Powder snow avalanches: Approximation as non-Boussinesq clouds with a Richardson number-dependent entrainment function, Journal of Geophysical Research: Earth Surface, vol.345, issue.F1, p.1005, 2004. ,
DOI : 10.1017/S0022112097006332
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.1, pp.169-200, 2007. ,
DOI : 10.1017/S0305004100028887
URL : https://hal.archives-ouvertes.fr/hal-00355730
Finite Volume Methods: Foundation and Analysis, p.27, 2004. ,
DOI : 10.1002/0470091355.ecm010
URL : http://www.mathematik.uni-freiburg.de/IAM/homepages/mario/postscript/finvol_script.pdf
Gravitational convection from instantaneous sources on inclined boundaries, Journal of Fluid Mechanics, vol.19, issue.-1, pp.407-422, 1981. ,
DOI : 10.1146/annurev.fl.04.010172.002013
Solution of the Sediment Transport Equations Using a Finite Volume Method Based on Sign Matrix, SIAM Journal on Scientific Computing, vol.31, issue.4, pp.2866-2889, 2009. ,
DOI : 10.1137/080727634
The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations, Journal of Fluid Mechanics, vol.537, issue.-1, pp.125-144, 2005. ,
DOI : 10.1017/S0022112005005033
The calibration of an avalanche mathematical model using field data, Natural Hazards and Earth System Science, vol.2, issue.3/4, pp.217-220, 2002. ,
DOI : 10.5194/nhess-2-217-2002
URL : https://hal.archives-ouvertes.fr/hal-00330889
Hydrodynamics of Turbid Underflows.???I: Formulation and Numerical Analysis, Journal of Hydraulic Engineering, vol.125, issue.10, pp.1006-1015, 1999. ,
DOI : 10.1061/(ASCE)0733-9429(1999)125:10(1006)
The motion of the front of a gravity current travelling down an incline, Journal of Fluid Mechanics, vol.3, issue.03, pp.531-543, 1980. ,
DOI : 10.1139/e66-038
Spreading of Gravity Plumes on an Incline, Coastal Engineering Journal, vol.94, issue.6, pp.221-237, 2001. ,
DOI : 10.1017/S0022112086001404
Avalanches: études effectuées dans la Vallée de la Sionne en 1999, Les Alpes, vol.2, issue.7, pp.9-15, 2001. ,
Mathematical Modeling of Powder-Snow Avalanche Flows, Studies in Applied Mathematics, vol.14, issue.180, pp.38-66, 2011. ,
DOI : 10.1063/1.1517298
URL : https://hal.archives-ouvertes.fr/hal-00354000
Geometric numerical schemes for the KdV equation, Computational Mathematics and Mathematical Physics, vol.53, issue.2, pp.221-236, 2013. ,
DOI : 10.1134/S0965542513020103
URL : https://hal.archives-ouvertes.fr/hal-00694896
Modified shallow water equations for significantly varying seabeds, Applied Mathematical Modelling, vol.40, issue.23-24, pp.23-249767, 2016. ,
DOI : 10.1016/j.apm.2016.06.033
URL : https://hal.archives-ouvertes.fr/hal-00675209
Finite volume methods for unidirectional dispersive wave models, International Journal for Numerical Methods in Fluids, vol.459, issue.6, pp.717-736, 2013. ,
DOI : 10.1098/rspa.2002.1067
URL : https://hal.archives-ouvertes.fr/hal-00538043
Turbulent entrainment in stratified flows, Journal of Fluid Mechanics, vol.3, issue.03, pp.423-448, 1959. ,
DOI : 10.1007/BF02021146
Numerical simulations of high density ratio lock-exchange flows, Physics of Fluids, vol.4, issue.3, p.36601, 2005. ,
DOI : 10.1016/S0045-7825(03)00262-7
URL : https://hal.archives-ouvertes.fr/hal-00222927
