Abstract
Naturally occurring flow along a long homogeneous slope is numerically simulated. It is taken into account that the flow is able to capture the slope material and to entrain it into motion. The flow depth and velocity increase with time at the expense of the capture. The medium in motion is simulated using different rheological models including those of Herschel & Bulkley and Cross, as well as the power-law fluid model. For all the models the time dependences of the total depth and the mean flow velocity are obtained. The slope inclination effect on the dynamic flow parameters is studied. For the Herschel–Bulkley model the yield strength effect is also investigated. On the basis of the numerical calculations some assumptions are made and then used to derive asymptotic formulas for the bottom material entrainment rate at large times from the entrainment onset for all the above-listed rheological models.
Similar content being viewed by others
References
M. E. Eglit and K. S. Demidov, “Mathematical Modeling of Snow Entrainment in Avalanche Motion,” Cold Reg. Sci. Technol. 43 (1–2), 10 (2005).
M. Naaim, T. Faug, and F. Naaim-Bouvet, “Dry Granular Flow Modelling Including Erosion and Deposition,” Surv. Geophys. 24, 569 (2003).
M. Naaim, F. Naaim-Bouvet, T. Faug, and A. Bouchet, “Dense Snow Avalanche Modeling: Flow, Erosion Deposition, and Obstacle Effects,” Cold Reg. Sci. Technol. 39, 193 (2004).
B. Sovilla, S. Margreth, and P. Bartelt, “On Snow Entrainment in Avalanche Dynamics Calculations,” Cold Reg. Sci. Technol. 47, 69 (2007).
D. Issler and M. Pastor Perez, “Interplay of Entrainment and Rheology in Snow Avalanches; a Numerical Study,” Ann. Glaciology 52 (58), 143 (2011).
E. Bovet and B. Chiaia, “A New Model for Snow Avalanche Dynamics Based on Non-Newtonian Fluids,” Meccanica 45, 753 (2010).
M. E. Eglit and A. E. Yakubenko, “Numerical Modeling of Slope Flows Entraining Bottom Material,” Cold Reg. Sci. Technol. 108, 139 (2014).
M. Chowdhury and F. Testik, “Laboratoty Testing of Mathematical Models for High-Concentration Fluid Mud Turbidity Currents,” Ocean Engineering 38, 256 (2011).
A. M. Kutepov, A. D. Polyanin, Z. D. Zapryanov, A. V. Vyaz’min, and D. A. Kazenin, Chemical Fluid Dynamics [in Russian], Kvantum, Moscow (1996).
W.L. Wilkinson, Non-Newtonian Fluids. Fluid Mechanics, Mixing and Heat Transfer, Pergamon Press, London (1960).
M. A. Kern, F. Tiefenbacher, and J.N. McElwaine, “The Rheology of Snow in Large Chute Flows,” Cold Reg. Sci. Technol. 39, 181 (2004).
J. Rougier and M. Kern, “Predicting Snow Velocity in Large Chute Flows under Different Environmental Conditions,” J. Royal Statistical Society: Ser. A (Appl. Statistics) 59, 737 (2010).
R. Haldenwang, “Flow of Non-Newtonian Fluids in Open Channels,” Doctor Technologiae Dissertation, Cape Technikon (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.S. Zaiko, 2016, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2016, Vol. 51, No. 4, pp. 3–11.
Rights and permissions
About this article
Cite this article
Zaiko, Y.S. Numerical modeling of downslope flows of different rheology. Fluid Dyn 51, 443–450 (2016). https://doi.org/10.1134/S0015462816040013
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462816040013