Beishuizen NA, Naud B, Roekaerts D (2007) Evaluation of a modified Reynolds stress model for turbulent dispersed two-phase flows including two-way coupling. Flow Turbul Combust 79: 321–341
Article
Google Scholar
Bertodano ML, Saif AA (1997) Modified \({k-\varepsilon}\) model for two-phase turbulent jets. Nucl Eng Des 172: 187–196
Article
Google Scholar
Bertodano ML, Lee S-J, Lahey RT, Drew DA (1990) The prediction of two-phase turbulence and phase distribution phenomena using a Reynolds stress model. J Fluids Eng 112: 107–113
Article
Google Scholar
Bombardelli FA (2004) Turbulence in multiphase models for aeration bubble plumes. PhD Thesis. University of Illinois at Urbana-Champaign, Department of Civil and Environmental Engineering
Bombardelli FA, Gioia G (2006) Scouring of granular beds by jet-driven axisymmetric turbulent cauldrons. Phys Fluids 18: 088101
Article
CAS
Google Scholar
Bombardelli FA, Jha SK (2008) Hierarchical modeling of dilute, suspended-sediment transport in open channels. Environ Fluid Mech. doi:10.1007/s10652-008-9091-6
Bombardelli FA, Buscaglia GC, García MH (2003) Parallel computations of the dynamic behavior of bubble plumes. In: Brust FW (ed) Proceedings of the pressure vessels and pipe division conference, Cleveland, vol PVP-464, Residual Stress, Fitness-for-Service, and Manufacturing Processes. ASME-PVP Division
Brennen CE (2005) Fundamentals of multiphase flow. Cambridge University Press, Cambridge
Google Scholar
Buscaglia GC, Bombardelli FA, García MH (2002) Numerical modeling of large scale bubble plumes accounting for mass transfer effects. Int J Multiph Flow 28: 1763–1785
Article
CAS
Google Scholar
Cao Z, Carling PA (2002) Mathematical modeling of alluvial rivers: reality and myth. Part 2: special issues. Proc Inst Civ Eng Water Marit Eng 154(4): 297–308
Google Scholar
Cao Z, Wei L, Xie J (1995) Sediment-laden flow in open channels from two-phase flow viewpoint. J Hydraul Eng 121(10): 725–735
Article
Google Scholar
Chauchat J (2007) Contribution to two-phase flow modeling for sediment transport in estuarine and coastal zones. PhD Thesis, University of Caen, France (in French)
Chauchat J, Guillou S (2008) On turbulence closures for two-phase sediment-laden flow models. J Geophys Res 113(C11017)
Chen CP, Wood PE (1986) Turbulence closure modeling of the dilute gas-particle axisymmetric jet. AIChe J 32(1): 163–166
Article
CAS
Google Scholar
Choi S, Kang H (2004) Reynolds stress modeling of vegetated open-channel flows. J Hydraul Res 42(1): 3–11
Google Scholar
Cokljat D, Younis BA (1995) Second order closure study of open-channel flows. J Hydraul Eng 121(2): 94–107
Article
Google Scholar
Cokljat D, Ivanov VA, Sarasola FJ, Vasquez SA (2000) Multiphase k-epsilon models for unstructured meshes. In: ASME 2000 Fluids Engineering Division Summer Meeting, Boston
Cokljat D, Slack M, Vasquez SA, Bakker A, Montante G (2006) Reynolds-stress model for Eulerian multiphase. In: Nagano Y, Hanjalic K, Tummers MJ (eds) Proceedings of the 4th international symposium on turbulence heat and mass transfer, pp 1047–1054
Coleman NL (1986) Effects of suspended sediment on the open-channel distribution. Water Resour Res 22(10): 1377–1384
Article
Google Scholar
Drew DA (1975) Turbulent sediment transport over a flat bottom using momentum balance. J Appl Mech, Trans ASME 42: 38–44
Google Scholar
Drew D, Passman S (1999) Theory of multicomponent fluids. Applied mathematical sciences. Springer, Berlin
Google Scholar
Elghobashi S (1994) On predicting particle-laden turbulent flows. Appl Sci Res 52: 309–329
Article
Google Scholar
Elghobashi S, Abou-Arab TW (1983) A two-equation turbulence model for two-phase flows. Phys Fluids 26(4): 931–938
Article
Google Scholar
Einstein HA, Chien N (1955) Effects of heavy sediment concentration near the bed on velocity and sediment distribution. MRD Sediment Series Report No. 8, University of California, Berkeley, U.S. Army Corps of Engineers, Missouri Division
Gatski TB, Speziale CG (1993) On explicit algebraic stress models for complex turbulent flows. J Fluid Mech 254: 59–78
Article
CAS
Google Scholar
