L. Amoudry, T. J. Hsu, and P. L. Liu, Two-phase model for sand transport in sheet flow regime, Journal of Geophysical Research, vol.49, issue.12, pp.10-1029, 2008.
DOI : 10.1029/2007JC004179

P. Aussillous, J. Chauchat, M. Pailha, M. Médale, and E. Guazzelli, Investigation of the mobile granular layer in bed-load transport, J. Fluid Mech, 2012.

R. A. Bagnold, Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.225, issue.1160, pp.49-63, 1954.
DOI : 10.1098/rspa.1954.0186

R. A. Bagnold, The Flow of Cohesionless Grains in Fluids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.249, issue.964, pp.235-297, 1956.
DOI : 10.1098/rsta.1956.0020

D. Berzi, Analytical Solution of Collisional Sheet Flows, Journal of Hydraulic Engineering, vol.137, issue.10, pp.1200-1207, 2011.
DOI : 10.1061/(ASCE)HY.1943-7900.0000420

F. Bombardelli and S. Jha, Hierarchical modeling of the dilute transport of suspended sediment in open channels, Environmental Fluid Mechanics, vol.61, issue.1, pp.207-235, 2009.
DOI : 10.1007/s10652-008-9091-6

F. Boyer, E. Guazzelli, and O. Pouliquen, Unifying Suspension and Granular Rheology, Physical Review Letters, vol.107, issue.18, pp.10-1103, 2011.
DOI : 10.1103/PhysRevLett.107.188301

URL : https://hal.archives-ouvertes.fr/hal-01432411

C. Cassar, M. Nicolas, and O. Pouliquen, Submarine granular flows down inclined planes, Physics of Fluids, vol.17, issue.10, 2005.
DOI : 10.1063/1.2069864

J. Chauchat and M. Médale, A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.9-12, pp.439-449, 2010.
DOI : 10.1016/j.cma.2009.07.007

URL : https://hal.archives-ouvertes.fr/hal-00619372

S. Courrech-du-pont, P. Gondret, B. Perrin, and M. Rabaud, Granular Avalanches in Fluids, Granular avalanches in fluids, p.44301, 2003.
DOI : 10.1103/PhysRevLett.90.044301

E. A. Cowen, R. D. Dudley, Q. Liao, E. A. Variano, and P. L. Liu, An insitu borescopic quantitative imaging profiler for the measurement of high concentration sediment velocity, Experiments in Fluids, vol.113, issue.1, pp.77-88, 2010.
DOI : 10.1007/s00348-009-0801-8

A. Deboeuf, G. Gauthier, J. Martin, Y. Yurkovetsky, and J. F. Morris, Particle Pressure in a Sheared Suspension: A Bridge from Osmosis to Granular Dilatancy, Physical Review Letters, vol.102, issue.10, pp.10-1103, 2009.
DOI : 10.1103/PhysRevLett.102.108301

P. Dong and K. Zhang, Two-phase flow modelling of sediment motions in oscillatory sheet flow, Coastal Engineering, vol.36, issue.2, pp.87-10910, 1999.
DOI : 10.1016/S0378-3839(98)00052-0

Y. Forterre and O. Pouliquen, Flows of Dense Granular Media, Annual Review of Fluid Mechanics, vol.40, issue.1, pp.1-24, 2008.
DOI : 10.1146/annurev.fluid.40.111406.102142

URL : https://hal.archives-ouvertes.fr/hal-01432132

P. Gao, Transition between Two Bed-Load Transport Regimes: Saltation and Sheet Flow, Journal of Hydraulic Engineering, vol.134, issue.3, pp.340-349, 2008.
DOI : 10.1061/(ASCE)0733-9429(2008)134:3(340)

G. Midi, On dense granular flows, Eur. Phys, J. E, vol.14, pp.341-365, 2004.

G. K. Gilbert, The transportation of debris by running water, 1914.

W. D. Grant and O. S. Madsen, Movable bed roughness in unsteady oscillatory flow, Journal of Geophysical Research, vol.11, issue.12, pp.469-481, 1982.
DOI : 10.1029/JC087iC01p00469

B. Greimann and F. Holly, Two-Phase Flow Analysis of Concentration Profiles, Journal of Hydraulic Engineering, vol.127, issue.9, pp.753-761, 2001.
DOI : 10.1061/(ASCE)0733-9429(2001)127:9(753)

D. M. Hanes and A. J. Bowen, A granular-fluid model for steady intense bed-load transport, Journal of Geophysical Research, vol.6, issue.B5, p.90, 1985.
DOI : 10.1029/JC090iC05p09149

D. M. Hanes and D. L. Inman, Experimental evaluation of a dynamic yield criterion for granular fluid flows, Journal of Geophysical Research, vol.10, issue.B5, pp.3670-3674, 1985.
DOI : 10.1029/JB090iB05p03670

T. Hsu, J. T. Jenkins, and L. F. Liu, On two-phase sediment transport: Dilute flow, Journal of Geophysical Research, vol.113, issue.C3, p.14, 2003.
DOI : 10.1029/2001JC001276

