Abbott, D. E., and Kline, S. J. (1962). “Experimental investigation of subsonic turbulent flow over single and double backward facing steps.” J. of Basic Engineering 84(3), 317–325. Alauddin, M., and Basak, B. C. (2006). “Development of an expansion transition in open channel subcritical flow.” J. of Civil Engineering 34(2), 91–101. Alouri F., and Souhar M. (2000). “Experimental study of turbulent asymmetric flow in a flat duct symmetric sudden expansion.” J. of Fluids Engineering, 122(1), 174–177. Ansari, K., Morvan, H. P., and Hargreaves, D. M. (2011). "A numerical investigation into secondary currents and wall shear in trapezoidal channels.” J. of Hydraulic Engineering, ASCE, 137(4), p. 432 - 440. Asnaashari, A., Akhtari, A. A., Dehghani, A. A., and Bonakdari, H. (2016). “Experimental and numerical investigation of the flow field in the gradual transition of rectangular to trapezoidal open channels.” Engineering Applications of Computational Fluid Mechanics 10(1), 273–283. DOI: 10.1080/19942060.2016.1149102. Basak, B. C., and Alauddin, M. (2010). “Efficiency of an expansive transition in an open channel subcritical flow.” DUET Journal, Dhaka University of Engineering & Technology 1(1), 27–32. Booij, R. (2003). “Measurements and large eddy simulation in some curved flumes.” J. of turbulence 4, 8-16. Bodnar, T., and Prihoda, J. (2006). “Numerical simulation of turbulent free-surface flow in curved channel.” J. of Flow Turbulent Combust 76, 429-442. Brater E.F., and King H.W. (1976). “Handbook of Hydraulics.” McGraw-Hill, New York. Brundrett, E., and Baines, W.D. (1964). “The production and diffusion of vorticity in duct flow. J. of Fluid Mech. 19, 375. Cacqueray, N. D., Hargreaves, D. M., and Morvan, H. P. (2009). "A computational study of shear stress in smooth rectangular channels.” J. of Hydraulic Research, 47(1), p. 50 - 57. Carlson, J. J., Johnston, J. P., and Sagi, C. J. (1967). "Effects of Wall shape on flow regimes and performance in straight, two dimensional diffusers.” J. of Basic Engineering, No. 3, 151-160. Castillo, L., and George, W.K. (2001). “Similarity analysis for turbulent boundary layer with pressure gradient: Outer flow”. AIAA Journal, 39, pp. 41-47. Chang, P. K. (1976). “Control of flow separation.” Hemisphere publishing corporation, Washington, London. Chaturvedi, R. S. (1963). "Expansive subcritical flow in open channel transitions." J. of the Institution of Engineers, Civil Engineering Division, India, 43(May), 447–487. Cherdron, W., Durst, F. and Whitelaw, J. H. (1978). “Asymmetric flows and instabilities in symmetric ducts with sudden expansions.” J. Fluid Mech. 84, 13–31. Chow, V. T. (1959). “Open channel hydraulics.” McGraw-Hill, N.Y. Cokljat D., and Younis B.A (1995). “Second-order closure study of open channel flows.” J. of Hydraulic Engineering (ASCE); 121(2):94–107. Dargahi, B. (2004). “Three-dimensional flow modelling and sediment transport in the River Klarälven.” Earth Surface Processes and Landforms 29(7), 821–852. Daugherty, R. L., and Ingersoll, A. C. (1964). "Fluid mechanics." McGraw-Hill Book Co., Inc., New York. 759-764. El-Shewey, M. I. A., and Joshi, S. G. (1996). "A study of turbulence characteristics in open channel transitions as a function of Froude and Reynolds numbers using laser technique." Advanced Fluid Mechanics, 9, 363–372. Escudier, M. P., Oliveira, P. J., and Poole, R. J. (2002). “Turbulent flow through a plane sudden expansion of modest aspect ratio.” J. of Physics of Fluids – AIP 14(10): 3641–3654. Feil, O.G. (1962). "Vane system for very wide-angle sub-sonic diffusers." Report PD 7, Department of Mechanical Eng. Stanford University. Ferziger, J.H., and Peric, M. (2002). "Computational methods for fluid dynamics." third ed. Springer Verlag, New York. Feurich R. and Olsen N.R.B., (2012). “Finding Free Surface of Supercritical Flows-Numerical Investigation.” Engineering Applications of Computational Fluid Mechanics Vol. 6, Iss. 2, 2012 Filonovich, M.S., Azevedo, R., Rojas-Solórzano, L.R. and Leal, J.B. (2013). “Credibility analysis of computational fluid dynamic simulations for compound channel flow.” J. of Hydroinformatics 15(3): 926-938. Formica, G. (1955). "Esperienze preliminary sulle predate di carcico nei caneli, dovute a combiamenti di sezione (Preliminary test on head losses in channel due to cross-sectional changes).” L'Energia Electrica, Milan, Italy, 32(7), 554–568. Fox, R. W., Pritchard, P. J., and McDonald, A. T. (2009). “Introduction to fluid mechanics.” 