Gravity flow on steep slope

Buoyancy-Driven Flows

Volumn 9781107008878, Issue , 2012, Pages 372-432

  Ancey, Christophe ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

AVALANCHES (SNOWSLIDES); DEBRIS; GRAVITATION; GRAVITY WAVES; OCEAN CURRENTS; SEDIMENT TRANSPORT; VOLCANOES;

DENSITY DIFFERENCE; ESSENTIAL FEATURES; GRAVITATIONAL ACCELERATIONS; GRAVITY DRIVEN FLOW; PARTICLE SUSPENSIONS; RHEOLOGICAL BEHAVIORS; TURBIDITY CURRENT; VOLCANIC ERUPTIONS;

SUSPENSIONS (FLUIDS);

EID: 84925601247     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511920196.011     Document Type: Chapter

References (174)

1. Ancey, C., 2004: Powder-snow avalanches: Approximation as non-Boussinesq clouds with a Richardson-number-dependent entrainment function. J. Geophys. Res. 109, F01005.
2. Ancey, C., 2005: Monte Carlo calibration of avalanches described as Coulomb fluid flows. Phil. Trans. Roy. Soc. London A 363, 1529–1550.
3. Ancey, C., 2007: Plasticity and geophysical flows: A review. J. Non-Newtonian Fluid Mech. 142, 4–35.
4. Ancey, C., and S. Cochard, 2009: The dam-break problem for Herschel-Bulkley fluids down steep flumes. J. Non-Newtonian Fluid Mech. 158, 18–35.
5. Ancey, C., S. Cochard, and N. Andreini, 2009: The dam-break problem for viscous fluids in the high-capillary-number limit. J. Fluid Mech. 624, 1–22.
6. Ancey, C., S. Cochard, S. Wiederseiner, and M. Rentschler, 2006: Front dynamics of supercritical non-Boussinesq gravity currents. Water Resour. Res. 42, W08424.
7. Ancey, C., S. Cochard, S. Wiederseiner, and M. Rentschler, 2007: Existence and features of similarity solutions for supercritical non-Boussinesq gravity currents. Physica D 226, 32–54.
8. Ancey, C., and P. Evesque, 2000: Frictional-collisional regime for granular suspension flows down an inclined channel. Phys. Rev. E 62, 8349–8360.
9. Ancey, C., C. Gervasoni, and M. Meunier, 2004: Computing extreme avalanches. Cold Reg. Sci. Technol. 39, 161–180.
10. Ancey, C., R. M. Iverson, M. Rentschler, and R. P. Denlinger, 2008: An exact solution for ideal dam-break floods on steep slopes. Water Resour. Res. 44, W01430.
11. Ancey, C., and M. Meunier, 2004: Estimating bulk rheological properties of flowing snow avalanches from field data. J. Geophys. Res. 109, F01004.
12. Balmforth, N. J., and R. V. Craster, 1999:Aconsistent thin-layer theory for Bingham plastics. J. Non-Newtonian Fluid Mech. 84, 65–81.
13. Balmforth, N. J., R. V. Craster, and R. Sassi, 2002: Shallow viscoplastic flow on an inclined plane. J. Fluid Mech. 470, 1–29.
14. Balmforth, N. J., and R. R. Kerswell, 2005: Granular collapse in two dimensions. J. Fluid Mech. 538, 399–428.
15. Barbolini, M., and C. J. Keylock, 2002: A new method for avalanche hazard mapping using a combination of statistical and deterministic models. Nat. Hazard Earth. Sys. Sci. 2, 239–245.
16. Bartelt, P., and B.W. McArdell, 2009: Granulometric investigations of snow avalanches. J. Glac. 55, 829–833.
17. Beghin, P., and G. Brugnot, 1983: Contribution of theoretical and experimental results to powder-snow avalanche dynamics. Cold Regions Sci. Technol. 8, 63–73.
18. Beghin, P., E. J. Hopfinger, and R. E. Britter, 1981: Gravitational convection from instantaneous sources on inclined boundaries. J. Fluid Mech. 107, 407–422.
