Skip to main content
SpringerLink
Log in

A spectral model for estimating temporal and spatial evolution of rippled seabeds

  • Published:
Ocean Dynamics Aims and scope Submit manuscript

Abstract

Existing time variable ripple prediction models have focused on ripple wavelength and height yet have not accounted for the effect of wave directionality on ripple evolution. These models use an equilibrium ripple sub-module that provides the target geometry of the seabed. Temporal variability of the hydrodynamic conditions cause ripple geometry to lag behind and not always agree with that predicted by equilibrium models. In this contribution, previous work is extended through the development of a new 2-D, time variable, spectral ripple model that allows for the estimation of ripple wavelength, height, and orientation. Since ripple irregularity is associated with directionality, the new model also has the ability to predict the irregularity of the rippled seabed. A comparison of the 2-D and existing time-dependent models is carried out using both synthetic and field ripple data that consist of time series representing a variety of wave-forcing conditions. Under strong wave forcing with no orientation changes, the 2-D model predicts ripple wavelength and orientations that agree with those of existing models. During periods of change in wave directions, the 2-D model predicts a significantly smaller ripple height during ripple reorientation. Under weaker energy flows, the 2-D model yields improved estimates especially for relict ripple geometry. In addition, the 2-D model’s spectrum yields a prediction of the seabed irregularity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Amos CL, Bowden AJ, Huntley DA, Lewis FM (1988) Ripple generation under the combined influences of waves and currents on the Canadian continental shelf. Cont Shelf Res 8:1129–1153

    Article  Google Scholar 

  • Andersen KH (2001) A particle model of rolling grain ripples under waves. Phys Fluids 13:58–64

    Article  Google Scholar 

  • Ardhuin F, O’Reilly WC, Herbers THC, Jessen PF (2003) Swell transformation across the continental shelf. Part I: attenuation and directional broadening. J Phys Oceanogr 33:1921–1939

    Article  Google Scholar 

  • Barrantes AI, Madsen OS (2000) Near-bottom flow and flow resistance for currents obliquely incident to two-dimensional roughness elements. J Geophys Res 105(C11):26,253–26,264

    Article  Google Scholar 

  • Blondeaux P (1990) Sand ripples under sea waves. Part 1. Ripple formation. J Fluid Mech 218(1):17

    Google Scholar 

  • Boyd R, Forbes DL, Heffler DE (1988) Time-sequence observations of wave-formed sand ripples on an ocean shoreface. Sedimentology 35:449–464. doi:10.1111/j.1365-3091.1988.tb00997.x

    Article  Google Scholar 

  • Davis JP, Walker DJ, Townsend M, Young IR (2004) Wave-formed sediment ripples: transient analysis of ripple spectral development. J Geophys Res 109, C07020. doi:10.1029/2004JC002307

    Google Scholar 

  • Cheng NS (2002) Exponential formula for bedload transport. J Hydraul Eng 128:942. doi:10.1061/(ASCE)0733-9429(2002)128:10(942)

    Article  Google Scholar 

  • Faraci C, Foti E (2002) Geometry, migration and evolution of small-scale bedforms generated by regular and irregular waves. Coastal Eng 47(1):35–52. doi:10.1016/S0378-3839(02)00097-2

    Article  Google Scholar 

  • Fernandez-Luque R, van Beek R (1976) Erosion and transport of bedload sediment. J Hyd Res 14(2)

  • Goldstein EB, Coco G, Murray AB (2013) Prediction of wave ripple characteristics using genetic programming. Cont Shelf Res 71:1–15

    Article  Google Scholar 

  • Grant WD, Madsen OS (1982) Movable bed roughness in unsteady oscillatory flow. J Geophys Res 87(C1):469–481. doi:10.1029/JC087iC01p00469

    Article  Google Scholar 

  • Grant WD, Madsen OS (1986) The continental-shelf bottom boundary layer. Annu Rev Fluid Mech 18(1):265–305. doi:10.1146/annurev.fl.18.010186.001405

    Article  Google Scholar 

  • Grasmeijer BT, Kleinhans MG (2004) Observed and predicted bed forms and their effect on suspended sand concentrations. Coastal Eng 51(5):351–371. doi:10.1016/j.coastaleng.2004.05.001

    Article  Google Scholar 

  • Hanes DM, Alymov V, Chang YS, Jette C (2001) Wave‐formed sand ripples at Duck, North Carolina. J Geophys Res 106(C10):22575–22592. doi:10.1029/2000JC000337

    Article  Google Scholar 

  • Hay AE (2008) Near-bed turbulence and relict waveformed sand ripples: observations from the inner shelf. J Geophys Res 113, C04040. doi:10.1029/2006JC004013

    Google Scholar 

  • Hay AE (2011) Geometric bed roughness and the bed state storm cycle. J Geophys Res Oceans 116, C04017. doi:10.1029/2010JC006687