T. Hsu, J. T. Jenkins, and P. L. Liu, On two-phase sediment transport: sheet flow of massive particles, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.460, issue.2048, pp.2223-2250, 2004.
DOI : 10.1098/rspa.2003.1273

J. T. Jenkins, Dense shearing flows of inelastic disks, Physics of Fluids, vol.18, issue.10, pp.393-410, 2006.
DOI : 10.1063/1.2364168

J. T. Jenkins, Dense inclined flow of inelastic spheres, Granular matter, pp.47-52, 2007.

J. T. Jenkins and D. M. Hanes, Collisional sheet flows of sediment driven by a turbulent fluid, Journal of Fluid Mechanics, vol.370, issue.1, pp.29-52, 1998.
DOI : 10.1017/S0022112098001840

J. T. Jenkins and M. W. Richman, Grad's 13-moment system for a dense gas of inelastic spheres, Arch. Ration. Mech. Anal, vol.87, pp.355-377, 1985.

P. C. Johnson and R. Jackson, Frictional???collisional constitutive relations for granular materials, with application to plane shearing, Journal of Fluid Mechanics, vol.26, issue.-1, pp.67-93, 1987.
DOI : 10.1017/S0022112084002883

I. M. Krieger and T. J. Dougherty, A Mechanism for Non???Newtonian Flow in Suspensions of Rigid Spheres, Transactions of the Society of Rheology, vol.3, issue.1, pp.137-157, 1959.
DOI : 10.1122/1.548848

V. Kumaran, The constitutive relation for the granular flow of rough particles, and its application to the flow down an inclined plane, Journal of Fluid Mechanics, vol.561, pp.1-42, 2006.
DOI : 10.1017/S0022112006000279

L. Li and M. Sawamoto, Multi-phase model on sediment transport in sheet-flow regime under oscillatory flow, Coastal Eng. Jpn, vol.38, pp.157-178, 1995.

S. Longo, Two-phase flow modeling of sediment motion in sheetflows above plane beds, J. Hydraul. Eng, vol.131131, issue.5366, pp.366-3790733, 2005.

E. Meyer-peter and R. Muller, Formulas for bed-load transport, 2nd Meeting of the International Association of Hydraulic and Structural Research, pp.34-64, 1948.

F. N. Nnadi and K. C. Wilson, Motion of Contact???Load Particles at High Shear Stress, Journal of Hydraulic Engineering, vol.118, issue.12, pp.1670-16840733, 1061.
DOI : 10.1061/(ASCE)0733-9429(1992)118:12(1670)

M. Ouriemi, P. Aussillous, and E. Guazzelli, Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows, Journal of Fluid Mechanics, vol.33, pp.295-319, 2009.
DOI : 10.1007/BF02120313

URL : https://hal.archives-ouvertes.fr/hal-01432009

O. Pouliquen, Scaling laws in granular flows down rough inclined planes, Physics of Fluids, vol.11, issue.3, pp.542-548, 1999.
DOI : 10.1063/1.869928

F. J. Pugh and K. C. Wilson, Velocity and Concentration Distributions in Sheet Flow above Plane Beds, Journal of Hydraulic Engineering, vol.125, issue.2, pp.117-125, 1999.
DOI : 10.1061/(ASCE)0733-9429(1999)125:2(117)

J. F. Richardson and W. N. Zaki, Sedimentation and fluidization: Part i, Trans. Inst. Chem. Eng, vol.32, pp.35-53, 1954.

H. Rouse, Modern conceptions of the mechanics of turbulence, Trans, Am. Soc. Civ. Eng, vol.102, pp.463-505, 1937.

B. M. Sumer, A. Kozakiewicz, J. Fredsøe, and R. Deigaard, Velocity and Concentration Profiles in Sheet-Flow Layer of Movable Bed, Journal of Hydraulic Engineering, vol.122, issue.10, pp.549-5580733, 1996.
DOI : 10.1061/(ASCE)0733-9429(1996)122:10(549)

J. W. Thomas, Numerical Partial Differential Equations : Finite Difference Methods, 1995.
DOI : 10.1007/978-1-4899-7278-1

V. A. Vanoni, Sedimentation engineering, Manual 54, Am. Soc. Coastal Eng, vol.745, 1975.

K. Wilson, Analysis of Bed???Load Motion at High Shear Stress, Journal of Hydraulic Engineering, vol.113, issue.1, p.97103, 1987.
DOI : 10.1061/(ASCE)0733-9429(1987)113:1(97)

K. C. Wilson, Bed-load transport at high shear stress, Proc. A.S. C.E, 1966.

K. C. Wilson, Mobile???Bed Friction at High Shear Stress, Journal of Hydraulic Engineering, vol.115, issue.6, pp.825-8300733, 1989.
DOI : 10.1061/(ASCE)0733-9429(1989)115:6(825)