19. Beghin, P., and X. Olagne, 1991: Experimental and theoretical study of the dynamics of powder snow avalanches. Cold Reg. Sci. Technol. 19, 317–326.
20. Benjamin, T. B., 1968: Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.
21. Bouchut, F., A. Mangeney-Castelnau, B. Perthame, and J.-P. Vilotte, 2003: A new model of Saint Venant and Savage-Hutter type for gravity driven shallow flows. C. R. Acad. Sci. Paris Sér. I 336, 531–536.
22. Bozhinskiy, N., and K. S. Losev, 1998: The fundamentals of avalanche science. Tech. Rep. 55. EISFL.
23. Brugnot, G., and R. Pochat, 1981: Numerical simulation study of avalanches. J. Glaciol. 27, 77–88.
24. Bursik, M., A. Patra, E. B. Pitman, C. C. Nichita, J. L. Macias, R. Saucedo, and O. Girina, 2005: Advances in studies of dense volcanic granular flows. Rep. Prog. Phy. 68, 271–301.
25. Buser, O., and H. Frutiger, 1980: Observed maximum runout distance of snow avalanches and determination of the friction coefficients μ and ξ. J. Glaciol. 26, 121–130.
26. Chambon, G., A. Ghemmour, and D. Laigle, 2009: Gravity-driven surges of a viscoplastic fluid: an experimental study. J. Non-Newtonian Fluid Mech. 158, 54–62.
27. Chang, C., and R. L. Powell, 1994: Effect of particle size distributions on the rheology of concentrated bimodal suspensions. J. Rheol. 38, 85–98.
28. Chow, V. T. (ed.), 1959: Open-Channel Hydraulics. Mc Graw Hill, New York.
29. Christen, M., P. Bartelt, and U. Gruber, 2002: AVAL1D: Numerische Berechnung von Fliessund Staublawinen. Eidgenössisches Institut für Schnee- und Lawinenforschung, Davos.
30. Chugunov, V., J. M. N. T. Gray, and K. Hutter, 2003: Group theoretic methods and similarity solutions of the Savage-Hutter equations. In: K. Hutter and N. Kirchener (eds.), Dynamics Response of Granular and Porous Materials under Large and Catastrophic Deformations, pp. 251–261. Springer, Berlin.
31. Clague, J. J., and S. G. Evans, 2000: A review of catastrophic drainage of moraine-dammed lakes in British Columbia. Quaternary Sci. Rev. 19, 1763–1783.
32. Coaz, J.W., 1881: Die Lawinen der Schweizer Alpen. Schmid-Franke, Bern.
33. Cochard, S., and C. Ancey, 2008: Tracking the free surface of time-dependent flows: Image processing for the dam-break problem. Exper. Fluids 44, 59–71.
34. Cochard, S., and C. Ancey, 2009: Experimental investigation into the spreading of viscoplastic fluids on inclined planes. J. Non-Newtonian Fluid Mech. 158, 73–84.
35. Contreras, S. M., and T. R. H. Davies, 2000: Coarse-grained debris-flows: Hysteresis and time-dependent rheology. J. Hydraul. Eng. 126, 938–941.
36. Coussot, P., 1997: Mudflow Rheology and Dynamics. Balkema, Rotterdam.
37. Coussot, P., S. Proust, and C. Ancey, 1996: Rheological interpretation of deposits of yield stress fluids. J. Non-Newtonian Fluid Mech. 66, 55–70.
38. Cui, X., J. M. N. T. Gray, and T. Jóhannesson, 2007: Deflecting dams and the formation of oblique shocks in snow avalanches at Flateyri, Iceland. J. Geophys. Res. 122, F04012.
39. Dalbey, K., A. Patra, E. B. Pitman, M. I. Bursik, and M. Sheridan, 2008: Input uncertainty propagation methods and hazard mapping of geophysical mass flows. J. Geophys. Res. 113, B05203.