    Article  Google Scholar 

  • Huntley DA, Coco G, Bryan KR, Brad Murray A (2008) Influence of “defects” on sorted bedform dynamics. Geophys Res Lett 35, L02601. doi:10.1029/2007GL030512

    Article  Google Scholar 

  • Inman DL (1957) Wave-generated ripples in nearshore sands (No. TM-100), Scripps Institution of Oceanography, La Jolla, CA, United States

  • Jarno-Druaux A, Brossard J, Marin F (2004) Dynamical evolution of ripples in a wave channel. Eur J Mech B/Fluids 23:695–708

    Article  Google Scholar 

  • Jonsson IG (1966) Wave boundary layers and friction factors. Proc. Coastal Eng., 1(10), Tokyo, Japan, doi:10.9753/icce.v10

  • Khelifa A, Ouellet Y (2000) Prediction of sand ripple geometry under waves and currents. J Waterw Port Coast Ocean Eng 126(1):14–22

  • Kobayashi N, Madsen OS (1985) Turbulent flows over a wavy bed. J Geophys Res: Oceans (1978–2012) 90(C4):7323–7331

    Article  Google Scholar 

  • Lacy JR, Rubin DM, Ikeda H, Mokudai K, Hanes DM (2007) Bed forms created by simulated waves and currents in a large flume. J Geophys Res 112, C10018. doi:10.1029/2006JC003942

    Article  Google Scholar 

  • Laursen EM (1958) The total sediment load of streams. J Hydraul Div: Proc Am Soc Civ Eng 84(HY 1 paper 1530):1–36

    Google Scholar 

  • Madsen OS, Negara AS, Lim KY, and Cheong HF (2010) Near-bottom flow characteristics of currents at arbitrary angle to 2-D ripples. Proceedings of the 32nd International Conference on Coastal Engineering, Shanghai, China, Edited by J. McKee Smith and P. Lynett

  • Maier I, Hay AE (2009) Occurrence and orientation of anorbital ripples in near-shore sands. J Geophys Res Oceans 114, F04022. doi:10.1029/2008JF001126

    Article  Google Scholar 

  • Meyer F (1994) Topographic distance and watershed lines. Signal Process 38(1):113–125

    Article  Google Scholar 

  • Meyer-Peter E, and Müller R (1948) Formulas for bed-load transport. In Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research, Delft: International Association of Hydraulic Research, pp. 39–64.

  • Miller MC, Komar PD (1980) A field investigation of the relationship between oscillation ripple spacing and the near-bottom water orbital motions. J Sediment Res 50(1):183–191

    Article  Google Scholar 

  • Mogridge GR, and Kamphuis JW (1972) Experiments on bed form generation by wave action. Proc. Coastal Eng., 1(13), doi:doi:10.9753/icce.v13

  • Nelson TR, Voulgaris G (2014) Temporal and spatial evolution of wave-induced ripple geometry: regular versus irregular ripples. J Geophys Res Oceans 119:664–688. doi:10.1002/2013JC009020

    Article  Google Scholar 

  • Nelson TR, Voulgaris G, Traykovski P (2013) Predicting wave-induced ripple equilibrium geometry. J Geophys Res Oceans 118:3202–3220. doi:10.1002/jgrc.20241

    Article  Google Scholar 

  • Nielsen P (1981) Dynamics and geometry of wave‐generated ripples. J Geophys Res 86(C7):6467–6472. doi:10.1029/JC086iC07p06467

    Article  Google Scholar 

  • Nielsen P (1992) Coastal bottom boundary layers and sediment transport. World Sci, Singapore

    Google Scholar 

  • O’Donoghue T, Doucette J, Van der Werf J, Ribberink J (2005) Flow tunnel measurements of fullscale ripples in oscillatory flow. SANDPIT: Sans Transport and Morphology of Offshore Mining Pits’, Aqua Publications

  • Powell H, Voulgaris G, Collins MB, and Bastos AC (2000) Wave-current interaction over bedforms: observations and model predictions, Marine Sandwave Dynamics, March 23–24 2000, Lille 1 University, Lille, France, edited by Trentesaux, A. and Garlan, T., pp. 153–160

  • Ribberink JS (1998) Bed-load transport for steady flows and unsteady oscillatory flows. Coast Eng 34(1):59–82

    Article  Google Scholar 

  • Schwab WC, Gayes PT, Morton RA, Driscoll NW, BaldwinWE, Barnhardt WA, Denny JF, Harris MS, Katuna MP, Putney TR, Voulgaris G, Warner JC, and Wright EE (2009) Coastal change along the shore of Northeastern South Carolina—The South Carolina Coastal Erosion Study. Edited by W. A. Barnhardt USGS Circular 1339, 77 pp

  • Shields A (1936) Application of similarity principles and turbulence research to bed-load movement, Communications of the Prussian Laboratory of Hydraulics, 26. Prussian Laboratory of Hydraulics, Berlin, Germany

