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Experimental and numerical study on the shear velocity distribution along one or two dunes in tandem

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Abstract

This paper investigates, experimentally and numerically, the shear velocity distribution along a single transverse dune and along two closely spaced dunes, analyzing the flow effects of one dune upon the other. The paper focuses on two-dimensional models simulating transverse sand dunes. The shape of the two pile geometries studied is described by sinusoidal curves, one having a maximum slope of \(32^{\circ }\) and the other \(27.6^{\circ }\), with leeward flow separation. The tests were carried out for two undisturbed wind speeds and the experimental data obtained through wind-tunnel modeling encompass flow visualization and shear-velocity results. A generally good agreement is observed between the experimental measurements and computational results. From the inquiry between shear velocity distributions and published eroded contours for the same geometries, it appears the Bagnold’s approach is insufficient in the prediction of threshold conditions in wake flows formed in the dune’s leeward side.

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References

  1. van Dijk PM, Arens SM, van Boxel JH (1999) Aeolian processes across transverse dunes. II: Modeling the sediment transport and profile development. Earth Surf Proc Landf 24:319–333. doi:10.1002/(SICI)1096-9837(199904)24:4<319:AID-ESP963>3.0.CO;2-M

  2. Stam JMT (1997) On the modelling of two-dimensional aeolian dunes. Sedimentology 44:127–141. doi:10.1111/j.1365-3091.1997.tb00428.x

    Google Scholar 

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

  4. Bagnold RA (1941) The physics of blown sand and desert dunes. Methuen, London (reprinted 1954 1960, 2005. Dover, Mineola)

  5. Shields A (1936) Application of similarity principles and turbulence research to bed-load movement. In: Ott WP, van Uchelen JC (Translated) Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebe-bewegung. Mitteilungen der Preussischen Versuchsanstalt fur Wasserbau und Schiffbau, Berlin. California Institute of Technolgoy, W.M. Keck Laboratory for Hydraulics and Water Resources, Report No. 167

  6. Howard AD (1977) Effect of slope on the threshold of motion and its application to orientation of wind ripples. Geol Soc Am Bull 88:853–856. doi:10.1130/0016-7606(1977)88<853:EOSOTT>2.0.CO;2

  7. Cornforth DH (1964) Some experiments on the influence of strain conditions on the strength of sand. Géotechnique 14:143–167. doi:10.1680/geot.1964.14.2.143

    Article  Google Scholar 

  8. Bolton MD (1986) The strength and dilatancy of sands. Géotechnique 36:65–78. doi:10.1680/geot.1986.36.1.65

    Article  Google Scholar 

  9. Ferreira AD, Lambert RJ (2011) Numerical and wind tunnel modeling on the windbreak effectiveness to control the aeolian erosion of conical stockpiles. Environ Fluid Mech 11:61–76. doi:10.1007/s10652-010-9176-x

    Article  Google Scholar 

  10. Lancaster N (1995) Geomorphology of desert dunes. Routledge, London (reprinted 2005)

  11. Shao Y (2008) Physics and modelling of wind erosion. Atmospheric and oceanographic sciences library, 2nd edn, vol 37. Springer, Berlin

  12. Livingstone I, Wiggs GFS, Weaver CM (2007) Geomorphology of desert sand dunes: a review of recent progress. Earth-Sci Rev 80:239–257. doi:10.1016/j.earscirev.2006.09.004

    Article  Google Scholar 

  13. Ferreira AD, Fino MRM (2012) A wind tunnel study of wind erosion and profile reshaping of transverse sand piles in tandem. Geomorphology 139–140:230–241. doi:10.1016/j.geomorph.2011.10.024

    Article  Google Scholar 

  14. Wentworth CK (1922) A scale of grade and class terms for clastic sediments. J Geol 30:377–392. doi:10.1086/622910

    Article  Google Scholar 

  15. Dong Z, Liu X, Wang H, Wang X (2003) Aeolian sand transport: a wind tunnel model. Sediment Geol 161:71–83. doi:10.1016/S0037-0738(03)00396-2

    Article  Google Scholar 

  16. Irwin HPAH (1981) A simple omnidirectional sensor for wind-tunnel studies of pedestrian-level winds. J Wind Eng Ind Aerodyn 7:219–239. doi:10.1016/0167-6105(81)90051-9

    Article  Google Scholar 

  17. Ferreira AD, Silva M, Viegas D, Lopes A (1991) Wind tunnel simulation of the flow around two-dimensional hills. J Wind Eng Ind Aerodyn 38:109–122. doi:10.1016/0167-6105(91)90033-S

    Article  Google Scholar 

  18. Ansys (2010) http://ansys.com/Products/SimulationTechnology/FluidDynamics. Accessed 7 Jan 2013

  19. Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3:269–289. doi:10.1016/0045-7825(74)90029-2