40. Davies, T. R. H., 1986: Large debris flow: a macro-viscous phenomenon. Acta Mech. 63, 161–178.
41. Deboeuf, S., E. Lajeunesse, O. Dauchot, and B. Andreotti, 2006: Flow rule, self-channelization, and levees in unconfined granular flows. Phys. Rev. Lett. 97, 158303.
42. Delannay, R., M. Louge, P. Richard, N. Taberlet, and A. Valance, 2007: Towards a theoretical picture of dense granular flows down inclines. Nature Mater. 6, 99–108.
43. Dent, J. D., and T. E. Lang, 1980: Modelling of snow flow. J. Glaciol. 26, 131–140.
44. Dent, J. D., and T. E. Lang, 1982: Experiments on the mechanics of flowing snow. Cold Reg. Sci. Technol. 5, 243–248.
45. Eckert, N., E. Parent, M. Naaim, and D. Richard, 2008: Bayesian stochastic modelling for avalanche predetermination: From a general system framework to return period computations. Stoch. Env. Res. Risk Ass. 22, 185–206.
46. Eglit, E. M., 1983: Some mathematical models of snow avalanches. In: M. Shahinpoor (ed.) Advances in the Mechanics and the Flow of Granular Materials, pp. 577–588. Trans Tech Publications, Clausthal-Zellerfeld.
47. Ellison, T. H., and J. S. Turner, 1959: Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.
48. Elverhøi, A., D. Issler, F. V. De Blasio, T. Ilstad, C. B. Harbitz, and P. Gauer, 2005: Emerging insights into the dynamics of submarine debris flows. Nat. Hazard Earth. Sys. Sci. 5, 633–648.
49. Fannin, R. J., and T. P. Rollerson, 1993: Debris flows: Some physical characteristics and behaviour. Can. Geotech. J. 30, 71–81.
50. Félix, G., and N. Thomas, 2004: Relation between dry granular flow regimes and morphology of deposits: Formation of levées in pyroclastic deposits. Earth Planet. Sci. Lett. 221, 197–213.
51. Fernández-Nieto, E. D., P. Noble, and J.-P. Vila, 2010: Shallow water equation for non-Newtonian fluids. J. Non-Newtonian Fluid Mech. 165, 712–732.
52. Fernando, H. J. S., 1991: Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech. 23, 455–493.
53. Forterre, Y., and O. Pouliquen, 2008: Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24.
54. Fukushima, Y., T. Hagihara, and M. Sakamoto, 2000: Dynamics of inclined suspension thermals. Fluid Dyn. Res. 26, 337–354.
55. Fukushima, Y., and G. Parker, 1990: Numerical simulation of powder-snow avalanches. J. Glaciol. 36, 229–237.
56. Gauer, P., and D. Issler, 2003: Possible erosion mechanisms in snow avalanches. Ann. Glaciol. 38, 384–392.
57. Gauer, P., Z. Medina-Cetina, K. Lied, and K. Kristensen, 2009: Optimization and probabilistic calibration of avalanche-block models. Cold Reg. Sci. Technol. 59, 251–258.
58. Gratton, J., and C. Vigo, 1994: Self-similar gravity currents with variable inflow revisited: plane currents. J. Fluid Mech. 258, 77–104.
59. Gray, J. M. N. T., 2010: Particle size segregation in granular avalanches: A brief review of recent progress. In: J. D. Goddard, J. T. Jenkins and P. Giovine (eds.), IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows, vol. 1227, pp. 343–362. AIP, Melville, NY.
60. Gray, J. M. N. T., and C. Ancey, 2009: Particle size-segregation, recirculation, and deposition at coarse particle rich flow fronts. J. Fluid Mech. 629, 387–423.
61. Gray, J. M. N. T., and B. P. Kokelaar, 2010: Large particle segregation, transport and accumulation in granular free-surface flows. J. Fluid Mech. 652, 105–137.
62. Gray, J. M. N. T., M. Wieland, and K. Hutter, 1998: Gravity-driven free surface flow of granular avalanches over complex basal topography. Proc. R. Soc. London Ser. A 455, 1841–1874.