7th ed., John Wiley and Sons, Inc., Hoboken, NJ. Frizzel, C., and Werth, D. (2006). “Flow separation downstream of equal and opposing flow junctions in open channels”. Proceedings of the world Environmental and water Resources Congress Omaha, Nebraska, USA. Gandhi, B.K., Verma, H.K. and Abraham B. (2010). “Investigation of flow profile in open channels using CFD.” IGHEM- 21-23, AHEC, IIT Roorkee, India. Gessner, F.B., and Jones, J.B. (1965). “On some aspects of fully-developed turbulent flow in rectangular channels.” J. of Fluid Mech. 23, 689. Graber, S. D. (1982). “Asymmetric flow in symmetric expansions.” J. of the Hydraulics Division, ASCE 108(HY10): 1082–1101. Haque, A. (2008). “Some characteristics of open channel transition flow”. Master’s Thesis, Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Canada. Han, S. S., Ramamurthy, A. S., and Biron, P. M. (2011). “Characteristics of flow around open channel 90° bends with vanes.” J. of Irrigation and Drainage Engineering, ASCE 137(10), 668–676. DOI: 10.1061/ (ASCE) IR.1943-4774.0000337. Hashimi, S. A. H. (1966). “Open channel expansions for subcritical flow.” Master’s Thesis University of Arizona. Henderson, F. M. (1966). “Open channel flow.” Prentice-Hall, Upper Saddle River, N.J. 07458. Hinds, J. (1928). “The hydraulic design of flume and siphon transitions.” Proceedings of the American Society of Civil Engineers Paper No.1690, 1423–1459. Hinze, J. O. (1975). "Turbulence". 2nd Edition, McGraw-Hill Book Co., New York. 638-650. Hirt, CW. and Nicholls, B.D. (1981). "Volume of fluid (VOF) method for dynamics of free boundaries." J. of Computational Physics, 39, 201-221. Hyatt, M. L. (1965). “Design, calibration, and evaluation of a trapezoidal measuring flume by model study.” M.S. Thesis, Utah State University, Logan, Utah. Ippen, A. T. (1949). “Channel transitions and controls.” Engineering Hydraulics, Proceedings of the Fourth Hydraulics Conference Iowa Institute of Hydraulic Research, June 12–15, 496:588 Isbash, S. V., and Lebedev, I. V. (1961). "Change of natural streams during construction of hydraulic structures." Proceedings, 9th Congress of IAHR, Dubrovnik, Yugoslavia, 1114-1121. Issa, R.I. (1986), "Solution of the implicitly discretized fluid flow equations by operator splitting." J. of Computational Physics, 62, 40-65. Kang, H. and Choi, S. (2006). "Reynolds stress modelling of rectangular open-channel flow." International J. for Numerical Methods in Fluids, 51, 131 9-1 334. Kay, J. M. and Nedderman, R.M. (1985) “Fluid mechanics and transfer processes.” Cambridge University Press, Cambridge. Launder, B. E., Reece, G. J., and Rodi, W. (1975). "Progress in the development of a Reynolds-Stress turbulence closure." J. of Fluid Mechanics, 68(3), 537-566. Mazumder, S.K. (1967). “Optimum length of transition in open channel expansive subcritical flow”. J. of IE (I), Vol. XL VIII, No. 3, Pt. CI 2, Nov. 1967. Mazumder S.K. and Hager W.H., (1993). “Supercritical expansion flow in Rouse modified and reversed transitions.” Journal of Hydraulic Engineering 119(2):201-219. Mehta, P. R. (1979). “Flow characteristics in two-dimensional expansions.” J. of the Hydraulics Division, ASCE, 105(HY5), 501–516. Mehta, P. R. (1981). “Separated flow through large sudden expansions.” J. of the Hydraulics Division, ASCE, 107(HY4), 451–460. Mitra, A. C. (1940). "Report on the model experiments of fluming of bridges on Purva branch." Technical Memorandum. 9, United Provinces Irrigation Res. Inst., Roorkee, India, 94–98. Mohanta, A., Naik, B., Patra, K.C. and Khatua K.K. (2014). “Experimental and numerical Study of flow in prismatic and non-prismatic section of a converging compound channel.” International J. of Civil Engineering Research, ISSN 2278-3652 Volume 5, Number 3, 203-210. Morris, H. M., and Wiggert, J. M. (1972). “Applied hydraulics in engineering.” Second edition. The Ronald Press, N.Y. Najafi-Nejad-Nasser, A., and Li, S. S. (2015). “Reduction of flow separation and energy head losses in expansions using a hump.” J. of Irrigation and Drainage Engineering, ASCE 141(3), 04014057. DOI: 10.1061/ (ASCE) IR.1943-4774.0000803. Najmeddin, S., and Li, S.S. (2016). “Numerical study of reducing the flow separation zone in short open-channel expansions by using a hump.” J. of Irrigation