    Google Scholar 

  • Sleath JFA (1984) Sea bed mechanics, Wiley

  • Soulsby RL (1995) Bed shear-stresses due to combined waves and currents. In: Advances in Coastal Morphodynamics, Eds: Stive, M. J. F., De Vriend, H. J. Fredsøe, J., Hamm, L., Soulsby, R. L., Teisson, C., Winterwerp, J. C., pp 4–20 to 4–23, Delft Hydraulics, Delft, NL

  • Soulsby RL, and Whitehouse RJS (2005) Prediction of ripple properties in shelf seas, Mark 2 predictor for time evolution, Tech. Rep.TR 154 Release 2.0, HR Wallingford, Wallingford, U. K

  • Soulsby RL, Whitehouse RJS, Marten KV (2012) Prediction of time-evolving sand ripples in shelf seas. Cont Shelf Res 38:47–62. doi:10.1016/j.csr.2012.02.016

    Article  Google Scholar 

  • Styles R, Glenn SM (2002) Modeling bottom roughness in the presence of wave-generated ripples. J Geophys Res 107(C8):3110. doi:10.1029/2001JC000864

    Article  Google Scholar 

  • Sullivan CM, Warner JC, Martini MA, Voulgaris G, Work PA, Haas KA, and Hanes D (2006) South Carolina Coastal Erosion Study, Data Report for Observations, October 2003–April 2004, USGS Open-File Report 2005–1429

  • Testik FY, Voropayev SI, and Fernando HJS (2005) Adjustment of sand ripples under changing water waves, Physics of Fluids, 17, 072104–1:8

  • Traykovski P (2007) Observations of wave orbital scale ripples and a nonequilibrium time-dependent model, J. Geophys. Res., 112(C06026), doi:10.1029/2006JC003811

  • Traykovski P, Hay AE, Irish JD, Lynch JF (1999) Geometry, migration, and evolution of wave orbital ripples at LEO-15. J Geophys Res 104(C1):1505–1524. doi:10.1029/1998JC900026

    Article  Google Scholar 

  • Voulgaris G, and Morin JP (2008) A long-term real time sea bed morphology evolution system in the South Atlantic Bight, In Current Measurement Technology, 2008. CMTC 2008. IEEE/OES 9th Working Conference, IEEE., pp. 71–79, doi:10.1109/CCM.2008.4480847

  • Warner JC, Armstrong B, Sylvester CS, Voulgaris G, Nelson T, Schwab WC, Denny JF (2012) Storm-induced inner-continental shelf circulation and sediment transport: Long Bay, South Carolina. Cont Shelf Res 42:51–63

    Article  Google Scholar 

  • Werner BT, Kocurek G (1997) Bedform dynamics: does the tail wag the dog? Geology 25(9):771–774

    Article  Google Scholar 

  • Whitehouse RJS (1998) Scour at marine structures, scour at marine structures: a manual for practical applications. Telford, London, 198 pp

    Book  Google Scholar 

  • Wiberg PL, Harris CK (1994) Ripple geometry in wave-dominated environments. J Geophys Res 99(C1):775–789. doi:10.1029/93JC02726

    Article  Google Scholar 

  • Wiberg PL, Dungan Smith J (1989) Model for calculating bed load transport of sediment. J Hydraul Eng 115(1):101–123

    Article  Google Scholar 

  • Yalin S, and Russell R (1962) Similarity in sediment transport due to waves, Proceedings of the 8th International Conference on Coastal Engineering, Mexico City, Mexico, doi:10.9753/icce.v8.12

Download references

Acknowledgments

Financial support for this work was provided by the National Science Foundation (NSF Awards OCE-0,451,989 and OCE −0,535,893) and the cooperative agreement between the US Geological Survey and the University of South Carolina (the Carolinas Coastal Change Project). The GA dataset was collected with the assistance of the Skidaway Institute of Oceanography and the crew of the R/V Savannah who assisted in the deployment and recovery of the instrumentation. The LB dataset was collected with assistance from the US Geological Survey consisting of three cruises aboard the R/V Dan Moore.

Author information

Author notes

  1. Timothy R. Nelson

    Present address: US Geological Survey, St. Petersburg Coastal and Marine Science Center, 600 4th Street South, St. Petersburg, FL, 33701, USA

Authors and Affiliations

  1. Department of Earth and Ocean Sciences, College of Arts and Science, University of South Carolina, Columbia, SC, 29208, USA

    Timothy R. Nelson

  2. Marine Science Program, College of Arts and Science, University of South Carolina, Columbia, SC, 29208, USA

    George Voulgaris

Authors
  1. Timothy R. Nelson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. George Voulgaris
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Timothy R. Nelson.

Additional information

Responsible Editor: Bruno Castelle

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nelson, T.R., Voulgaris, G. A spectral model for estimating temporal and spatial evolution of rippled seabeds. Ocean Dynamics 65, 155–171 (2015). https://doi.org/10.1007/s10236-014-0801-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10236-014-0801-y

Keywords

Search

Navigation