63. Gubler, H., M. Hiller, G. Klausegger, and U. Suter, 1986: Messungen an Fliesslawinen. Tech. Rep. 41. SLF.
64. Hallworth, M. A., A. Hogg, and H. E. Huppert, 1998b: Effects of external flow on compositional and particle gravity currents. J. Fluid Mech. 359, 109–142.
65. Hampton, M. A., H. J. Lee, and J. Locat, 1996: Submarine landslides. Rev. Geophys. 34, 33–59.
66. Harbitz, C., A. Harbitz, and F. Nadim, 2001: On probability analysis in snow avalanche hazard zoning. Ann. Glaciol. 32, 290–298.
67. Hogg, A. J., 2006: Lock-release gravity currents and dam-break flows. J. Fluid Mech. 569, 61–87.
68. Hogg, A. J., and G. P. Matson, 2009: Slumps of viscoplastic fluids on slopes. J. Non-Newtonian Fluid Mech. 158, 101–112.
69. Hogg, A. J., and D. Pritchard, 2004: The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501, 179–212.
70. Hogg, A. J., M. Ungarish, and H. E. Huppert, 2000: Particle-driven gravity currents: asymptotic and box model solutions. Eur. J. Mech. B. Fluids 19, 139–165.
71. Hogg, A. H., and A.W. Woods, 2001: The transition from inertia- to bottom-drag-dominated motion of turbulent gravity current. J. Fluid Mech. 449, 201–224.
72. Holmes, M. H., 1995: Introduction to Perturbation Methods. Springer Verlag, New York.
73. Hopfinger, E. J., and J.-C. Tochon-Danguy, 1977: A model study of powder-snow avalanches. J. Glaciol. 81, 343–356.
74. Huang, X., and M. H. Garcìa, 1997: A perturbation solution for Bingham-plastic mudflows. J. Hydraul. Eng. 123, 986–994.
75. Huang, X., and M. H. Garcìa, 1998: A Herschel-Bulkley model for mud flow down a slope. J. Fluid Mech. 374, 305–333.
76. Hunt, B., 1994: Newtonian fluid mechanics treatment of debris flows and avalanches. J. Hydraul. Eng. 120, 1350–1363.
77. Huppert, H. E., and W. B. Dade, 1998: Natural disasters: explosive volcanic eruptions and gigantic landslides. Theor. Comput. Fluid Dyn. 10, 202–212.
78. Hürlimann, M., D. Rickenmann, and C. Graf, 2003: Field and monitoring data of debris-flow events in the Swiss Alps. Can. Geotech. J. 40, 161–175.
79. Hutter, K., 1996: Avalanche dynamics. In: V. P. Singh (ed.), Hydrology of Disasters, pp. 317–392. Kluwer Academic Publications, Dordrecht.
80. Issler, D., 1998: Modelling of snow entrainment and deposition in powder-snow avalanches. Ann. Glaciol. 26, 253–258.
81. Issler, D., 2003: Experimental information on the dynamics of dry-snow avalanches. In: K. Hutter and N. Kirchner (eds.), Dynamic Response of Granular and Porous Materials Under Large and Catastrophic Deformation pp. 109–160. Springer, Berlin.
82. Iverson, R. M., 1997: The physics of debris flows. Rev. Geophys. 35, 245–296.
83. Iverson, R. M., 2003a: The debris-flow rheology myth. In: C. L. Chen and D. Rickenmann (eds.), Debris Flow Mechanics and Mitigation Conference, pp. 303–314. Davos: Mills Press.
84. Iverson, R. M., 2003b: How should mathematical models of geomorphic processus be judged? In: P. R.Wilcock and R. M. Iverson (ed.), Prediction in Geomorphology, pp. 83–94. American Geophysical Union, Washington, DC.
85. Iverson, R. M., 2005: Debris-flow mechanics. In: M. Jakob and O. Hungr (eds.), Debris-Flow Hazards and Related Phenomena, pp. 105–134. Springer, Berlin.
