Closure to “Negative Surges in Open Channels: Physical and Numerical Modeling” by Martina Reichstetter and Hubert Chanson Discussions and Closures Closure to “Negative Surges in Open Channels: Physical and Numerical Modeling” by Martina Reichstetter and Hubert Chanson DOI: 10.1061/(ASCE)HY.1943-7900.0000674 Martina Reichstetter1 and Hubert Chanson2 1Ph.D. Student, School of Geography, Planning and Environmental Management, Univ. of Queensland, Brisbane, QLD 4072, Australia; formerly, Graduate Student, School of Civil Engineering, Univ. of Queensland, Brisbane, QLD 4072, Australia. 2Professor, Hydraulic Engineering, School of Civil Engineering, Univ. of Queensland, Brisbane, QLD 4072, Australia (corresponding author). E-mail: h.chanson@uq.edu.au The authors thank the discussers for their pertinent comment. Indeed, a negative surge is observed in the upstream reservoir during a dam break wave, and there is an abundant literature on the topic. The complete solution of dam break wave is com- monly treated in modern textbooks (Henderson 1966; Montes 1998; Sturm 2001; Chanson 2004a, b). The analytical solution of dam break wave advancing over some water was first solved by Barré de Saint-Venant (1871) for a rising tide in a channel with initial water depth. Relevant experimental evidences included Bazin (1865, pp. 536–553) [see also Darcy and Bazin (1865), Schoklitsch (1917), Cavaillé (1965), and Estrade (1967)]. Interestingly, Bazin (1865) repeated experiments in a large canal with different initial conditions to check his findings, whereas Cavaillé (1965) repeated identical experiments on smooth and rough inverts for three initial water depth-to-reservoir height ratios. Hager and Chervet (1996) reviewed the historical developments. Experimental studies of negative surges included the free- surface measurements of Favre (1935) and the unsteady velocity data of Reichstetter and Chanson (2013) and Leng and Chanson (2013). Numerical studies of negative surges are more numerous (Tan and Chu 2009; Reichstetter and Chanson 2013), albeit restricted by the limited amount of detailed validation data sets. In relation to the original data at x ¼ 10.8 m [Fig. 4 in Reichstetter and Chanson (2013)], the water depth data were recorded 0.35 m upstream of the tainter gate, itself located 0.85 m of a free overfall (Fig. 1). Fig. 1 presents an undistorted dimensioned sketch of the channel downstream end. The longitu- dinal flow profile was substantially determined by the hydraulic control mechanism operating within the system (Henderson 1966; Chanson 2004b). Prior to gate opening, the channel flow was controlled by the undershoot tainter gate. The flow was sub- critical upstream of the gate and supercritical between the tainter gate and free overfall (Fig. 1, solid line). During the rapid complete gate opening, a transient flow took place during which the channel flow was controlled briefly by critical flow conditions at the gate location. This was followed by a gradually varied flow motion in the flume, which became controlled by the critical flow conditions at the overfall (Fig. 1, dashed line). The channel flow experienced a shift in downstream control location that was responsible for a slight increase in water depth at x ¼ 10.8 m beyond a certain time, as recorded by the acoustic displacement meter [Fig. 4 in Reichstetter and Chanson (2013)] and observed with video camera and digital photography. Notation The following symbols are used in this paper: d = water depth (m) measured above the invert; h = initial undershoot gate opening (m); x = longitudinal distance (m) positive downstream, with x ¼ 0 at test section upstream end; and 0.30 m Free overfall h d x = 10.8 m Fig. 1. Sketch of the negative surge generated by the rapid tainter gate opening © ASCE 