Competition between kinematic and dynamic waves in floods on steep slopes

Journal of Fluid Mechanics

Volumn 645, Issue , 2010, Pages 375-409

  Bohorquez, P ^a,b  

^a EPFL   (Switzerland)

^b UNIVERSITY OF JAÉN   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

DECAY (ORGANIC); EQUATIONS OF MOTION; FLOODS; FROUDE NUMBER; KINEMATICS; NUMERICAL MODELS;

ASYMPTOTIC SOLUTIONS; ASYMPTOTIC THEORIES; MULTIPLE-SCALE ANALYSIS; PLANE-PARALLEL FLOW; SHALLOW WATER EQUATIONS; SMALL DISTURBANCES; STABILITY ANALYSIS; TIME-DEPENDENT CHARACTERISTICS;

PARALLEL FLOW;

BOTTOM STRESS; DAM FAILURE; FLOOD WAVE; FLOW STABILITY; FROUDE NUMBER; KINEMATICS; NUMERICAL MODEL; SHALLOW-WATER EQUATION; SLOPE;

EID: 77952424485     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211200999276X     Document Type: Article

References (60)

1. Ancey, C. 2007 Plasticity and geophysical flows: a review. J. Non-Newton. Fluid Mech. 142, 4-35.
2. Ancey, C., Cochard, S. & Andreini, N. 2009 The dam-break problem for viscous fluids in the high-capillary-number limit. J. Fluid Mech. 624, 1-22.
3. Ancey, C., Iverson, R. M., Rentschler, M. & Denlinger, R. P. 2008 An exact solution for ideal dam-break floods on steep slopes. Water Resour. Res. 44, W01430.
4. Arattano, M. & Savage, W. Z. 1994 Modelling debris flows as kinematic waves. Bull. Intl Assoc. Engng Geol. 49, 3-13.
5. Balmforth, N. J. & Mandre, S. 2004 Dynamics of roll waves. J. Fluid Mech. 514, 1-33.
6. Blayo, E. & Debreu, L. 2005 Revisiting open boundary conditions from the point of view of characteristic variables. Ocean Model. 9, 231-252.
7. Bohorquez, P. 2008 On the wavefront shape and the advancing of the wetting front of a dam-break flood over an inclined plane of arbitrary bottom slope. Roll waves in floods on inclines. In Numerical Modelling of Hydrodynamics for Water Resources (ed. P. Garcia-Navarro &E. Playan), pp. 355-366. Taylor and Francis.
8. Bohorquez, P. & Darby, S. E. 2008 The use of one-and two-dimensional hydraulic modelling to reconstruct a glacial outburst flood in a steep Alpine valley. J. Hydrol. 361, 240-261.
9. Bohorquez, P. & Fernandez-Feria, R. 2008 Transport of suspended sediment under the dam-break flow on an inclined plane bed of arbitrary slope. Hydrol. Process. 22 (14), 2615-2633.
10. Brauner, N. & Maron, D. M. 1982 Characteristics of inclined thin films, waviness and the associated mass transfer. Intl J. Heat Mass Transfer 25 (1), 99-110.
11. Brock, R. R. 1969 Development of roll-wave trains in open channels. J. Hydraul. Div. 95, 1401-1427.
12. Brook, B. S., Falle, S. A. E. G. & Pedley, T. J. 1999 Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state. J. Fluid Mech. 396, 223-256.
13. Castro, M., Gallardo, J. M. & Parés, C. 2006 High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems. Math. Comput. 75, 1103-1134.
14. Castro, M., Gallardo, J. M. & Parés, C. 2008 Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes J. Comput. Phys. 227, 8107-8129.
15. Chang, H. C., Demekhin, E. A. & Kalaidin, E. 2000 Coherent structures, self-similarity, and universal roll wave coarsening dynamics. Phys. Fluids 12 (9), 2268-2278.
16. Crnjarić Zic, N., Vuković, S. & Sopta, L. 2004 Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations. J. Comput. Phys. 200, 512-548.
17. Demekhin, E. A., Kalaidin, E. N. & Shapar', E. M. 2005 On the theory of roll waves in inclined channels. Dokl. Phys. 50 (4), 220-222.
18. Denlinger, R. P. & O'Connell, D. R. H. 2008 Computing nonhydrostatic shallow-water flow over steep terrain. J. Hydraul. Engng 134 (11), 1590-1602.
19. Dressler, R. F. 1949 Mathematical solution of the problem of roll-waves in inclined open channels. Comm. Pure Appl. Math. 2, 149-194.
20. Dressler, R. F. 1952 Hydraulic resistance effect upon the dam-break functions. J. Res. Natl Bur. Stand. 49, 217-225.
21. Dressler, R. F. 1954 Comparison of theories and experiments for the hydraulic dam-break wave. In Assembĺee Ǵeńeral de Rome, vol.3, pp. 319-328. Intl Assoc. of Hydrology.
22. Dressler, R. F. 1958 Unsteady nonlinear waves in sloping channels. Proc. R. Soc. A 247, 186-198.
23. Dressler, R. F. 1978 New nonlinear shallow-flow equations with curvature. J. Hydraul. Res. 16, 205-222.
24. Dumbser, M., Enaux, C. & Toro, E. F. 2008 Finite volume schemes of very high order accuracy for stiff hyperbolic balance laws. J. Comput. Phys. 227, 3971-4001.
25. Eguiazaroff, I. B. 1935 Regulation of the water level in the reaches of canalized rivers. In XVI International Congress of Navigation, Brussels.