86. Iverson, R. M., and R. P. Denlinger, 2001: Flow of variably fluidized granular masses across three-dimensional terrain. 1. Coulomb mixture theory. J. Geophys. Res. 106, 537–552.
87. Iverson, R. M., M. Logan, and R. G. LaHusen, 2010: The perfect debris flow? Aggregated results from 28 large-scale experiments. J. Geophys. Res. 115, F03005.
88. Iverson, R. M., M. E. Reid, and R. G. LaHusen, 1997: Debris-flow mobilization from landslides. Annu. Rev. Earth. Planet. Sci. 25, 85–138.
89. Iverson, R. M., and J. Vallance, 2001: New views of granular mass flows. Geology 29, 115–118.
90. Johnson, A. M., and J. R. Rodine, 1984: Debris flow. In: D. Brunsden and D. B. Prior (eds.), Slope Instability, pp. 257–362. JohnWiley and Sons, Chichester.
91. Jomelli, V., and P. Bertran, 2001:Wet snow avalanche deposits in the French Alps: Structure and sedimentology. Geografiska Annaler Series A—Physical Geography 83, 15–28.
92. Jop, P., Y. Forterre, and O. Pouliquen, 2005: Crucial role of side walls for granular surface flows: Consequences for the rheology. J. Fluid Mech. 541, 167–192.
93. Josserand, C., P.-Y. Lagrée, and D. Lhuillier, 2004: Stationary shear flows of dense granular materials: A tentative continuum modelling. Eur. Phys. J. E 14, 127–135.
94. Karelsky, K. V., V. V. Papkov, A. S. Petrosyan, and D. V. Tsygankov, 2000: Particular solutions of shallow-water equations over a non-flat surface. Phys. Lett. A 271, 341–348.
95. Keller, J. B., 2003: Shallow-water theory for arbitrary slopes of the bottom. J. Fluid Mech. 489, 345–348.
96. Kern, M. A., P. Bartelt, B. Sovilla, and O. Buser, 2009: Measured shear rates in large dry and wet snow avalanches. J. Glaciol. 55, 327–338.
97. Kern, M. A., F. Tiefenbacher, and J. N. McElwaine, 2004: The rheology of snow in large chute flows. Cold Reg. Sci. Technol. 39, 181–192.
98. Kerswell, R. R., 2005: Dam break with Coulomb friction: a model for granular slumping? Phys. Fluids 17, 057101.
99. Keylock, C. J., 2005: An alternative form for the statistical distribution of extreme avalanche runout distances. Cold Reg. Sci. Technol. 42, 185–193.
100. Kulikovskiy, A. G., and E. I. Svehnikova, 1977: Model dlja rascheta dvizhija pilevoi snezhnoi lavini (a model for computing powdered snow avalanche motion) [in Russian]. Materiali Glatsiologicheskih Issledovanii [Data of Glaciological Studies] 31, 74–80.
101. Leighton, D., and A. Acrivos, 1987: The shear-induced migration of particles in a concentrated suspensions. J. Fluid Mech. 181, 415–439.
102. LeVeque, R. J., 2002: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge.
103. Lighthill, M. J., and G. B. Whitham, 1955: On kinematic waves. I. Flood movement in long rivers. Proc. R. Soc. London Ser. A 229, 281–316.
104. Linares-Guerrero, E., C. Goujon, and R. Zenit, 2007: Increased mobility of bidisperse granular avalanches. J. Fluid Mech. 593, 475–504.
105. Liu, K. F. and C. C. Mei, 1990a: Approximate equations for the slow spreading of a thin sheet of Bingham plastic fluid. Phys. Fluids A2, 30–36.
106. Liu, K. F., and C. C. Mei, 1990b: Slow spreading of a sheet of Bingham fluid on an inclined plane. J. Fluid Mech. 207, 505–529.
107. Lootens, D., H. Van Damme, and P. Hébraud, 2003: Giant stress fluctuations at the jamming transition. Phys. Rev. Lett. 90, 178301.
