Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T00:42:38.078Z Has data issue: false hasContentIssue false
  • English
  • Français

Subaqueous barchan dunes in turbulent shear flow. Part 2. Fluid flow

Published online by Cambridge University Press:  24 January 2012

F. Charru  and
E. M. Franklin
F. Charru*
Affiliation:
Université de Toulouse – Institut de Mécanique des Fluides de Toulouse – CNRS, Allée C. Soula, 31400 Toulouse, France
E. M. Franklin
Affiliation:
Université de Toulouse – Institut de Mécanique des Fluides de Toulouse – CNRS, Allée C. Soula, 31400 Toulouse, France
*
†Email address for correspondence: Francois.Charru@imft.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We report an experimental study of the turbulent flow above a barchan dune in a channel, from particle image velocimetry measurements, for Reynolds numbers ranging from 9000, just below the threshold for particle motion, up to 24 000, where the dune moves. Two calculations of the speed-up over the dune are compared, the usual ‘same-elevation’ and the more relevant ‘Lagrangian’, showing that the latter is smaller by a factor of two. The two-layer structure of the flow disturbance – an essentially inviscid outer layer and a turbulent inner layer of thickness – is assessed. In the outer layer, streamline curvature is shown to be responsible for half of the Lagrangian speed-up, from the comparison of the velocity measurements with two Bernoulli calculations. In the inner layer, detailed measurements of the velocity and stresses are provided, down to , and the momentum budget is discussed. The Reynolds shear stress decreases monotonically towards the dune surface, according to the standard mixing-length closure, whereas the total shear stress increases strongly in the viscous sublayer. Along the dune surface, the shear stress increases up to the crest where it reaches twice its unperturbed value. A good estimate of the surface stress is provided by a parabolic fit of the inner velocity profile matching the outer flow at . Doubling the Reynolds number, the surface shear stress and the speed-up decrease by ∼30 %. The implications of these results on the dune motion, presented in Part 1 of this study (Franklin & Charru, J. Fluid Mech., vol. 675, 2011, pp. 199–222), are finally discussed.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 694 , 10 March 2012 , pp. 131 - 154
Copyright
Copyright © Cambridge University Press 2012