    Article  Google Scholar 

  20. Nikuradse J (1933) Laws of flow in rough pipes. Strömungsgesetze in rauhen Rohren (Translation). VDI-Forschungsheft 361. Beilage zu “Forschung auf dem Gebiete des Ingenieurwesens” Ausgabe B Band 4

  21. Schlichting H (1987) Boundary-layer theory. McGraw-Hill, New York, NY

    Google Scholar 

  22. Finnigan JJ (1988) Air flow over complex terrain. In: Steffen WL, Denmead OT (eds) Flow and transport in the natural environment: advances and applications. Springer, Heidelberg, pp 183–229

    Chapter  Google Scholar 

  23. Sweet ML, Kocurek G (1990) An empirical model of aeolian dune lee-face airflow. Sedimentology 37:1023–1038. doi:10.1111/j.1365-3091.1990.tb01843.x

    Article  Google Scholar 

  24. Schatz V, Herrmann HJ (2006) Flow separation in the lee side of transverse dunes: a numerical investigation. Geomorphology 81:207–216. doi:10.1016/j.geomorph.2006.04.009

    Article  Google Scholar 

  25. Herrmann HJ, Andrade JS Jr, Schatz V, Sauermann G, Parteli EJR (2005) Calculation of the separation streamlines of barchans and transverse dunes. Physica A 357:44–49. doi:10.1016/j.physa.2005.05.057

    Article  Google Scholar 

  26. Walker IJ, Nickling WG (2002) Dynamics of secondary airflow and sediment transport over and in the lee of transverse dunes. Prog Phys Geogr 26:47–75. doi:10.1191/0309133302pp325ra

    Google Scholar 

  27. Durán O, Herrmann H (2006) Modelling of saturated sand flux. J Stat Mech Theory Exp P07011. doi:10.1088/1742-5468/2006/07/P07011

  28. Andreotti B (2004) A two species model of aeolian sand transport. J Fluid Mech 510:47–70. doi:10.1017/s0022112004009073

    Article  Google Scholar 

  29. Pähtz T, Kok JF, Herrmann HJ (2012) The apparent roughness of a sand surface blown by wind from an analytical model of saltation. New J Phys 14:043035. doi:10.1088/1367-2630/14/4/043035

    Article  Google Scholar 

  30. Poggi D, Katul GG, Albertson JD, Ridolfid L (2007) An experimental investigation of turbulent flows over a hilly surface. Phys Fluids 19:036601. doi:10.1063/1.2565528

    Article  Google Scholar 

  31. Wiggs GFS, Livingstone I, Warren A (1996) The role of streamline curvature in sand dune dynamics: evidence from field and wind tunnel measurements. Geomorphology 17:29–46. doi:10.1016/0169-555x(95)00093-k

    Article  Google Scholar 

  32. Walker IJ, Nickling WG (2003) Simulation and measurement of surface shear stress over isolated and closely spaced transverse dunes in a wind tunnel. Earth Surf Process Landf 28:1111–1124. doi:10.1002/esp.520

    Article  Google Scholar 

  33. Lyles L, Krauss RK (1971) Threshold velocities and initial particle motion as influenced by air turbulence. Trans ASAE 14:563–566

    Article  Google Scholar 

  34. Vollmer S, Kleinhans MG (2007) Predicting incipient motion, including the effect of turbulent pressure fluctuations in the bed. Water Resour Res 43:1–16. doi:10.1029/2006WR004919

    Article  Google Scholar 

  35. McLean SR, Smith JD (1986) A model for flow over two-dimensional bed forms. J Hydraul Eng 112:300–317. doi:10.1061/(ASCE)0733-9429(1986)112:4(300)

    Google Scholar 

  36. Kroy K (2002) Minimal model for aeolian sand dunes. Phys Rev E 66:031302–1-031302-18. doi:10.1103/PhysRevE.66.031302

    Google Scholar 

  37. Kroy K, Sauermann G, Herrmann HJ (2002) Minimal model for sand dunes. Phys Rev Lett 88:054301. doi:10.1103/PhysRevLett.88.054301

    Google Scholar 

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Acknowledgments

The authors are very thankful to Juanita and Alan Atkins for the careful proofreading of the manuscript. The contribution made by Ana Ramos is also acknowledged.

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Correspondence to Almerindo D. Ferreira.

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Ferreira, A.D., Pinheiro, S.R. & Francisco, S.C. Experimental and numerical study on the shear velocity distribution along one or two dunes in tandem. Environ Fluid Mech 13, 557–570 (2013). https://doi.org/10.1007/s10652-013-9282-7

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