108. Maeno, O., 1993: Rheological characteristics of snow flows. In: International Workshop on Gravitational Mass Movements (ed. L. Buisson and G. Brugnot), pp. 209–220. Cemagref, Grenoble.
109. Major, J. J., and T. C. Pierson, 1992: Debris flow rheology: Experimental analysis of fine-grained slurries. Water Resour. Res. 28, 841–857.
110. Mangeney, A., P. Heinrich, and R. Roche, 2000: Analytical solution for testing debris avalanche numerical models. Pure Appl. Geophys. 157, 1081–1096.
111. Mangeney, A., O. Roche, O. Hungr, N. Mangold, G. Faccanoni, and A. Lucas, 2010: Erosion and mobility in granular collapse over sloping beds. J. Geophys. Res. 115, F03040.
112. Mangeney, A., L. S. Tsimring, I. S. Volfson, and F. Bouchut, 2007: Avalanche mobility induced by the presence of an erodible bed and associated entrainment. Geophys. Res. Lett. 34, L22401.
113. Marquez, M., A. Robben, B. P. Grady, and I. Robb, 2006: Viscosity and yield stress reduction in non-colloidal concentrated suspensions by surface modification with polymers and surfactants and/or nanoparticle addition. J. Colloid. Interface Sci. 295, 374–387.
114. Matson, G. P., and A. J. Hogg, 2007: Two-dimensional dam break flows of Herschel-Bulkley fluids: The approach to the arrested state. J. Non-Newtonian Fluid Mech. 142, 79–94.
115. McArdell, B.W., P. Bartelt, and J. Kowalski, 2006: Field observations of basal forces and fluid pore pressure in a debris flow. Geophys. Res. Lett. 34, L07406.
116. McClung, D. M., and K. Lied, 1987: Statistical and geometrical definition of snow avalanche runout. Cold Reg. Sci. Technol. 13, 107–119.
117. McElwaine, J. N., 2005: Rotational flow in gravity current heads. Phil. Trans. Roy. Soc. London A 363, 1603–1623.
118. Mei, C. C., K. F. Liu, and M. Yuhi, 2001: Mud flows—Slow and fast. In: N. J. Balmforth and A. Provenzale (eds.), Geomorphological Fluid Mechanics: Selected topics in geological and geomorphological fluid mechanics, pp. 548–577. Springer, Berlin.
119. Mei, C. C., and M. Yuhi, 2001: Slow flow of a Bingham fluid in a shallow channel of finite width. J. Fluid Mech. 431, 135–159.
120. Meunier, M., and C. Ancey, 2004: Towards a conceptual approach to predetermining long-return-period avalanche run-out distances. J. Glaciol. 50, 268–278.
121. Meunier, M., C. Ancey, and J.-M. Taillandier, 2004: Fitting avalanche-dynamics models with documented events from the Col du Lautaret site (France) using the conceptual approach. Cold Regions Sci. Technol. 39, 55–66.
122. Morris, J. F., 2009: A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta 48, 909–923.
123. Morris, J. F., and F. Boulay, 1999: Curvilinear flows of noncolloidal suspensions: The role of normal stresses. J. Rheol. 43, 1213–1238.
124. Mougin, P., 1922: Les avalanches en Savoie, vol. IV. Ministère de l’Agriculture, Direction Générale des Eaux et Forêts, Service des Grandes Forces Hydrauliques, Paris.
125. Nazarov, A. N., 1991: Mathematical modelling of a snow-powder avalanche in the framework of the equations of two-layer shallow water. Fluid Dyn. 12, 70–75.
126. Norem, H. F., F. Irgens, and B. Schieldrop, 1986: A continuum model for calculating snow avalanche velocities. In: H. Gubler and B. Salm (eds.), Avalanche Formation, Movement and Effects, pp. 363–379. IAHS, Wallingford, Oxfordshire, UK, Davos.