Gelfenbaum G, Smith JD (1986) Experimental evaluation of a generalized suspended-sediment transport theory. In: Knight RJ, McLean JR (eds) Shelf and sandstones. Canadian Society of Petroleum Geologists Memoir II. pp 133–144
Gioia G, Bombardelli FA (2002) Scaling and similarity in rough channel flows. Phys Rev Lett 88(1): 014501
Article
CAS
Google Scholar
Gioia G, Bombardelli FA (2005) Localized turbulent flows on scouring granular beds. Phys Rev Lett 95: 014501
Article
CAS
Google Scholar
Gioia G, Chakraborty P, Bombardelli FA (2006) Rough-pipe flows and the existence of fully developed turbulence. Phys Fluids 18: 038107
Article
CAS
Google Scholar
Greimann BP, Holly FM Jr (2001) Two-phase flow analysis of concentration profiles. J Hydraul Eng 127(9): 753–762
Article
Google Scholar
Greimann BP, Muste M, Holly FM Jr (1999) Two-phase formulation of suspended sediment transport. J Hydraul Res 37: 479–500
Google Scholar
Hsu T, Jenkins JT, Liu PLF (2003) On two-phase sediment transport: dilute flow. J Geophys Res 108(C3): 3057
Article
Google Scholar
Jaw SY, Chen CJ (1998) Present status of second order closure turbulence models. II Applications. J Eng Mech 124(5): 502–512
Article
Google Scholar
Jiang J, Law AW, Cheng NS (2004) Two-phase analysis of vertical sediment laden jets. J Eng Mech 131(3): 308–318
Article
Google Scholar
Kang H, Choi S-Uk (2006) Reynolds stress modeling of rectangular open-channel flow. Int J Numer Methods Fluids 51: 1319–1334
Article
Google Scholar
Kataoka I, Serizawa A (1989) Basic equations of turbulence in gas-liquid two-phase flow. Int J Multiph Flow 15(5): 843–885
Article
CAS
Google Scholar
Kobayashi N, Seo SN (1985) Fluid and sediment interaction over a plane bed. J Hydraul Eng 111(6): 903–919
Article
Google Scholar
Kumar R (1995) An algebraic stress/flux model for two-phase turbulent flow. In: Second ISHMIT-ASME heat and mass conference, Karnataka, India, 28–30 Dec
Laín S, Aliod R (2003) Discussion on second-order dispersed phase Eulerian equations applied to turbulent particle-laden jet flows. Chem Eng Sci 58: 4527–4535
Article
CAS
Google Scholar
Launder BE, Reece GJ, Rodi W (1975) Progress in the development of a Reynolds-stress turbulent closure. J Fluid Mech 68(3): 537–566
Article
Google Scholar
Lien FS, Leschzinger MA (1994) Assessment of turbulence-transport models concluding non-linear RNG eddy-viscosity formulation and second-moment closure for flow over a backward-facing step. Comput Fluids. 23(8): 983–1004
Article
Google Scholar
López F, García MH (1998) Open-channel flow through simulated vegetation: suspended sediment transport modeling. Water Resour Res 34(9): 2341–2352
Article
Google Scholar
López F, García M (2001) Mean flow and turbulence structure of open-channel flow through non-emergent vegetation. J Hydraul Eng 127(5): 392–402
Article
Google Scholar
Loth E (2007) Computational fluid dynamics of bubbles, drops and particles. Cambridge University Press, Cambridge
Google Scholar
Lyn DA (1988) A similarity approach to turbulent sediment-laden flows in open channels. J Fluid Mech 193: 1–26
Article
CAS
Google Scholar
Lyn DA (2008) Sedimentation engineering: theories, measurements, modeling and practice. In: García M (ed) Manual No. 110, ASCE, 1150 pp
Ma D, Ahmadi G (1988) A kinetic model for rapid granular flows of nearly elastic particles including interstitial fluid effects. Powder Technol 56: 191–207
Article
CAS
Google Scholar
Mashayek F, Taulbee DB (2002) A four-equation model for prediction of gas-solid turbulent flows. Numer Heat Transf 41: 95–116
Article
Google Scholar
McTigue DF (1981) Mixture theory for suspended sediment transport. J Hydraul Div 107(HY6):659–673
Google Scholar
Muste M, Patel VC (1997) Velocity profiles for particles and liquid in open-channel flow with suspended sediment. J Hydraul Eng 123(9): 742–751
Article
Google Scholar
Muste M, Fujita K, Yu I, Ettema R (2005) Two-phase versus mixed-flow perspective on suspended sediment transport in turbulent channel flows. Water Resour Res 41: W10402
Article
Google Scholar
Nezu I (2005) Open-channel flow turbulence and its research prospect in the 21st century. J Hydraul Eng 131(4): 229–246