Numerical viscosity reduction in the resolution of the shallow water equations with turbulent term, International Journal for Numerical Methods in Fluids, vol.42, issue.1, pp.781-802, 2008. ,
DOI : 10.1007/978-1-4757-5592-3
Experimental validation of two depth-averaged turbulence models, International Journal for Numerical Methods in Fluids, vol.30, issue.HY10, pp.177-202, 2009. ,
DOI : 10.1007/978-3-642-97651-3
Observations of mixing near the sides of a deep lake in winter, Limnology and Oceanography, vol.47, issue.2, pp.535-544, 2002. ,
DOI : 10.4319/lo.2002.47.2.0535
A new Savage???Hutter type model for submarine avalanches and generated tsunami, Journal of Computational Physics, vol.227, issue.16, pp.7720-7754, 2008. ,
DOI : 10.1016/j.jcp.2008.04.039
URL : https://hal.archives-ouvertes.fr/hal-00385939
Detonation: Theory and Experiment, p.26, 1979. ,
Experiments on the entrainment of sediment into suspension by a dense bottom current, Journal of Geophysical Research: Oceans, vol.64, issue.3, pp.4793-4807, 1993. ,
DOI : 10.1051/lhb/1964004
Hydraulic Jumps in Sediment???Driven Bottom Currents, Journal of Hydraulic Engineering, vol.119, issue.10, pp.1094-1117, 1993. ,
DOI : 10.1061/(ASCE)0733-9429(1993)119:10(1094)
The Free Streaming of Gases in Sloping Galleries, Proc. R. Soc. A, pp.484-493, 1942. ,
DOI : 10.1098/rspa.1942.0052
Hyperbolic systems of conservation laws, p.27, 1990. ,
URL : https://hal.archives-ouvertes.fr/hal-00113734
A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb, vol.47, issue.28, pp.271-290, 1959. ,
Reminiscences about Difference Schemes, Journal of Computational Physics, vol.153, issue.1, pp.6-25, 1999. ,
DOI : 10.1006/jcph.1999.6271
Difference Schemes. North-Holland, p.34, 1987. ,
Computing Qualitatively Correct Approximations of Balance Laws: Exponential- Fit, Well-Balanced and Asymptotic-Preserving, p.34, 2013. ,
DOI : 10.1007/978-88-470-2892-0
Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries, Journal of Fluid Mechanics, vol.418, issue.9 7, pp.189-212, 2000. ,
DOI : 10.1017/S0022112000001221
On the discontinuous movements of fluids, Monthly Reports of the Royal Prussian Academy of Philosophy in Berlin, vol.23, issue.12, pp.215-230, 1868. ,
Snow Avalanche Motion and Related Phenomena, Annual Review of Fluid Mechanics, vol.15, issue.1, pp.47-76, 1983. ,
DOI : 10.1146/annurev.fl.15.010183.000403
Numerical Model of Turbidity Currents with a Deforming Bottom Boundary, Journal of Hydraulic Engineering, vol.131, issue.4, pp.283-293, 2005. ,
DOI : 10.1061/(ASCE)0733-9429(2005)131:4(283)
The slumping of gravity currents, Journal of Fluid Mechanics, vol.31, issue.04, pp.785-799, 1980. ,
DOI : 10.1146/annurev.fl.04.010172.002013
Three-dimensional modeling of density current. I. Flow in straight confined and unconfined channels, Journal of Hydraulic Research, vol.108, issue.6, pp.578-590, 2004. ,
DOI : 10.1061/(ASCE)0733-9429(1984)110:11(1613)
Currents in Submarine Canyons: An Air-Sea-Land Interaction, Annual Review of Fluid Mechanics, vol.8, issue.1, pp.275-310, 1976. ,
DOI : 10.1146/annurev.fl.08.010176.001423
Entraining gravity currents, Journal of Fluid Mechanics, vol.443, pp.477-508, 2013. ,