127. Osmond, D. I., and R.W. Griffiths, 2001: The static shape of yield strength fluids slowly emplaced on slopes. J. Geophys. Res. B 106, 16241–16250.
128. Ottino, J. M., and D. V. Khakhar, 2000: Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32, 55–91.
129. Ovarlez, G., F. Bertrand, and S. Rodts, 2006: Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging. J. Rheol. 50, 259–292.
130. Parker, G., 1982: Conditions for the ignition of catastrophically erosive turbidity currents. Mar. Geol. 46, 307–327.
131. Parker, G., Y. Fukushima, and H. M. Pantin, 1986: Self-accelerating turbidity currents. J. Fluid Mech. 171, 145–181.
132. Parsons, J. D., K. X. Whipple, and A. Simoni, 2001: Experimental study of the grain-flow, fluid-mud transition in debris flows. J. Geol. 109, 427–447.
133. Phillips, J. C., A. J. Hogg, R. R. Kerswell, and N. Thomas, 2006: Enhanced mobility of granular mixtures of fine and coarse paricles. Earth Planet. Sci. Lett. 246, 466–480.
134. Piau, J.-M., 1996: Flow of a yield stress fluid in a long domain. Application to flow on an inclined plane. J. Rheol. 40, 711–723.
135. Platzer, K., P. Bartelt, and M. A. Kern, 2007: Measurements of dense snow avalanche basal shear to normal stress ratios (S/N). Geophys. Res. Lett. 34, L07501.
136. Pouliquen, O., and Y. Forterre, 2002: Friction law for dense granular flow: Application to the motion of a mass down a rough inclined plane. J. Fluid Mech. 453, 133–151.
137. Princevac, M., H. J. S. Fernando, and C. D. Whiteman, 2005: Turbulent entrainment into natural gravity-driven flows. J. Fluid Mech. 533, 259–268.
138. Pudasaini, S. P., and K. Hutter, 2003: Rapid shear flows of dry granular masses down curved and twisted channels. J. Fluid Mech. 495, 193–208.
139. Pudasaini, S. P., and K. Hutter, 2006: Avalanche Dynamics. Berlin, Springer.
140. de Quervain, R., 1981: Avalanche Atlas. Unesco, Paris.
141. Rammer, L., M. A. Kern, U. Gruber, and F. Tiefenbacher, 2007: Comparison of avalanche-velocity measurements by means of pulsed Doppler radar, continuous wave radar and optical methods. Cold Reg. Sci. Technol. 54, 35–54.
142. Rentschler, M., 2010: Simulating viscoplastic avalanches. PhD thesis, École Polytechnique Fédérale de Lausanne.
143. Rickenmann, D., 1999: Empirical relationships for debris flows. Nat. Hazard 19, 47–77.
144. Salm, B., 1966: Contribution to avalanche dynamics. In: Scientific Aspects of Snow and Ice Avalanche, pp. 199–214. IAHS Press, Wallingford, Oxfordshire, UK, Davos.
145. Salm, B., 2004: A short and personal history of snow avalanche dynamics. Cold Reg. Sci. Technol. 39, 83–92.
146. Salm, B., A. Burkard, and H. Gubler, 1990: Berechnung von Fliesslawinen, eine Anleitung für Praktiker mit Beispielen. Tech. Rep. No 47. Eidgenössisches Institut für Schnee- und Lawinenforschung (Davos).
147. Savage, S. B., 1982: Granular flows down rough inclined—Review and extension. In: J. T. Jenkins and M. Satake (eds.), U.S./Japan Seminar on New Models and Constitutive Relations in the Mechanics of Granular Materials, pp. 261–282. Elseviers Science Publishers, Amsterdam, Ithaca.
148. Savage, S. B., 1989: Flow of granular materials. In: P. Germain, J.-M. Piau, and D. Caillerie (eds.), Theoretical and Applied Mechanics, pp. 241–266. Elsevier, Amsterdam.
149. Savage, S. B., and K. Hutter, 1989: The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177–215.
150. Savage, S. B., and K. Hutter, 1991: The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis. Acta Mech. 86, 201–223.