Article
Google Scholar
Nezu I, Azuma R (2004) Turbulence characteristics and interaction between particles and fluid in particle-laden open-channel flows. J Hydraul Eng 130: 988–1001
Article
Google Scholar
Parker G (2004) 1D sediment transport morphodynamics with application to rivers and turbidity currents. e-book downloadable at: http://cee.uiuc.edu/people/parkerg/morphodynamics_ebook.htm
Parthasarathy RN, Faeth GM (1987) Structure of particle-laden turbulent water jets in still water. Int J Multiph Flow 13(5): 699–716
Article
CAS
Google Scholar
Pope SB (1975) A more general effective viscosity hypothesis. J Fluid Mech 72(2): 331–340
Article
Google Scholar
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge
Google Scholar
Rodi W (1984) Turbulence models and their application in hydraulics. International Association for Hydraulic Research, Delft, The Netherlands
Rubinstein R, Zhou Y, Younis BA (1997) The dissipation rate transport equation in rotating turbulent shear flow. In: Proceedings of the 13th symposium on turbulent shear flows
Sijercic M, Belosevic S, Stevanovic Z (2007) Simulation of free turbulent particle-laden jet using Reynolds-stress gas turbulence model. Appl Math Model 31: 1001–1014
Article
Google Scholar
Sokolichin A, Eigenberger G (1999) Applicability of the standard turbulence model to the dynamic simulation of bubble columns: Part I. Detailed numerical simulations. Chem Eng Sci 54: 2273–2284
Article
CAS
Google Scholar
Sokolichin A, Eigenberger G, Lapin A (2004) Simulation of buoyancy driven bubbly flow: established simplifications and open questions. AIChe J 50: 24–45
Article
CAS
Google Scholar
Speziale CG, Younis BA, Berger SA (2000) Analysis and modeling of turbulent flow in an axially rotating pipe. J Fluid Mech 407: 1–26
Article
Google Scholar
Squires KD, Eaton JK (1994) Effect of selective modification of turbulence on two-equation models for particle-laden turbulent flows. J Fluid Eng 116: 778–784
Article
CAS
Google Scholar
Taggart WC, Yermoli CA, Montes S, Ippen AT (1972) Effects of sediment size and gradation on concentration profiles for turbulent flow. M.I.T. Report No. 152
Taulbee DB, Mashayek F, Barre C (1999) Simulation and Reynolds stress modeling of particle-laden turbulent shear flows. Int J Heat Fluid Flow 20: 368–373
Article
Google Scholar
Toorman EA (2008) Vertical mixing in the fully developed turbulent layer of sediment-laden open channel flow. J Hydraul Eng 134(9): 1225–1235
Article
Google Scholar
Van Rijn LC (1984) Sediment transport. Part II: suspended load transport. J Hydraul Eng 110(11): 1613–1641
Article
Google Scholar
Vanoni VA (1946) Transportation of suspended sediment by water. Trans ASCE 111: 67–133
Google Scholar
Villaret C, Davies AG (1995) Modeling sediment-turbulent flow interactions. Appl Mech Rev 48(9): 601–609
Article
Google Scholar
Villaret C, Trowbridge JH (1991) Effects of stratification by suspended sediments on turbulent shear flows. J Geophys Res 96(6): 10659–10680
Article
Google Scholar
Wilcox DC (1988) Reassessment of the scale-determining equation for advanced turbulence models. AIAA J 26(11): 1299–1310
Article
Google Scholar
Xu Y, Subramaniam S (2006) A multiscale model for dilute turbulence gas-particle flows based on the equilibration of energy concept. Phys Fluids 18: 033301–033317
Article
CAS
Google Scholar
Yoon J, Kang S (2005) A numerical model for sediment-laden turbulent flow in an open channel. Can J Civ Eng 32: 233–240
Article
Google Scholar
Younis BA (1996) Progress in turbulence modeling for open-channel flows. In: Anderson MG, Walling DE, Bates PD (eds) Flood plain processes, chap 9. Wiley, New York, pp 299–332
Google Scholar
Zaichik LI, Alipchenkov VM (1999) A kinetic model for the transport of arbitrary-density particles in turbulent shear flows. In: Proceedings on turbulence and shear flow phenomena 1, Santa Barbara
Zhou LX, Chen T (2001) Simulation of swirling gas-particle flows using USM and \({k- \varepsilon - kp}\) two-phase turbulence models. Powder Technol 114: 1–11
Article
CAS
Google Scholar