and Drainage Engineering, ASCE, htpp://doi.org/10.1061/ (ASCE) IR.1943-4774.0001034. Nashta, C. F., and Garde, R. J. (1988). “Subcritical flow in rigid-bed open channel expansions.” J. of Hydraulic Research 26(1): 49–65. Papanicolaou, A., and Hilldale, R. (2002). "Turbulence characteristics in a gradual channel transition." J. of Engineering Mechanics 128(9), 948–960. Perkins, H.J. (1970). “The formation of stream-wise vorticity in turbulent flow.” J. of Fluid Mech. 44, 721. Pezzinga, G. (1994), "Velocity distribution in compound channel flows by numerical modeling." J. of Hydraulic Engineering, ASCE, 120(10), 1176-1198. Prandtl, L. (1952). “Essentials of fluid mechanics.” London and Glasgow, Blackie & Son Ltd. Ramamurthy, A. S., Basak, S., and Rao, P. R. (1970). "Open channel expansions fitted with local hump." J. of the Hydraulic Division, ASCE, 96(HY5), 1105–1113. Ramamurthy A.S., Han S.S., and Biron P.M. (2013). “Three-dimensional simulation parameters for 90° open channel bend flows.” J. of Computing in Civil Engineering, ASCE; https://doi.org/10.1061/ (ASCE) CP.1943-5487.0000209. Rhodes, D. G., and Knight, D. W. (1994). "Distribution of shear force on boundary of smooth rectangular duct." J. of Hydraulic Engineering, ASCE, 120(7), p.787-807. Roshko, A. (1953). “On the drag and shedding frequency of two-dimensional bluff bodies.” NACA Technical Note 3169. Schlichting, H., and Gersten, H. (2000). "Boundary layer theory." 8th English Edition, Springer, New York, 29-112. Scobey, F. C. (1933). “The flow of waters in flumes.” U.S. Department of Agriculture Technical Bulletin 393. Seetharamia, K., and Ramamurthy, A. S. (1968). "Triangular sills in open channel expansions." Civil Engineering and Public Works Review, Vol. 63, 283. Seyedashraf, O., Ali A., and Shahidi, M.K. (2012). “Numerical study of channel convergence effects on flow pattern in 90° bends.” 9th International Congress on Civil Engineering, Isfahan University of Technology (IUT), Isfahan, Iran. Simmons, W. P. Jr. (1964). "Hydraulic design of transitions for small canals." Engineering Monograph No. 33, U.S. Dept. of the Interior, Bureau of Reclamation. Skogerboe, G. V., Austin, L. H., and Bennett, R. S. (1971). “Energy loss analysis for open channel expansions.” J. of the Hydraulics Division, ASCE 97(HY10): 1719–1735. Smagorinsky, J. (1963). "General circulation experiments with the primitive equations". Monthly Weather Review; 91 (3): 99–164. Bibcode: 1963MWRv...91...99S; https://doi:10.1175/1520-0493 (1963)091<0099: GCEWTP>2.3.CO; 2. Smith, C. D., and Yu, J. N. G. (1966). "Use of baffles in open channel expansions." J. of the Hydraulic Division, ASCE, 92(HY2), 1–17. Squire H. B., and Winter K. G. (1951). “The secondary flow in a cascade of airfoils in a non-uniform stream.” J. of Aero. Sci. 18, pp. 271-277. Swamee, P. K., and Basak, B. C. (1991). “Design of rectangular open-channel expansion transitions.” J. of Irrigation and Drainage Engineering, ASCE, 117(6), 827–838. Swamee, P. K., and Basak, B.C. (1992). “Design of trapezoidal expansive transitions.” J. of Irrigation and Drainage Engineering, ASCE, 118(1), 61–73. Swamee, P. K., and Basak, B.C. (1993). “Comprehensive open channel expansion transition design.” J. of Irrigation and Drainage Engineering, ASCE, 119(1), 1–17. Thapa D.R., Li S.S., and Ramamurthy A.S. (2016). “Non-intrusive laboratory measurements of flow velocity in open channel transition.” River Flow 2016: Iowa City, USA, July 11-14, 2016. U. S. Department of Transportation (1983). “Hydraulic design of energy dissipaters for culverts and channels.” Hydraulic Engineering Circular Number 14, Third Edition. Van Balen W., Uijttewaal W.S.J., and Blanckaert, K. (2009). “Large-eddy simulation of a mildly curved open-channel flow.” J. of Fluid Mechanics 630:413-442. Viegas, J.R., Rubesin, M.W., and Horstman, C.C. (1985)."On the use of wall functions as boundary conditions for two-dimensional separated compressible flows." Technical Report AIAA-85-0180, AIAA 23rd Aerospace Sciences Meeting, Reno, Nevada. Vittal, N., and Chiranjeevi, V. V. (1983). “Open channel transitions: rational method of design.” J. of Hydraulic Engineering, ASCE 109 (1), 99–115. Wilcox, D.C. (2004). "Turbulence modeling for CFD." DCW industries. Yakhot, V., and Orszag, S. A. (1986). “Renormalization group analysis of turbulence: basic theory.” J. of Scientific Computing, 1, 3–51.