M. S. Yalin, Mechanics of sediment transport, 1977.

A. Armanini, H. Capart, L. Fraccarollo, and M. Larcher, Rheological stratification in experimental free-surface flows of granular???liquid mixtures, Journal of Fluid Mechanics, vol.532, pp.269-319, 2005.
DOI : 10.1017/S0022112005004283

P. Aussillous, J. Chauchat, M. Pailha, M. Médale, and E. Guazzelli, Investigation of the mobile granular layer in bedload transport by laminar shearing flows, Journal of Fluid Mechanics, vol.736, pp.594-615, 2013.
DOI : 10.1017/jfm.2013.546

URL : https://hal.archives-ouvertes.fr/hal-00915257

R. A. Bagnold, 1954 Experiments on a gravity-free dispersion of large solid spheres in a newtonian fluid under shear, Phil. Trans. R. Soc. Lond, vol.225, pp.49-63

R. A. Bagnold, The Flow of Cohesionless Grains in Fluids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.249, issue.964, pp.235-297
DOI : 10.1098/rsta.1956.0020

D. Berzi and L. Fraccarollo, 2013 Inclined, collisional sediment transport, Physics of Fluids, vol.25, issue.10

J. Best, S. Bennett, J. Bridge, and M. Leeder, Turbulence Modulation and Particle Velocities over Flat Sand Beds at Low Transport Rates, Journal of Hydraulic Engineering, vol.123, issue.12, pp.1118-1129, 1997.
DOI : 10.1061/(ASCE)0733-9429(1997)123:12(1118)

H. Capart and L. Fraccarollo, Transport layer structure in intense bed-load, Geophysical Research Letters, vol.47, issue.2, 2011.
DOI : 10.1029/2011GL049408

C. Cassar, M. Nicolas, and O. Pouliquen, Submarine granular flows down inclined planes, Physics of Fluids, vol.17, issue.10, p.103301, 2005.
DOI : 10.1063/1.2069864

O. Castro-orgaz, J. V. Giráldez, L. Mateos, and S. Dey, 2012 Is the von kármán constant affected by sediment suspension, Journal of Geophysical Research: Earth Surface, vol.117, issue.F4

F. X. Chassagneux and D. Hurther, Wave bottom boundary layer processes below irregular surfzone breaking waves with light-weight sheet flow particle transport, Journal of Geophysical Research: Oceans, vol.103, issue.C6, pp.1668-1690, 2014.
DOI : 10.1029/2010JC006443

URL : https://hal.archives-ouvertes.fr/hal-00960674

J. Chauchat and S. Guillou, On turbulence closures for two-phase sediment-laden flow models, Journal of Geophysical Research, vol.9, issue.C3, 2008.
DOI : 10.1029/2007JC004708

URL : https://hal.archives-ouvertes.fr/hal-00343574

E. A. Cowen, R. D. Dudley, Q. Liao, E. A. Variano, P. L. Liu et al., An insitu borescopic quantitative imaging profiler for the measurement of high concentration sediment velocity, Experiments in Fluids, vol.113, issue.1, pp.77-88, 2010.
DOI : 10.1007/s00348-009-0801-8

. Daniel, SM 1965 Flow of suspension in a rectangular channel

H. A. Einstein, 1950 The bed load function for sedimentation in open channel channel flows

J. Ferry and S. Balachandar, A fast Eulerian method for disperse two-phase flow, International Journal of Multiphase Flow, vol.27, issue.7, pp.1199-1226, 2001.
DOI : 10.1016/S0301-9322(00)00069-0

Y. Forterre and O. Pouliquen, Flows of Dense Granular Media, Annual Review of Fluid Mechanics, vol.40, issue.1, pp.1-24, 2008.
DOI : 10.1146/annurev.fluid.40.111406.102142

URL : https://hal.archives-ouvertes.fr/hal-01432132

R. Gaudio, A. Miglio, and S. Dey, Non-universality of von K??rm??n's ?? in fluvial streams, Journal of Hydraulic Research, vol.7, issue.5, pp.658-663, 2010.
DOI : 10.1080/00221680109499822

W. H. Graf and M. Cellino, Suspension flows in open channels; experimental study, Journal of Hydraulic Research, vol.115, issue.4, pp.435-447, 2002.
DOI : 10.1061/(ASCE)0733-9429(1996)122:10(549)

B. P. Greimann, M. Muste, and F. M. Jr, Two-phase formulation of suspended sediment transport, Journal of Hydraulic Research, vol.7, issue.4, pp.479-500
DOI : 10.1016/S0301-9322(96)00080-8

D. M. Hanes, . Inman, and L. Douglas, Experimental evaluation of a dynamic yield criterion for granular fluid flows, Journal of Geophysical Research, vol.10, issue.B5, pp.3670-3674, 1985.
DOI : 10.1029/JB090iB05p03670

T. J. Hsu, J. T. Jenkins, and P. L. Liu, On two-phase sediment transport: sheet flow of massive particles, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.460, issue.2048, pp.2223-2250, 2004.
DOI : 10.1098/rspa.2003.1273

