A Surface Model for Aeolian Dune Topography

Abstract

A surface model for aeolian bedform topography is adapted from a surface model of subaqueous bedform topography. The aeolian bedform surface model is developed using a uniform grid with a cell-centered finite volume approximation of the sediment continuity equation. The resulting modeling framework approximates the dynamic motions of aeolian bedform topography driven by bedform field boundary conditions. The numerical model is applied to simulate bedforms growing from unimodal and bimodal transport regimes from both a fixed elevation (sediment source area) and within a domain with fully periodic boundary conditions. The rates at which modeled aeolian bedforms grow and morphologically mature are sensitive to the chosen boundary conditions. Video files of model simulations and source code for the presented aeolian bedform surface modeling framework are available in supplemental materials. The aeolian bedform surface model code is malleable and readily modified for exploratory study of dynamic bedform topography that inherits morphological traits from aeolian bedform field boundary conditions.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

References

  1. Baas JH (1994) A flume study on the development and equilibrium morphology of current ripples in very fine sand. Sedimentology 41(2):185–209. doi:10.1111/j.1365-3091.1994.tb01400.x

    Article  Google Scholar 

  2. Bagnold RA (1941) The physics of blown sand and desert dunes. Methuen, London

    Google Scholar 

  3. Barabási A-L (1995) Fractal concepts in surface growth. Cambridge University Press, Cambridge. doi:10.1017/CBO9780511599798

    Google Scholar 

  4. Diniega S (2010) Modeling aeolian dune and dune field evolution. Dissertation, The University of Arizona

  5. du Pont SC, Narteau C, Gao X (2014) Two modes for dune orientation. Geology 42(9):743–746. doi:10.1130/G35657.1

    Google Scholar 

  6. Eastwood EN, Kocurek G, Mohrig D, Swanson T (2012) Methodology for reconstructing wind direction, wind speed and duration of wind events from aeolian cross-strata. J Geophys Res Earth 117(F3):F03035. doi:10.1029/2012jf002368

    Google Scholar 

  7. Ewing RC, Kocurek G, Lake LW (2006) Pattern analysis of dune-field parameters. Earth Surf Process Landf 31(9):1176–1191. doi:10.1002/esp.1312

    Article  Google Scholar 

  8. Exner FM (1925) Über die Wechselwirkung zwischen Wasser und Geschiebe in Flüssen (in German). Sitz Acad Wiss Wien Math Naturwiss Abt 2a 134:165–203

  9. Hersen P (2004) On the crescentic shape of barchan dunes. Eu Phys J B Condens Matter Complex Syst 37(4):507–514. doi:10.1140/epjb/e2004-00087-y

    Article  Google Scholar 

  10. Jackson P, Hunt J (1975) Turbulent wind flow over a low hill. Q J R Meteorol Soc 101(430):929–955. doi:10.1002/qj.49710143015

    Article  Google Scholar 

  11. Jerolmack DJ, Ewing RC, Falcini F, Martin RL, Masteller C, Phillips C, Reitz MD, Buynevich I (2012) Internal boundary layer model for the evolution of desert dune fields. Nat Geosci 5(3):206–209. doi:10.1038/ngeo1381

    Article  Google Scholar 

  12. Jerolmack DJ, Mohrig D (2005) A unified model for subaqueous bed form dynamics. Water Resour Res 41(12):W12421. doi:10.1029/2005WR004329

    Article  Google Scholar 

  13. Khosronejad A, Sotiropoulos F (2014) Numerical simulation of sand waves in a turbulent open channel flow. J Fluid Mech 753:150–216. doi:10.1017/jfm.2014.335

    Article  Google Scholar 

  14. Kocurek G, Ewing RC, Mohrig D (2010) How do bedform patterns arise? New views on the role of bedform interactions within a set of boundary conditions. Earth Surf Process Landf 35(1):51–63. doi:10.1002/esp.1913

    Article  Google Scholar 

  15. Kocurek G, Townsley M, Yeh E, Havholm K, Sweet M (1992) Dune and dune-field development on Padre Island, Texas, with implications for interdune deposition and water-table-controlled accumulation. J Sediment Res 62(4):

  16. Kroy K, Sauermann G, Herrmann HJ (2002) Minimal model for aeolian sand dunes. Phys Rev E 66(3):031302. doi:10.1103/physreve.66.031302

    Article  Google Scholar 

  17. Lancaster N, Nickling W, Neuman CM, Wyatt V (1996) Sediment flux and airflow on the stoss slope of a barchan dune. Geomorphology 17(1):55–62. doi:10.1016/0169-555X(95)00095-M

    Article  Google Scholar 

  18. Meyer-Peter E, Müller R (1948) Formulas for bed-load transport. Proceedings of the 2nd meeting. IAHR, Stockholm, pp 39–64

  19. Murray AB, Thieler ER (2004) A new hypothesis and exploratory model for the formation of large-scale inner-shelf sediment sorting and “rippled scour depressions”. Cont Shelf Res 24(3):295–315. doi:10.1016/j.csr.2003.11.001

    Article  Google Scholar 

  20. Murray AB (2007) Reducing model complexity for explanation and prediction. Geomorphology 90(3):178–191. doi:10.1016/j.geomorph.2006.10.020

    Article  Google Scholar 

  21. Ping L, Narteau C, Dong Z, Zhang Z, Courrech du Pont S (2014) Emergence of oblique dunes in a landscape-scale experiment. Nat Geosci 7(2):99–103. doi:10.1038/ngeo2047

    Article  Google Scholar 

  22. Press WH, Teukolsky S, Vetterling W, Flannery B (1988) Numerical recipes in C. Cambridge University Press, Cambridge

    Google Scholar 

  23. Rubin DM, Hunter RE (1987) Bedform alignment in directionally varying flows. Science 237(4812):276–278. doi:10.1126/science.237.4812.276

    Article  Google Scholar 

  24. Werner BT (1995) Eolian dunes: computer simulations and attractor interpretation. Geology 23(12):1107–1110. doi:10.1130/0091-7613(1995)023<1107:EDCSAA>2.3.CO;2

    Article  Google Scholar 

Download references

Acknowledgments

Caroline Hern generously provided continuous feedback and conceptual steering for this project. We thank Matthew Wolinsky and Mauricio Perillo for helpful guidance and suggestions concerning code development. The authors are grateful for the thoughts and comments provided by Roussos Dimitrakopoulos and Brad Murray during the revision of this manuscript. Funding for this work was provided by Shell International Exploration & Production Inc. This work does not reflect the views of Shell International Exploration & Production Inc.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Travis Swanson.

Electronic supplementary material

Appendix: Fitted Parameters

Appendix: Fitted Parameters

See Table 3.

Table 3 Fit parameters

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Swanson, T., Mohrig, D., Kocurek, G. et al. A Surface Model for Aeolian Dune Topography. Math Geosci 49, 635–655 (2017). https://doi.org/10.1007/s11004-016-9654-x

Download citation

Keywords

  • Aeolian
  • Dune
  • Bedform
  • Exploratory numerical model