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

1. Abrams, J. & Hanratty, T. J. 1985 Relaxation effects observed for turbulent flow over a wavy surface. J. Fluid Mech. 151, 443–455.CrossRefGoogle Scholar
2. Andreotti, B., Claudin, P. H. & Douady, S. 2002 Selection of dune shapes and velocities. Part 2. A two-dimensional modelling. Eur. Phys. J. B 28, 341–352.Google Scholar
3. Athanassiadou, M. & Castro, I. P. 2001 Neutral flow over a series of rough hills: a laboratory experiment. Boundary-Layer Meteorol. 101, 1–30.Google Scholar
4. Belcher, S. E. & Hunt, J. C. R. 1998 Turbulent flow over hills and waves. Annu. Rev. Fluid Mech. 30, 507–538.Google Scholar
5. Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205.Google Scholar
6. Best, J. 2005 The fluid dynamics of river dunes: a review and some future research directions. J. Geophys. Res. 110, F04S02.Google Scholar
7. van Boxel, J. H., Arens, S. M. & van Dijk, P. M. 1999 Aeolian processes across transverse dunes. Part I. Modelling the air flow. Earth Surf. Process. Landf. 24, 255–270.Google Scholar
8. Britter, R. E., Hunt, J. C. R. & Richards, K. J. 1981 Air flow over a two-dimensional hill: studies of velocity speed-up, roughness effects and turbulence. Q. J. R. Meteorol. Soc. 107, 91–110.Google Scholar
9. Buckles, J., Hanratty, T. J. & Adrian, R. J. 1984 Turbulent flow over large-amplitude wavy surfaces. J. Fluid Mech. 140, 27–44.Google Scholar
10. Colombini, M. & Stocchino, A. 2008 Finite-amplitude river dunes. J. Fluid Mech. 611, 283–306.Google Scholar
11. Colombini, M. & Stocchino, A. 2011 Ripple and dune formation in rivers. J. Fluid Mech. 673, 121–131.CrossRefGoogle Scholar
12. Davidson, P. A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
13. De Angelis, V., Lombardi, P. & Banerjee, S. 1997 Direct numerical simulation of turbulent flow over a wavy wall. Phys. Fluids 9, 2429–2442.Google Scholar
14. Finnigan, J. J. & Belcher, S. E. 2004 Flow over a hill covered with a plant canopy. Q. J. R. Meteorol. Soc. 130, 1–29.CrossRefGoogle Scholar
15. Finnigan, J. J., Raupach, M. R., Bradley, E. F. & Aldis, G. K. 1990 A wind tunnel study of turbulent flow over a two-dimensional ridge. Boundary-Layer Meteorol. 50, 277–317.Google Scholar
16. Fourrière, A., Claudin, P. & Andreotti, B. 2010 Bedforms in a turbulent stream: formation of ripples by primary linear instability and of dunes by nonlinear pattern coarsening. J. Fluid Mech. 649, 287–328.CrossRefGoogle Scholar
17. Franklin, E. M. & Charru, F. 2011 Subaqueous barchan dunes in turbulent shear flow. Part 1. Dune motion. J. Fluid Mech. 675, 199–222.CrossRefGoogle Scholar
18. Gong, W. & Ibbetson, A. 1989 A wind tunnel study of turbulent flow over model hills. Boundary-Layer Meteorol. 49, 113–148.CrossRefGoogle Scholar
19. Gong, W., Taylor, P. A. & Dörnbrack, A. 1996 Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves. J. Fluid Mech. 312, 1–37.Google Scholar
20. Henn, D. S. & Sykes, R. I. 1999 Large-eddy simulation of flow over wavy surfaces. J. Fluid Mech. 383, 75–112.CrossRefGoogle Scholar
21. Hunt, J. C. R., Eames, I. & Westerweel, J. 2006 Mechanics of inhomogeneous turbulence and interfacial layers. J. Fluid Mech. 554, 499–519.Google Scholar
22. Hunt, J. C. R., Leibovich, S. & Richards, K. J. 1988 Turbulent shear flows over low hills. Q. J. R. Meteorol. Soc. 114, 1435–1470.Google Scholar
23. Jackson, P. S. & Hunt, J. C. R. 1975 Turbulent wind flow over a low hill. Q. J. R. Meteorol. Soc. 101, 929–955.Google Scholar
24. Kostaschuk, R., Villard, P. & Best, J. 2004 Measuring velocity and shear stress over dunes with acoustic Doppler profiler. J. Hydraul. Engng ASCE 130, 932–936.CrossRefGoogle Scholar
25. Kroy, K., Sauermann, G. & Herrmann, H. J. 2002 Minimal model for aeolian sand dunes. Phys. Rev. E 66, 031302.Google Scholar
26. Livingstone, I., Wiggs, G. F. S. & Weaver, C. M. 2007 Geomorphology of desert sand dunes: a review of recent progress. Earth-Sci. Rev. 80, 239–257.CrossRefGoogle Scholar
27. Mason, P. J. & Sykes, R. I. 1979 Flow over an isolated hill of moderate slope. Q. J. R. Meteorol. Soc. 105, 383–395.Google Scholar
28. Panton, R. L. 2007 Composite asymptotic expansions and scaling wall turbulence. Phil. Trans. R. Soc. Lond. A 365, 733–754.Google Scholar
29. Poggi, D., Katul, G. G., Albertson, J. D. & Ridolfi, L. 2007 An experimental investigation of turbulent flow over a hilly surface. Phys. Fluids 19, 036601.Google Scholar
30. Richards, K. J. 1980 The formation of ripples and dunes on an erodible bed. J. Fluid Mech. 99, 597–618.Google Scholar
31. Ross, A. N., Arnold, S., Vosper, S. B., Mobbs, S., Dixon, N. & Robins, A. G. 2004 A comparison of wind-tunnel experiments and numerical simulations of neutral and stratified flow over a hill. Boundary-Layer Meteorol. 113, 427–459.CrossRefGoogle Scholar
32. Sauermann, G., Andrade, J. S., Maia, L. P., Costa, U. M. S., Araújo, A. D. & Herrmann, H. J. 2003 Wind velocity and sand transport on a barchan dune. Geomorphology 54, 245–255.Google Scholar
33. Scheichl, B., Kluwick, A. & Smith, F. T. 2011 Break-away separation for high turbulence intensity and large Reynolds number. J. Fluid Mech. 670, 260–300.CrossRefGoogle Scholar
34. Schlichting, H. & Gesten, K. 2000 Boundary-Layer Theory. Springer.Google Scholar
35. Smith, J. D. & McLean, S. R. 1977 Spatially averaged flow over a wavy surface. J. Geophys. Res. 82, 1735–1746.Google Scholar
36. Sumer, B. & Bakioglu, M. 1984 On the formation of ripples on an erodible bed. J. Fluid Mech. 144, 177–190.Google Scholar
37. Sykes, R. I. 1980 An asymptotic theory of incompressible turbulent boundary-layer flow over a small hump. J. Fluid Mech. 101, 647–670.Google Scholar
38. Taylor, P. A., Mason, P. J. & Bradley, E. F. 1987 Boundary-layer flow over low hills. A review. Boundary-Layer Meteorol. 39, 107–132.CrossRefGoogle Scholar
39. Teunissen, H. W., Shokr, M. E., Bowen, A. J., Wood, C. J. & Green, D. W. R. 1987 The Askervein Hill project: wind-tunnel simulations at three length scales. Boundary-Layer Meteorol. 40, 1–29.CrossRefGoogle Scholar
40. Walker, I. J. & Nickling, W. G. 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.Google Scholar
41. Weng, W. 1997 Stably stratified boundary-layer flow over low hills: a comparison of model results and field data. Boundary-Layer Meteorol. 85, 223–241.Google Scholar
42. Weng, W. S., Hunt, J. C. R., Carruthers, D. J., Warren, A., Wiggs, G. F. S., Livingstone, I. & Castro, I. 1991 Air flow and sand transport over sand-dunes. Acta Mechanica Suppl. 2, 1–22.Google Scholar
43. Wiggs, G. F. S., 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.Google Scholar
44. Yue, W., Lin, C.-L. & Patel, V. C. 2006 Large-eddy simulation of turbulent flow over a fixed two-dimensional dune. J. Hydraul. Engng ASCE 132, 643–651.CrossRefGoogle Scholar
45. Zeman, O. & Jensen, N. O. 1987 Modification of turbulence characteristics in flow over hills. Q. J. R. Meteorol. Soc. 113, 55–80.Google Scholar
Supplementary material: PDF

Charru and Franklin supplementary material

Supplementary figures

Download Charru and Franklin supplementary material(PDF)
PDF 177.2 KB