26. Fernandez-Feria, R. 2006 Dam-break flow for arbitrary slopes of the bottom. J. Engng Math. 54 (7), 319-331.
27. Gaster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222-224.
28. Gottlieb, S., Ketcheson, D. I. & Shu, C.-W. 2009 High order strong stability preserving time discretizations. J. Sci. Comput. 38 (3), 251-289.
29. Hogg, A. J. 2006 Lock-release gravity currents and dam-break flows. J. Fluid Mech. 569, 61-87.
30. Hogg, A. J. & Pritchard, D. 2004 The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501, 179-212.
31. Hunt, B. 1982 Asymptotic solution for dam-break problem. J. Hydraul. Div. 108 (1), 115-126.
32. Hunt, B. 1984 Perturbation solution for dam-break floods. J. Hydraul. Engng 110 (8), 1058-1071.
33. Hunt, B. 1987 An inviscid dam-break solution. J. Hydraul. Res. 25 (3), 313-327.
34. Hwang, S. H. & Chang, H. C. 1987 Turbulent and inertial roll waves in inclined film flow. Phys. Fluids 30 (5), 1259-1268.
35. Jánosi, I. M., Jan, D., Szabó, K. G. & Tél, T. 2004 Turbulent drag reduction in dam-break flows. Exp. Fluids 37, 219-229.
36. Jeffreys, H. J. 1925 The flow of water in an inclined channel of rectangular section. Phil. Mag. 49, 793-807.
37. Ketcheson, D. I. & LeVeque, R. J. 2008 WENOCLAW: a higher order wave propagation method. In Hyperbolic Problems: Theory, Numerics, Applications (ed. S. Benzoni-Gavage & D. Serre), pp. 609-616. Springer.
38. Kluwick, A. 2006 The effect of surface topography on weakly nonlinear roll waves. Proc. Appl. Math. Mech. 6, 607-608.
39. Lauber, G. & Hager, W. H. 1998a Experiments to dambreak wave: horizontal channel. J. Hydraul. Res. 36 (3), 291-307.
40. Lauber, G. & Hager, W. H. 1998b Experiments to dambreak wave: sloping channel. J. Hydraul. Res. 36 (5), 761-773.
41. Lighthill, M. J. & Whitham, G. B. 1955 On kinematic waves. Part I. Flood movement in long rivers. Part II. Theory of traffic flow on long crowded roads. Proc. R. Soc. A 229, 281-345.
42. Logan, M. & Iverson, R. M. 2007 Video documentation of experiments at the USGS debris-flow flume 1992-2006. Tech Rep. Open-File Report 2007-11315 US Geological Survey. http://pubs.usgs.gov/of/2007/1315/.
43. Martin, J. C. & Moyce, W. J. 1952 Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Phil. Trans. R. Soc. A 224 (88), 312-324.
44. Needham, D. J. & Merkin, J. H. 1984 On roll waves down an open inclined channel. Proc. R. Soc. A 394 (1807), 259-278.
45. Noelle, S., Xing, Y. & Shu, C.-W. 2007 High-order well-balanced finite volume WENO schemes for shallow water equation with moving water. J. Comput. Phys. 226, 29-58.
46. Pritchard, D. 2005 On fine sediment transport by a flood surge. J. Fluid Mech. 543, 239-248.
47. Prokopiou, Th., Cheng, M. & Chang, H. C. 1991 Long waves on inclined films at high Reynolds number. J. Fluid Mech. 222, 665-691.
48. Ritter, A. 1892 Die fortpflanzung der wasserwellen. Z. Verein. Deutch. Ing. 36, 947-954.
49. Ruyer-Quil, C. 2006 Hydrodynamic instability of a film flowing down an inclined plane: modelling, mechanisms and analogy to river flows. In Wave Dynamics and Stability of Thin Film Flow Systems (ed. R. Usha, A. Sharma & B. S. Dandapat), pp. 106-169. Narosa.
50. de Saint-Venant, A. J. C. 1871 Théorie du mouvement non-permanent des eaux, avec application aux crues des rivìiere at à l'introduction des marées dans leur lit. C. R. Acad. Sci. Paris 73, 147-154.
51. Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129-162.
52. Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.
53. Schoklistsch, A 1917 über dambruchwellen. Sitzber Akad. Wiss. Wien. 126, 1489-1514.
54. Shu, C.-W. 2009 High order weighted essentially nonoscillatory schemes for convection dominated problems. SIAM Rev. 51, 82-126.
55. Weir, G. J 1983 The asymptotic behaviour of simple kinematic waves of finite volume. Proc. R. Soc. A 387, 459-467.
56. Whitham, G. B. 1955 The effects of hydraulic resistance in the dam-break problem. Proc. R. Soc. A 227, 399-407.
57. Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
58. Xing, Y. & Shu, C.-W. 2005 High order finite difference WENO schemes with the exact conservation property for the shallow water equations. J. Comput. Phys. 208, 206-227.
59. Yu, J. & Kevorkian, J. 1992 Nonlinear evolution of small disturbances into roll waves in an inclined open channel. J. Fluid Mech. 243, 575-594.
60. Zanuttigh, B. & Lamberti, A. 2007 Instability and surge development in debris flow. Rev. Geophys. 45, RG3006.