D. Hurther and U. Lemmin, Shear stress statistics and wall similarity analysis in turbulent boundary layers using a high-resolution 3-D ADVP, IEEE Journal of Oceanic Engineering, vol.25, issue.4, pp.446-457, 2001.
DOI : 10.1109/48.895352

URL : https://hal.archives-ouvertes.fr/hal-00230300

D. Hurther and U. Lemmin, Improved Turbulence Profiling with Field-Adapted Acoustic Doppler Velocimeters Using a Bifrequency Doppler Noise Suppression Method, Journal of Atmospheric and Oceanic Technology, vol.25, issue.3, pp.452-463, 2008.
DOI : 10.1175/2007JTECHO512.1

URL : https://hal.archives-ouvertes.fr/hal-00400143

D. Hurther, . Thorne, and D. Peter, Suspension and near-bed load sediment transport processes above a migrating, sand-rippled bed under shoaling waves, Journal of Geophysical Research, vol.109, issue.C4, 2011.
DOI : 10.1029/2010JC006774

URL : https://hal.archives-ouvertes.fr/hal-00607983

D. Hurther, P. D. Thorne, M. Bricault, U. Lemmin, and J. M. Barnoud, A multi-frequency Acoustic Concentration and Velocity Profiler (ACVP) for boundary layer measurements of fine-scale flow and sediment transport processes, Coastal Engineering, vol.58, issue.7, pp.594-605
DOI : 10.1016/j.coastaleng.2011.01.006

URL : https://hal.archives-ouvertes.fr/hal-00614448

H. M. Ismail, 1951 Turbulent transfer mechanism and suspended sediment in closed channels, Proc. ASCE, vol.77, issue.6

J. T. Jenkins, Dense inclined flow of inelastic spheres. Granular matter 10, pp.47-52, 2007.

J. T. Jenkins and D. M. Hanes, Collisional sheet flows of sediment driven by a turbulent fluid, Journal of Fluid Mechanics, vol.370, issue.1, pp.29-52, 1998.
DOI : 10.1017/S0022112098001840

S. S. Lu and W. W. Willmarth, Measurements of the structure of the Reynolds stress in a turbulent boundary layer, Journal of Fluid Mechanics, vol.11, issue.03, pp.481-511
DOI : 10.1063/1.1762431

E. Meyer-peter and R. Muller, Formulas for bed-load transport, 2nd Meeting of the International Association of Hydraulic and Structural Research, pp.34-64, 1948.

E. Mignot, D. Hurther, and E. Barthelemy, On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow, Journal of Fluid Mechanics, vol.32, pp.423-452, 2009.
DOI : 10.1017/S0022112081002164

M. Muste, K. Yu, and M. Spasojevic, Practical aspects of ADCP data use for quantification of mean river flow characteristics; Part I: moving-vessel measurements, Flow Measurement and Instrumentation, vol.15, issue.1, pp.1-16, 2004.
DOI : 10.1016/j.flowmeasinst.2003.09.001

S. Naqshband, J. S. Ribberink, D. Hurther, and S. J. Hulscher, Bed load and suspended load contributions to migrating sand dunes in equilibrium, Journal of Geophysical Research: Earth Surface, vol.120, issue.4, 2014.
DOI : 10.1029/2006JF000683

URL : https://hal.archives-ouvertes.fr/hal-00990144

P. Nielsen and I. A. Teakle, Turbulent diffusion of momentum and suspended particles: A finite-mixing-length theory, Physics of Fluids, vol.16, issue.7, pp.2342-2348, 2004.
DOI : 10.1063/1.1738413

F. N. Nnadi and K. C. Wilson, Motion of Contact???Load Particles at High Shear Stress, Journal of Hydraulic Engineering, vol.118, issue.12, pp.1670-1684, 1992.
DOI : 10.1061/(ASCE)0733-9429(1992)118:12(1670)

M. Ouriemi, P. Aussillous, and E. Guazzelli, Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows, Journal of Fluid Mechanics, vol.33, pp.295-319, 2009.
DOI : 10.1007/BF02120313

URL : https://hal.archives-ouvertes.fr/hal-01432009

J. M. Pasini and J. T. Jenkins, Aeolian transport with collisional suspension, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.363, issue.1832, pp.1625-1646, 1832.
DOI : 10.1098/rsta.2005.1598

F. J. Pugh and K. C. Wilson, Velocity and Concentration Distributions in Sheet Flow above Plane Beds, Journal of Hydraulic Engineering, vol.125, issue.2, pp.117-125, 1999.
DOI : 10.1061/(ASCE)0733-9429(1999)125:2(117)

T. Revil-baudard and J. Chauchat, A two-phase model for sheet flow regime based on dense granular flow rheology, Journal of Geophysical Research: Oceans, vol.115, issue.6, pp.619-634
DOI : 10.1061/(ASCE)0733-9429(1989)115:6(825)

URL : https://hal.archives-ouvertes.fr/hal-00860868

H. Rouse, 1937 Modern conceptions of the mechanics of turbulence, Trans. Am. Soc. Civ. Eng, vol.102, pp.463-505

T. Song and W. H. Graf, Non uniform open-channel flow over a rough bed, Journal of Hydroscience and Hydraulic Engineering, vol.12, issue.1, pp.1-25, 1994.

