Inlet effects on roll-wave development in shallow turbulent open-channel flows

Balmforth, N.J., Mandre, S., 2004. Dynamics of roll waves. J. Fluid Mech., 514, 1–33.10.1017/S0022112004009930Search in Google Scholar

Berlamont, J.F., 1976. Roll-waves in inclined rectangular open channels, A2, BHRA Fluid Eng., Newcastle, U.K., 13–26.Search in Google Scholar

Berlamont, J.F., Vanderstappen, N., 1981. Unstable turbulent flow in open channels. J. Hydraul. Div., 1074, 427–449.10.1061/JYCEAJ.0005647Search in Google Scholar

Brock, R., 1967. Development of roll waves in open channels. W.M. Keck Lab. of Hydraul. and Water Resources, California Inst. of Tech., Report KH-R-16, 226.Search in Google Scholar

Brock, R., 1969. Development of roll-wave trains in open channel. J. Hydraul. Div. ASCE, 95, HY4, 1401–1427.10.1061/JYCEAJ.0002132Search in Google Scholar

Brock, R., 1970. Periodic permanent roll waves. J. Hydraul. Div., 9612, 2565–2580.10.1061/JYCEAJ.0002801Search in Google Scholar

Cao, Z., Hu, P., Hu, K., Pender, G., Liug Q., 2015. Modelling roll waves with shallow water equations and turbulent closure. J. Hydraul. Res., 53, 2, 161–177.10.1080/00221686.2014.950350Search in Google Scholar

Chanson, H., 2004. The Hydraulics of Open Channel Flow: an Introduction. Elsevier, Amsterdam.10.1016/B978-075065978-9/50006-4Search in Google Scholar

Di Cristo, C., Vacca, A., 2005. On the convective nature of roll waves instability. J. Appl. Math., 2005, 259–271.10.1155/JAM.2005.259Search in Google Scholar

Di Cristo, C., Iervolino, M., Vacca, A., Zanuttigh, B., 2008. Minimum channel length for roll-waves generation. J. Hydraul. Res., 46, 1, 73–79.10.1080/00221686.2008.9521844Search in Google Scholar

Di Cristo, C., Iervolino, M., Vacca, A., Zanuttigh, B., 2010. Influence of relative roughness and Reynolds number on the roll waves spatial evolution. J. Hydraul. Eng., 136, 1, 24–33.10.1061/(ASCE)HY.1943-7900.0000139Search in Google Scholar

Di Cristo, C., Iervolino, M., Vacca, A., 2012a. Green’s function of the linearized Saint–Venant equations in laminar and turbulent flows. Acta Geophysica, 60, 1, 173–190.10.2478/s11600-011-0039-8Search in Google Scholar

Di Cristo, C., Iervolino, M., Vacca, A., 2012b. Discussion of “Analysis of dynamic wave model for unsteady flow in an open channel”. J. Hydr. Engrg. ASCE, 138, 915–917.10.1061/(ASCE)HY.1943-7900.0000538Search in Google Scholar

Di Cristo, C., Iervolino, M., Vacca, A., 2015. On the stability of gradually varying mudflows in open channels. Meccanica, 50, 4, 963–979.10.1007/s11012-014-0075-ySearch in Google Scholar

Dracos, T.A., Glenne, B., 1967. Stability criteria for open-channel flow. J. Hydraul. Div., 93(HY6), 79–101.10.1061/JYCEAJ.0001737Search in Google Scholar

Gottlieb, S., Shu, C.W., 1998. Total variation diminishing Runge–Kutta schemes. Math. Comp., 67, 221, 73–85.10.1090/S0025-5718-98-00913-2Search in Google Scholar

Harten, A., 1983. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 3, 357–393.10.1016/0021-9991(83)90136-5Search in Google Scholar

Huang, Z., Lee, J.J., 2015. Modeling the Spatial Evolution of Roll Waves with Diffusive Saint Venant Equations. J. Hydraul. Eng., 141, 2, 06014022-1.10.1061/(ASCE)HY.1943-7900.0000959Search in Google Scholar

Kenyon, K.E., 1998. Roll wave theory. Phys. Essays, 11, 531–540.10.4006/1.3025334Search in Google Scholar