151. Savage, S. B., and Y. Nohguchi, 1988: Similarity solutions for avalanches of granular materials down curved bed. Acta Mech. 75, 153–174.
152. Sengun, M. Z., and R. F. Probstein, 1989: Bimodal model of slurry viscosity with applications to coal slurries. Part 1. Theory and experiment. Rheol. Acta 28, 382–393.
153. Siavoshi, S., and A. Kudrolli, 2005: Failure of a granular step. Phys. Rev. E 71, 051302.
154. Simpson, J. E., 1972: Effects of a lower boundary on the head of a gravity current. J. Fluid Mech. 53, 759–768.
155. Simpson, J. E., 1997: Gravity Currents in the Environment and the Laboratory. Cambridge University Press, Cambridge.
156. Singh, A., A. Nir, and R. Semiat, 2006: Free-surface flow of concentrated suspensions. Int. J. Multiphase Flow 32, 775–790.
157. Siviglia, A., and A. Cantelli, 2005: Effect of bottom curvature on mudflow dynamics: Theory and experiments. Water Resour. Res. 41, W11423.
158. Sovilla, B., and P. Bartelt, 2006: Field experiments and numerical modeling of mass entrainment in snow avalanches. J. Geophys. Res. 111, F03007.
159. Stickel, J. J., and R. L. Powell, 2005: Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.
160. Tai, Y.-C., K. Hutter, and J. M. N. T. Gray, 2001: Dense granular avalanches: mathematical description and experimental validation. In: N. J. Balmforth and A. Provenzale (eds.), Geomorphological Fluid Mechanics, pp. 339–366. Springer, Berlin.
161. Timberlake, B. D., and J. F. Morrison, 2005: Particle migration and free-surface topography in inclined plane flow of a suspension. J. Fluid Mech. 538, 309–341.
162. Tognacca, C., 1997: Debris-flow initiation by channel-bed failure. In: C. L. Chen (ed.), First International Conference on Debris Flow Hazards Mitigation, pp. 44–53. ASCE, New-York.
163. Tsai, J.-C., W. Losert, and G. A. Voth, 2001: Two-dimensional granular Poiseuille flow on an incline: Multiple dynamical regimes. Phys. Rev. E 65, 011306.
164. Turnbull, B., J. McElwaine, and C. Ancey, 2007: The Kulikovskiy–Sveshnikova–Beghin model of powder snow avalanches: Development and application. J. Geophys. Res. 112, F01004.
165. Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge University Press, Cambridge.
166. Ungarisch, M., 2009: An Introduction to Gravity Currents and Intrusions. CRC Publishers, Boca Raton.
167. VanDine, D. F., 1985: Debris flows and debris torrents in the Southern Canadian Cordillera. Can. Geotech. J. 22, 44–68.
168. Vila, J. P., 1986: Sur la théorie et l’approximation numérique des problèmes hyperboliques non-linéaires, application aux équations de Saint-Venant et à la modélisation des avalanches denses. Ph. D. thesis, Paris VI.
169. Voellmy, A., 1955: Über die Zerstörungskraft von Lawinen. Schweizerische Bauzeitung 73, 159–162, 212–217, 246–249, 280–285.
170. Voight, B., 1990: The 1985 Nevado del Ruiz volcano catastrophe: Anatomy and restropection. J. Volcan. Geoth. Res. 44, 349–386.
171. Wilcock, P. R., and R. M. Iverson, eds., 2003: Prediction in Geomorphology. American Geophysical Union, Washington, DC.
172. Zanuttigh, B., and A. Lamberti, 2007: Instability and surge development in debris flows. Rev. Geophys. 45, RG3006.
173. Zarraga, I. E., D. A. Hill, and D. T. Leighton, 2000: The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185–221.
174. Zimmermann, M., P. Mani, P. Gamma, P. Gsteiger, O. Heiniger, and G. Hunizker, 1997: Murganggefahr und Klimaänderung – ein GIS-basierter Ansatz. VDF, Zürich.