B. Spinewine, H. Capart, L. Fraccarollo, and M. Larcher, Laser stripe measurements of near-wall solid fraction in channel flows of liquid-granular mixtures, Experiments in Fluids, vol.79, issue.6, pp.1507-1525, 2011.
DOI : 10.1007/s00348-010-1009-7

B. M. Sumer, A. Kozakiewicz, J. Fredsøe, and R. Deigaard, Velocity and Concentration Profiles in Sheet-Flow Layer of Movable Bed, Journal of Hydraulic Engineering, vol.122, issue.10, pp.549-558, 1996.
DOI : 10.1061/(ASCE)0733-9429(1996)122:10(549)

P. D. Thorne and D. M. Hanes, A review of acoustic measurement of small-scale sediment processes, Continental Shelf Research, vol.22, issue.4, pp.603-632
DOI : 10.1016/S0278-4343(01)00101-7

P. D. Thorne and D. Hurther, An overview on the use of backscattered sound for measuring suspended particle size and concentration profiles in non-cohesive inorganic sediment transport studies, Continental Shelf Research, vol.73, issue.0, pp.97-118, 2014.
DOI : 10.1016/j.csr.2013.10.017

URL : https://hal.archives-ouvertes.fr/hal-00930916

P. D. Thorne, D. Hurther, and B. D. Moate, Acoustic inversions for measuring boundary layer suspended sediment processes, The Journal of the Acoustical Society of America, vol.130, issue.3, pp.1188-1200, 2011.
DOI : 10.1121/1.3618728

URL : https://hal.archives-ouvertes.fr/hal-00619237

L. C. Van-rijn, Sediment Transport, Part II: Suspended Load Transport, Journal of Hydraulic Engineering, vol.110, issue.11, pp.1613-1641, 1984.
DOI : 10.1061/(ASCE)0733-9429(1984)110:11(1613)

V. Vanoni, A. 1977 Sedimentation engineering
URL : https://hal.archives-ouvertes.fr/jpa-00223337

C. Villaret and J. H. Trowbridge, Effects of stratification by suspended sediments on turbulent shear flows, Journal of Geophysical Research, vol.11, issue.C6, pp.10659-10680, 1991.
DOI : 10.1029/91JC01025

K. C. Wilson, Bed-load transport at high shear stress, Proc. A.S.C.E, 1966.

K. C. Wilson, Mobile???Bed Friction at High Shear Stress, Journal of Hydraulic Engineering, vol.115, issue.6, pp.825-830, 1989.
DOI : 10.1061/(ASCE)0733-9429(1989)115:6(825)

M. S. Yalin, Mechanics of sediment transport 2nd edition, 1977.

S. Yang and A. T. Chow, Turbulence structures in non-uniform flows, Advances in Water Resources, vol.31, issue.10, pp.1344-1351, 2008.
DOI : 10.1016/j.advwatres.2008.06.006

A. Armanini, H. Capart, L. Fraccarollo, and M. Larcher, Rheological stratification in experimental free-surface flows of granular???liquid mixtures, Journal of Fluid Mechanics, vol.532, pp.269-31910, 2005.
DOI : 10.1017/S0022112005004283

P. Aussillous, J. Chauchat, M. Pailha, M. Médale, and E. Guazzelli, Investigation of the mobile granular layer in bedload transport by laminar shearing flows, Journal of Fluid Mechanics, vol.736, pp.594-615, 2013.
DOI : 10.1017/jfm.2013.546

URL : https://hal.archives-ouvertes.fr/hal-00915257

R. A. Bagnold, Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.225, issue.1160, pp.49-63, 1954.
DOI : 10.1098/rspa.1954.0186

G. K. Batchelor, Diffusion in a field of homogeneous turbulence ii. the relative motion of particles, pp.345-362, 1948.

C. Berni, Processus de mobilisation et de transport de sédiments dans la zone de déferlement, 2011.

D. Berzi, Analytical Solution of Collisional Sheet Flows, Journal of Hydraulic Engineering, vol.137, issue.10, pp.1200-1207, 2011.
DOI : 10.1061/(ASCE)HY.1943-7900.0000420

J. Best, S. Bennett, J. Bridge, and M. Leeder, Turbulence Modulation and Particle Velocities over Flat Sand Beds at Low Transport Rates, Journal of Hydraulic Engineering, vol.123, issue.12, pp.1118-11290733, 1118.
DOI : 10.1061/(ASCE)0733-9429(1997)123:12(1118)

O. Blaj, Comment coule une pâte granulaire ? études des composantes primaire et secondaire et des fluctuations de l'écoulement, 2012.