Kevorkian, J., Yu, J., Wang, L., 1995. Weakly nonlinear waves for a class of linearly unstable hyperbolic conservation laws with source terms. SIAM Journal on Applied Mathematics, 55, 2, 446–484.10.1137/S003613999326931XSearch in Google Scholar

Khatsuria R.M., 2004. Hydraulics of Spillways and Energy Dissipators. CRC Press.10.1201/9780203996980Search in Google Scholar

Kranenburg, C., 1990. On the stability of gradually varying flow in wide open channels. J. Hydraul. Res., 28, 5, 621–628, doi:10.1080/00221689009499050.10.1080/00221689009499050Search in Google Scholar

Kranenburg, C., 1992. On the evolution of roll waves. J. Fluid Mech., 245, 249–261.10.1017/S0022112092000442Search in Google Scholar

Liggett, J.A., 1975. Stability. Unsteady flow in open channel. In: Mahmood, K., Yevjevich, V. (Eds.): Water Resources Publications, Vol. 1. Englewood, Colorado.Search in Google Scholar

Liu, K.F., Mei, C.C., 1989. Slow spreading of a sheet of Bingham fluid on an inclined plane. J. Fluid Mech., 207, 505–529.10.1017/S0022112089002685Search in Google Scholar

Liu, Q.Q., Chen, L., Li, J.C., Singh, V.P., 2005. Roll waves in overland flow. J. Hydrol. Eng., 10, 2, 110–117.10.1061/(ASCE)1084-0699(2005)10:2(110)Search in Google Scholar

Logan, M., Iverson, R.M., 2007. Video documentation of experiments at the USGS debris-flow flume 1992–2006 (amended to include 2007–2013). US Geological Survey, 2007-1315.10.3133/ofr20071315Search in Google Scholar

Montuori, C., 1963. Discussion of stability aspect of flow in open channels. J. Hydraul. Div., 894, 264–273.Search in Google Scholar

Murdock, J.A., 1999. Perturbations: Theory and Methods. Classic in Applied Mathematics, SIAM.10.1137/1.9781611971095Search in Google Scholar

Ponce, V.M., Simon, D.B., 1977. Shallow water propagation in open channel flow. J. Hydraul. Div., 103, 1461–1476.10.1061/JYCEAJ.0004892Search in Google Scholar

Ridolfi, L., Porporato, A., Revelli R., 2006. Green’s function of the linearized de Saint–Venant equations. J. Eng. Mech., 132, 2, 125–132.10.1061/(ASCE)0733-9399(2006)132:2(125)Search in Google Scholar

Roe, P.L., 1986. Characteristic-based schemes for the Euler equations. Ann. Rev. Fluid Mech., 18, 337–365, doi:10.1146/annurev.fl.18.010186.00200510.1146/annurev.fl.18.010186.002005Search in Google Scholar

Stoker, J.J., 1957. Water Waves, the Mathematical Theory with Applications. Interscience, London.Search in Google Scholar

Supino, G., 1960. Sopra le onde di traslazione nei canali. [Bore waves in channels]. Rend. Accad. Naz. Lincei, 295, 6, 543–552. (In Italian.)Search in Google Scholar

Thual, O., Plumerault, L.R., Astruc, D., 2010. Linear stability of the 1D Saint-Venant equations and drag parameterizations. J. Hydraul. Res., 48, 3, 348–353.10.1080/00221686.2010.481837Search in Google Scholar

Witham, G.B., 1974. Linear and Nonlinear Waves. John Wiley & Sons Interscience, New York.Search in Google Scholar

Venutelli M., 2011. Analysis of dynamic wave model for unsteady flow in an open channel. J. Hydr. Engrg. ASCE, 137, 9, 1072–1078.10.1061/(ASCE)HY.1943-7900.0000405Search in Google Scholar

Zanuttigh, B., Lamberti, A. 2002. Roll waves simulation using shallow water equations and weighted average flux method. J. Hydraul. Res., 405, 610–622.Search in Google Scholar

Zoppou, C., Roberts, S., 2003. Explicit schemes for dam-break simulations. J. Hydr. Engrg. ASCE, 129, 1, 11–34.10.1061/(ASCE)0733-9429(2003)129:1(11)Search in Google Scholar