DOI : 10.1017/S002211200600108X
Nonlinear Ordinary Differential Equations: Problems and Solutions, p.17, 2007. ,
Three-dimensional modeling of density current. II. Flow in sinuous confined and uncontined channels, Journal of Hydraulic Research, vol.100, issue.6, pp.591-602, 2004. ,
DOI : 10.1029/96WR00998
Numerical modeling of hyperpycnal plume, Marine Geology, vol.222, issue.223, pp.222-223193, 2005. ,
DOI : 10.1016/j.margeo.2005.06.025
Turbidity Currents and Cable Breaks in the Western New Britain Trench, Geological Society of America Bulletin, vol.81, issue.7, pp.2153-2160, 1970. ,
DOI : 10.1130/0016-7606(1970)81[2153:TCACBI]2.0.CO;2
Experimental and numerical study of topographic effects on deposition from two-dimensional, particle-driven density currents, Sedimentary Geology, vol.164, issue.3-4, pp.311-326, 2004. ,
DOI : 10.1016/j.sedgeo.2003.11.002
Laboratory experiments and numerical simulation of sediment-wave formation by turbidity currents, Marine Geology, vol.192, issue.1-3, pp.105-121, 2002. ,
DOI : 10.1016/S0025-3227(02)00551-0
Turbulence in Fluids of Fluid Mechanics and Its Applications, 2008. ,
Mixing Layer on the Lee Side of an Obstacle, Journal of Applied Mechanics and Technical Physics, vol.45, issue.2, pp.199-203, 2004. ,
DOI : 10.1023/B:JAMT.0000017582.70655.d9
Mathematical models of long wave propagation in an inhomogeneous fluid, Izd. Sib. Otd. Ross. Akad. Nauk, vol.15, p.35, 2000. ,
A Severe Downslope Windstorm and Aircraft Turbulence Event Induced by a Mountain Wave, Journal of the Atmospheric Sciences, vol.35, issue.1, pp.59-77, 1978. ,
DOI : 10.1175/1520-0469(1978)035<0059:ASDWAA>2.0.CO;2
Overdriven detonation phenomenon in high explosive, AIP Conference Proceedings, pp.227-230, 2000. ,
DOI : 10.1063/1.1303462
The General Problem of the Stability of Motion, pp.1892-1913 ,
Experiments on gravity currents propagating down slopes. Part 2. The evolution of a fixed volume of fluid released from closed locks into a long, open channel, Journal of Fluid Mechanics, vol.19, issue.17, pp.27-51, 2010. ,
DOI : 10.1111/j.1365-3091.1976.tb00108.x
Modelling the dynamics of turbulent floods, SIAM J. Appl. Math, vol.63, issue.2 7, pp.423-458, 2003. ,
Turbidity Currents and Their Deposits, Annual Review of Fluid Mechanics, vol.42, issue.1, pp.135-156, 2006. ,
DOI : 10.1146/annurev-fluid-121108-145618
Velocity and Energy Relaxation in Two-Phase Flows, Studies in Applied Mathematics, vol.30, issue.1, pp.179-212, 2010. ,
DOI : 10.1007/978-1-4613-9293-4
URL : https://hal.archives-ouvertes.fr/hal-00440852
EXPERIMENTS ON DENSITY AND TURBIDITY CURRENTS: III. DEPOSITION OF SEDIMENT, Canadian Journal of Earth Sciences, vol.119, issue.3, pp.475-505, 1967. ,
DOI : 10.1111/j.1365-3091.1965.tb01563.x
On a Shallow Water Model for the Simulation of Turbidity Currents, Communications in Computational Physics, vol.6, issue.4, pp.848-882, 2009. ,
DOI : 10.4208/cicp.2009.v6.p848
Two-phase Numerical Model of Powder Avalanche. Theory and Application, Natural Hazards, vol.117, issue.8, pp.129-145, 1998. ,
Doppler Lidar Observations of a Downslope Windstorm, Monthly Weather Review, vol.116, issue.11, pp.2265-2275, 1988. ,