F. Boyer, É. Guazzelli, and O. Pouliquen, Unifying Suspension and Granular Rheology, Physical Review Letters, vol.107, issue.18, 2011.
DOI : 10.1103/PhysRevLett.107.188301

URL : https://hal.archives-ouvertes.fr/hal-01432411

W. P. Breugem, B. J. Boersma, and R. E. Uittenbogaard, The influence of wall permeability on turbulent channel flow, Journal of Fluid Mechanics, vol.562, pp.35-72, 2006.
DOI : 10.1017/S0022112006000887

H. Capart and L. Fraccarollo, Transport layer structure in intense bed-load, Geophysical Research Letters, vol.47, issue.2, pp.10-1029, 2011.
DOI : 10.1029/2011GL049408

F. X. Chassagneux and D. Hurther, Wave bottom boundary layer processes below irregular surfzone breaking waves with light-weight sheet flow particle transport, Journal of Geophysical Research: Oceans, vol.103, issue.C6, pp.1668-169010, 2014.
DOI : 10.1029/2010JC006443

URL : https://hal.archives-ouvertes.fr/hal-00960674

J. Chauchat, Contribution à la modélisation diphasique du transport sédimentaire en milieux côtiers et estuariens, 2007.

P. Chiodi, P. Claudin, and B. Andreotti, A two-phase flow model of sediment transport: transition from bedload to suspended load, Journal of Fluid Mechanics, vol.89, 2014.
DOI : 10.1061/(ASCE)HY.1943-7900.0000686

URL : https://hal.archives-ouvertes.fr/hal-01060152

E. A. Cowen, R. D. Dudley, Q. Liao, E. A. Variano, and P. L. Liu, An insitu borescopic quantitative imaging profiler for the measurement of high concentration sediment velocity, Experiments in Fluids, vol.113, issue.1, pp.77-88, 2010.
DOI : 10.1007/s00348-009-0801-8

G. T. Csanady, Turbulent diffusion in the environment, Geophysics and Astrophysics Monographs, 1973.

S. Daniel, Flow of suspension in a rectangular channel, 1965.

E. Deutsch and O. Simonin, Large eddy simulation applied to the motion of particles in stationary homogeneous fluid turbulence, Turbulence Modification in Multiphase Flows ASME-FED, pp.35-42, 1991.

P. Dong and K. Zhang, Two-phase flow modelling of sediment motions in oscillatory sheet flow, Coastal Engineering, vol.36, issue.2, pp.87-109, 1999.
DOI : 10.1016/S0378-3839(98)00052-0

D. A. Drew and R. T. Lahey, Analytical modelling of multiphase-flow, Particulate two-phase flows, -Heinemann series on chemical engineering, pp.509-566, 1993.

H. Einstein, Formulas for the transportation of bed load, Transactions of the, pp.561-597, 1942.

F. Engelund and J. Fredsoe, Sediment Ripples and Dunes, Sediment ripples and dunes, pp.13-37, 1982.
DOI : 10.1146/annurev.fl.14.010182.000305

Y. Forterre and O. Pouliquen, Flows of Dense Granular Media, Annual Review of Fluid Mechanics, vol.40, issue.1, pp.1-24, 2008.
DOI : 10.1146/annurev.fluid.40.111406.102142

URL : https://hal.archives-ouvertes.fr/hal-01432132

J. L. Garbini, F. K. Forster, and J. E. Jorgensen, Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 2. Experimental investigation, Journal of Fluid Mechanics, vol.118, issue.-1, pp.471-50510, 1982.
DOI : 10.1017/S0022112073000194

R. Gaudio, A. Miglio, and F. Calomino, Friction factor and von K??rm??n's ?? in open channels with bed-load, Journal of Hydraulic Research, vol.28, issue.2, pp.239-247, 2011.
DOI : 10.1061/(ASCE)0733-9429(2002)128:1(20)

G. Midi, On dense granular flows, The European Physical Journal E, vol.4, issue.4, pp.341-365, 2004.
DOI : 10.1140/epje/i2003-10153-0

URL : https://hal.archives-ouvertes.fr/hal-00000959

W. Graf, Hydraulics of Sediment Transport, 513 pp, 1971.

B. Greimann and F. Holly, Two-Phase Flow Analysis of Concentration Profiles, Journal of Hydraulic Engineering, vol.127, issue.9, pp.753-761, 2001.
DOI : 10.1061/(ASCE)0733-9429(2001)127:9(753)

D. M. Hanes and A. J. Bowen, A granular-fluid model for steady intense bed-load transport, Journal of Geophysical Research, vol.6, issue.B5, 1985.
DOI : 10.1029/JC090iC05p09149

T. Hsu, J. T. Jenkins, and L. F. Liu, On two-phase sediment transport: Dilute flow, Journal of Geophysical Research, vol.113, issue.C3, p.14, 2003.
DOI : 10.1029/2001JC001276

T. Hsu, J. T. Jenkins, and P. L. Liu, On two-phase sediment transport: sheet flow of massive particles, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.460, issue.2048, pp.2223-2250, 2004.
DOI : 10.1098/rspa.2003.1273

D. Hurther and U. Lemmin, Shear stress statistics and wall similarity analysis in turbulent boundary layers using a high-resolution 3-D ADVP, IEEE Journal of Oceanic Engineering, vol.25, issue.4, pp.446-457, 2001.
DOI : 10.1109/48.895352

