Investigation of velocity distribution and turbulence characteristics in subcritical circular open channel flows using a modified Reynolds stress model

Berlamont, 2003, Shear stress distribution in partially filled pipes, J. Hydrol. Eng., 129, 697, 10.1061/(ASCE)0733-9429(2003)129:9(697) Celik, 1984, Simulation of free-surface effects in turbulent channel flows, PCH PhysicoChem. Hydrodyn., 5, 217 Christensen, 1998, Bed shear stress distribution in straight channels with arbitrary cross section Clark, 2011, Turbulent flow characteristics in circular corrugated culverts at mild slopes, J. Hydrol. Res., 49, 676, 10.1080/00221686.2011.596399 Clark, 2014, Beyond average velocity: modelling velocity distributions in partially filled culverts to support fish passage guidelines, Int. J. River Basin Manage., 12, 101, 10.1080/15715124.2013.879591 Cokljat, D., 1993. Turbulence models for non-circular ducts and channels. PhD thesis, Dep. of Civil Eng., City Univ., London. Cokljat, 1995, Second-order closure study of open-channel flows, J. Hydrol. Eng., 121, 94, 10.1061/(ASCE)0733-9429(1995)121:2(94) Duggleby, 2007, Dynamical eigenfunction decomposition of turbulent pipe flow, J. Turbul., 8, 1 Dunbar, 1997, The average distance between points in geometric figures, The College Math. J., 28, 187, 10.1080/07468342.1997.11973860 Ead, 2000, Turbulent open-channel flow in circular corrugated culverts, J. Hydrol. Eng., 126, 750, 10.1061/(ASCE)0733-9429(2000)126:10(750) Einstein, 1958, Secondary currents in straight channels, Eos Trans. AGU, 39, 1085, 10.1029/TR039i006p01085 Guo, 2013, Theoretical solution for laminar flow in partially-filled pipes, J. Hydrol. Res., 51, 408, 10.1080/00221686.2013.784881 Guo, 2015, Turbulent velocity distribution with dip phenomenon in conic open channels, J. Hydrol. Res., 53, 73, 10.1080/00221686.2014.928807 Hanjalic, 1972, A Reynolds stress model of turbulence and its application to thin shear flows, J. Fluid Mech., 52, 609, 10.1017/S002211207200268X Hoohlo, 1994 Imamoto, 1988, Measurement of secondary flow in an open channel, 513 Kang, 2006, Reynolds stress modelling of rectangular open-channel flow, Int. J. Numer. Meth. Fluids, 51, 1319, 10.1002/fld.1157 Kang, 2006, Turbulence modeling of compound open-channel flows with and without vegetation on the floodplain using the Reynolds stress model, Adv. Water Resour., 29, 1650, 10.1016/j.advwatres.2005.12.004 Kim, 2011, Turbulence characteristics in a circular open channel by PIV measurement, J. Korean Soc. Mar. Eng., 35, 930, 10.5916/jkosme.2011.35.7.930 Knight, 2000, Boundary shear in circular pipes running partially full, J. Hydrol. Eng., 126, 263, 10.1061/(ASCE)0733-9429(2000)126:4(263) Launder, 1975, Progress in the development of a Reynolds stress turbulence closure, J. Fluid Mech., 68, 537, 10.1017/S0022112075001814 Liu, 2017, Simulation of exchange flow between open water and floating vegetation using a modified RNG k-ε turbulence model, Environ. Fluid Mech., 17, 355, 10.1007/s10652-016-9489-5 Nalluri, 1973, Turbulence characteristics in a smooth open channel of circular cross-section, J. Hydrol. Res., 11, 343, 10.1080/00221687309499768 Naot, 1982, Calculation of secondary currents in channel flow, J. Hydraul. Div., 108, 948, 10.1061/JYCEAJ.0005897 Nezu, 1985, Experimental study on secondary currents in open channel flow, 115 Nezu, 1986, Open-channel flow measurements with a laser Doppler anemometer, J. Hydrol. Eng., 112, 335, 10.1061/(ASCE)0733-9429(1986)112:5(335) Nezu, I., Nakagawa, H., 1993. Turbulence in open-channel flows. IAHR Monograph. Balkema, Rotterdam, the Netherlands. Peakall, 1996, Surface tension in small hydraulic river models—the significance of the Weber number, J. Hydrol.N.Z., 35, 199 Reece, G.J., 1977. Development and Application of a Generalized Reynolds-stress Model of Turbulence. PhD thesis, the Univ. of London, London. Rodi, 1993 Tominaga, 1989, Three-dimensional turbulent structure in straight open channel flows, J. Hydrol. Res., 27, 149, 10.1080/00221688909499249 Yoon, 2012, Velocity profiles and friction coefficients in circular open channels, J. Hydrol. Res., 50, 304, 10.1080/00221686.2012.673745 Younis, B.A., 1982. Boundary layer calculations with Reynolds stress turbulence models. Rep. FS/82/25, Dep. of Mech. Eng., Imperial College, Univ. of London, London, England. Zhong, 2014, Coherent structures and their interactions in smooth open channel flows, Environ. Fluid Mech., 15, 653, 10.1007/s10652-014-9390-z