DOI : 10.1175/1520-0493(1988)116<2265:DLOOAD>2.0.CO;2
Three-Dimensional Turbulent Bottom Density Currents from a High-Order Nonhydrostatic Spectral Element Model, Journal of Physical Oceanography, vol.34, issue.9, pp.2006-2026, 2006. ,
DOI : 10.1175/1520-0485(2004)034<2006:TTBDCF>2.0.CO;2
Large eddy simulation of stratified mixing in two-dimensional dam-break problem in a rectangular enclosed domain. Ocean Modelling, pp.106-140, 2007. ,
Interaction between velocity and effective density in turbidity flow: Phase-plane analysis, with criteria for autosuspension, Marine Geology, vol.31, issue.1-2, pp.59-99, 1979. ,
DOI : 10.1016/0025-3227(79)90057-4
Conditions for the ignition of catastrophically erosive turbidity currents, Marine Geology, vol.46, issue.3-4, pp.307-327, 1982. ,
DOI : 10.1016/0025-3227(82)90086-X
Self-accelerating turbidity currents, Journal of Fluid Mechanics, vol.65, issue.-1, pp.145-181, 1986. ,
DOI : 10.1016/0025-3227(82)90086-X
The Mechanics of Marine Sediment Gravity Flows, Continental Margin Sedimentation, pp.275-337, 2007. ,
DOI : 10.1002/9781444304398.ch6
Vortex dynamics in a spatially accelerating shear layer, Journal of Fluid Mechanics, vol.376, issue.12, pp.1-35, 1998. ,
DOI : 10.1017/S002211209800250X
Mixing and entrainment in developing stratified currents, Journal of Fluid Mechanics, vol.424, issue.15, pp.45-73, 2000. ,
DOI : 10.1017/S0022112000001877
BANG1D:, Computers & Geosciences, vol.27, issue.6, pp.701-716, 2001. ,
DOI : 10.1016/S0098-3004(00)00123-0
Sediment-entraining suspension clouds: a model of powder-snow avalanches, Journal of Fluid Mechanics, vol.509, pp.181-206, 2004. ,
DOI : 10.1017/S0022112004009322
URL : https://hal.archives-ouvertes.fr/hal-00221403
Axisymmetric gravity currents on a cone, Journal of Fluid Mechanics, vol.565, issue.25, pp.227-253, 2006. ,
DOI : 10.1017/S0022112006001601
Systems of quasilinear equations and their application to gas dynamics, p.33, 1978. ,
Role of fine-grained sediment in turbidity current flow dynamics and resulting deposits, Marine Geology, vol.171, issue.1-4, pp.1-421, 2000. ,
DOI : 10.1016/S0025-3227(00)00114-6
Experimental study on self-accelerating turbidity currents, Journal of Geophysical Research, vol.31, issue.1, p.5025, 2005. ,
DOI : 10.1063/1.3128495
URL : http://onlinelibrary.wiley.com/doi/10.1029/2008JC005149/pdf
Fluid turbulence, Reviews of Modern Physics, vol.1, issue.2, pp.383-395, 1999. ,
DOI : 10.1115/1.3099004
Etude des courants de gravité sur forte pente avec application aux avalanches poudreuses, Thèse, p.33, 1977. ,
The Structure of Turbulent Shear Flow, 1980. ,
Kulikovskiy???Sveshnikova???Beghin model of powder snow avalanches: Development and application, Journal of Geophysical Research, vol.39, issue.F1, p.1004, 2007. ,
DOI : 10.1063/1.3128495
Buoyancy Effects in Fluids, 1973. ,
DOI : 10.1063/1.3128495
An Introduction to Gravity Currents and Intrusions, 2009. ,
DOI : 10.1201/9781584889045
Studies of unsteady self preserving turbulent flows, Water Res. Lab, vol.23, issue.24, p.33, 1965. ,
France E-mail address: Denys.Dutykh@univ-smb.fr URL ,
-mail address: Marguerite.Gisclon@univ-smb.fr URL ,