URL : https://hal.archives-ouvertes.fr/hal-00230300

D. Hurther and U. Lemmin, Improved Turbulence Profiling with Field-Adapted Acoustic Doppler Velocimeters Using a Bifrequency Doppler Noise Suppression Method, Journal of Atmospheric and Oceanic Technology, vol.25, issue.3, pp.452-463, 2008.
DOI : 10.1175/2007JTECHO512.1

URL : https://hal.archives-ouvertes.fr/hal-00400143

D. Hurther and P. D. Thorne, Suspension and near-bed load sediment transport processes above a migrating, sand-rippled bed under shoaling waves, Journal of Geophysical Research, vol.109, issue.C4, pp.10-1029, 2011.
DOI : 10.1029/2010JC006774

URL : https://hal.archives-ouvertes.fr/hal-00607983

D. Hurther, P. D. Thorne, M. Bricault, U. Lemmin, and J. Barnoud, A multi-frequency Acoustic Concentration and Velocity Profiler (ACVP) for boundary layer measurements of fine-scale flow and sediment transport processes, Coastal Engineering, vol.58, issue.7, pp.594-605, 2011.
DOI : 10.1016/j.coastaleng.2011.01.006

URL : https://hal.archives-ouvertes.fr/hal-00614448

J. T. Jenkins, Dense shearing flows of inelastic disks, Physics of Fluids, vol.18, issue.10, pp.393-410, 2006.
DOI : 10.1063/1.2364168

J. T. Jenkins, Dense inclined flow of inelastic spheres, Granular matter, pp.47-52, 2007.

J. T. Jenkins and D. M. Hanes, Collisional sheet flows of sediment driven by a turbulent fluid, Journal of Fluid Mechanics, vol.370, issue.1, pp.29-52, 1998.
DOI : 10.1017/S0022112098001840

J. Jiménez, TURBULENT FLOWS OVER ROUGH WALLS, Annual Review of Fluid Mechanics, vol.36, issue.1, pp.173-196, 2004.
DOI : 10.1146/annurev.fluid.36.050802.122103

T. Lanckriet, J. Puleo, G. Masselink, I. Turner, D. Conley et al., FIELD MEASUREMENTS OF SHEET FLOW SEDIMENT TRANSPORT IN THE SWASH ZONE, Coastal Engineering Proceedings, vol.1, issue.33, 2012.
DOI : 10.9753/icce.v33.sediment.78

S. Li, Multi-phase model on sediment transport in sheet-flow regime under oscillatory flow, Coastal engineering Japan, vol.38, pp.157-178, 1995.

S. Longo, Two-Phase Flow Modeling of Sediment Motion in Sheet-Flows above Plane Beds, Journal of Hydraulic Engineering, vol.131, issue.5, pp.366-3790733, 2005.
DOI : 10.1061/(ASCE)0733-9429(2005)131:5(366)

F. López and M. García, Wall Similarity in Turbulent Open-Channel Flow, Journal of Engineering Mechanics, vol.125, issue.7, pp.789-7960733, 1999.
DOI : 10.1061/(ASCE)0733-9399(1999)125:7(789)

S. S. Lu and W. W. Willmarth, Measurements of the structure of the Reynolds stress in a turbulent boundary layer, Journal of Fluid Mechanics, vol.11, issue.03, pp.481-511, 1973.
DOI : 10.1063/1.1762431

C. Manes, D. Poggi, and L. Ridolfi, Turbulent boundary layers over permeable walls: scaling and near-wall structure, Journal of Fluid Mechanics, vol.102, pp.141-170, 2011.
DOI : 10.1063/1.869889

E. Meyer-peter and R. Muller, Formulas for bed-load transport, 2nd Meeting of the International Association of Hydraulic and Structural Research, pp.34-64, 1948.

E. Mignot, D. Hurther, and E. Barthelemy, On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow, Journal of Fluid Mechanics, vol.32, pp.423-45210, 2009.
DOI : 10.1017/S0022112081002164

S. Naqshband, J. S. Ribberink, D. Hurther, and S. Hulscher, Bed load and suspended load contributions to migrating sand dunes in equilibrium, Journal of Geophysical Research: Earth Surface, vol.120, issue.4, pp.10-1002, 2014.
DOI : 10.1029/2006JF000683

URL : https://hal.archives-ouvertes.fr/hal-00990144

P. Nielsen and I. A. Teakle, Turbulent diffusion of momentum and suspended particles: A finite-mixing-length theory, Physics of Fluids, vol.16, issue.7, pp.2342-2348, 2004.
DOI : 10.1063/1.1738413

V. Nikora and D. Goring, Flow Turbulence over Fixed and Weakly Mobile Gravel Beds, Journal of Hydraulic Engineering, vol.126, issue.9, pp.679-6900733, 2000.
DOI : 10.1061/(ASCE)0733-9429(2000)126:9(679)

F. N. Nnadi and K. C. Wilson, Motion of Contact???Load Particles at High Shear Stress, Journal of Hydraulic Engineering, vol.118, issue.12, pp.1670-16840733, 1670.
DOI : 10.1061/(ASCE)0733-9429(1992)118:12(1670)

M. Ouriemi, P. Aussillous, and E. Guazzelli, Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows, Journal of Fluid Mechanics, vol.33, pp.295-319, 2009.
DOI : 10.1007/BF02120313

URL : https://hal.archives-ouvertes.fr/hal-01432009

D. Poggi, A. Porporato, L. Ridolfi, J. Albertson, and G. Katul, The effect of vegetation density on canopy sub-layer turbulence, Boundary-Layer Meteorology, pp.565-587, 2004.

