red). Small panels indicate the time development of the particle flow rate (left panel) and of the free-stream velocity (right panel). PART 4.

Download Mazzuoli et al. supplementary movie 4(Video)
Video 9.8 MB

Mazzuoli et al. supplementary movie 5

Top view of the bed: particles are coloured according to their distance form the wall (increasing blue to red). Small panels indicate the time development of the particle flow rate (left panel) and of the free-stream velocity (right panel). PART 5.

Download Mazzuoli et al. supplementary movie 5(Video)
Video 9.3 MB

Mazzuoli et al. supplementary movie 6

Top view of the bed: particles are coloured according to their distance form the wall (increasing blue to red). Small panels indicate the time development of the particle flow rate (left panel) and of the free-stream velocity (right panel). PART 6.

Download Mazzuoli et al. supplementary movie 6(Video)
Video 9.2 MB

Mazzuoli et al. supplementary movie 7

Top view of the bed: particles are coloured according to their distance form the wall (increasing blue to red). Small panels indicate the time development of the particle flow rate (left panel) and of the free-stream velocity (right panel). PART 7.

Download Mazzuoli et al. supplementary movie 7(Video)
Video 9.4 MB

Mazzuoli et al. supplementary movie 8

Top view of the bed: particles are coloured according to their distance form the wall (increasing blue to red). Small panels indicate the time development of the particle flow rate (left panel) and of the free-stream velocity (right panel). PART 8.

Download Mazzuoli et al. supplementary movie 8(Video)
Video 8 MB