F. J. Pugh and K. C. Wilson, Velocity and Concentration Distributions in Sheet Flow above Plane Beds, Journal of Hydraulic Engineering, vol.125, issue.2, pp.117-125, 1999.
DOI : 10.1061/(ASCE)0733-9429(1999)125:2(117)

M. R. Raupach, Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers, Journal of Fluid Mechanics, vol.15, issue.-1, pp.363-382, 1981.
DOI : 10.1063/1.861724

A. Recking, P. Frey, A. Paquier, P. Belleudy, and J. Y. Champagne, Feedback between bed load transport and flow resistance in gravel and cobble bed rivers, Water Resources Research, vol.128, issue.1, pp.10-1029, 2008.
DOI : 10.1029/2007WR006219

URL : https://hal.archives-ouvertes.fr/hal-00445071

T. Revil-baudard and J. Chauchat, A two-phase model for sheet flow regime based on dense granular flow rheology, Journal of Geophysical Research: Oceans, vol.115, issue.6, pp.619-63410, 2013.
DOI : 10.1061/(ASCE)0733-9429(1989)115:6(825)

URL : https://hal.archives-ouvertes.fr/hal-00860868

H. Rouse, Modern conceptions of the mechanics of turbulence, Trans, Am. Soc. Civ. Eng, vol.102, pp.463-505, 1937.

B. Spinewine, H. Capart, L. Fraccarollo, and M. Larcher, Laser stripe measurements of near-wall solid fraction in channel flows of liquid-granular mixtures, Experiments in Fluids, vol.79, issue.6, pp.1507-152510, 2011.
DOI : 10.1007/s00348-010-1009-7

L. Suarez, E. Barthélémy, C. Berni, J. Chauchat, H. Michallet et al., Vertical distribution of skewness and asymmetry in a boundary layere on a mobile bed. experiment and k ? ? model comparison, 2014.

B. M. Sumer, A. Kozakiewicz, J. Fredsøe, and R. Deigaard, Velocity and Concentration Profiles in Sheet-Flow Layer of Movable Bed, Journal of Hydraulic Engineering, vol.122, issue.10, pp.549-5580733, 1996.
DOI : 10.1061/(ASCE)0733-9429(1996)122:10(549)

C. M. Tchen, Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid, 1947.

P. D. Thorne and D. M. Hanes, A review of acoustic measurement of small-scale sediment processes, Continental Shelf Research, vol.22, issue.4, pp.603-632, 2002.
DOI : 10.1016/S0278-4343(01)00101-7

P. D. Thorne and D. Hurther, An overview on the use of backscattered sound for measuring suspended particle size and concentration profiles in non-cohesive inorganic sediment transport studies, Continental Shelf Research, vol.73, issue.0, pp.97-118, 2014.
DOI : 10.1016/j.csr.2013.10.017

URL : https://hal.archives-ouvertes.fr/hal-00930916

P. D. Thorne, D. Hurther, and B. D. Moate, Acoustic inversions for measuring boundary layer suspended sediment processes, The Journal of the Acoustical Society of America, vol.130, issue.3, pp.1188-1200, 2011.
DOI : 10.1121/1.3618728

URL : https://hal.archives-ouvertes.fr/hal-00619237

A. A. Townsend, The Structure of Turbulent Shear Flow, 433 pp, 1976.

L. C. Van-rijn, Sediment Pick???Up Functions, Sediment pickup functions, pp.1494-1502, 1984.
DOI : 10.1061/(ASCE)0733-9429(1984)110:10(1494)

M. R. Wells and D. E. Stock, The effects of crossing trajectories on the dispersion of particles in a turbulent flow, Journal of Fluid Mechanics, vol.11, issue.-1, pp.421-435, 1983.
DOI : 10.1017/S0022112078000117

K. Wilson, Analysis of Bed???Load Motion at High Shear Stress, Journal of Hydraulic Engineering, vol.113, issue.1, pp.97-103, 1987.
DOI : 10.1061/(ASCE)0733-9429(1987)113:1(97)

K. C. Wilson, Bed-load transport at high shear stress, Proc. A.S.C.E, 1966.

M. S. Yalin, Mechanics of sediment transport 2nd edition, 1977.

S. Yang and A. T. Chow, Turbulence structures in nonuniform flows, Advances in Water Resources, issue.10, pp.31-1344, 2008.