07014010-1 J. Hydraul. Eng. J. Hydraul. Eng. 2014.140. D ow nl oa de d fr om a sc el ib ra ry .o rg b y T he U ni ve rs it y of Q ue en sl an d L ib ra ry o n 08 /1 6/ 14 . C op yr ig ht A S C E . F or p er so na l us e on ly ; al l ri gh ts r es er ve d. xGate = longitudinal coordinate (m) of the tainter gate (xGate ¼ 11.15 m herein). Subscripts Gate = flow properties at tainter gate; and x = longitudinal direction positive downstream. References Barré de Saint-Venant, A. J. C. (1871). “Théorie du mouvement non permanent des eaux, avec application aux crues de rivieres et a l’intro- duction des marees dans leur lit.” Comptes Rendus des séances de l’A- cadémie des Sciences, 73(4), 237–240 (in French). Bazin, H. (1865). “Recherches experimentales sur la propagation des ondes (Experimental research on wave propagation).” Mémoires présentés par divers savants à l’Académie des Sciences, Vol. 19, 495–644 (in French). Cavaillé, Y. (1965). “Contribution à l’etude de l’ecoulement variable accompagnant la vidange brusque d’une retenue (Contribution to the study of unsteady flow following a dam break).” Publication Scientifique et Technique du Ministère de l’Air, Vol. 410, 165 (in French). Chanson, H. (2004a). Environmental hydraulics of open channel flows, Elsevier-Butterworth-Heinemann, Oxford, U.K., 483. Chanson, H. (2004b). The hydraulics of open channel flow: An introduction, 2nd Ed., Butterworth-Heinemann, Oxford, U.K., 585. Darcy, H. P. G., and Bazin, H. (1865). “Recherches hydrauliques (Hydraulic research).” Imprimerie imperiales, Paris, Parties 1ère et 2ème (in French). Estrade, J. (1967). “Contribution à l’etude de la suppression d’un barrage. Phase initiale de l’ecoulement (Contribution to the study of dam break. Initial stages of the wave).” Bulletin de la Direction des Etudes et Re- cherches, Series A, Nucléaire, Hydraulique et Thermique, Vol. 1, EDF Chatou, France, 3–128 (in French). Favre, H. (1935). Etude theorique et experimentale des ondes de translation dans les canaux decouverts (Theoretical and experi- mental study of travelling surges in open channels), Dunod, Paris (in French). Hager, W. H., and Chervet, A. (1996). “Geschichte der dammbruchwelle.” Wasser Energie Luft, 88(3–4), 49–54 (in German). Henderson, F. M. (1966). Open channel flow, MacMillan, New York. Leng, X., and Chanson, H. (2013). “Effect of bed roughness on the propa- gation of negative surges in rivers and estuaries.” Proc., 21ème Congrès Français de Mécanique CFM 2013, Association Française de Mécani- que, Paris, France, 6 (in French). Montes, J. S. (1998). Hydraulics of open channel flow, ASCE Press, New York, 697. Reichstetter, M., and Chanson, H. (2013). “Negative surges in open channels: Physical and numerical modeling.” J. Hydraul. Eng., 10 .1061/(ASCE)HY.1943-7900.0000674, 341–346. Schoklitsch, A. (1917). “Über dambruchwellen.” Sitzungberichten der Königliche Akademie der Wissenschaften, Vol. 126, Part IIa, 1489–1514 (in German). Sturm, T. W. (2001). “Open channel hydraulics.” Water resources and envi- ronmental engineering series, McGraw Hill, Boston, 493. Tan, L., and Chu, V. H. (2009). “Lauber and hager’s dam-break wave data for numerical model validation.” J. Hydraul. Res., 47(4), 524–528. © ASCE 07014010-2 J. Hydraul. Eng. J. Hydraul. Eng. 2014.140. D ow nl oa de d fr om a sc el ib ra ry .o rg b y T he U ni ve rs it y of Q ue en sl an d L ib ra ry o n 08 /1 6/ 14 . C op yr ig ht A S C E . F or p er so na l us e on ly ; al l ri gh ts r es er ve d. http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000674 http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000674 http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000674 http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000674 http://dx.doi.org/10.1080/00221686.2009.9522028 http://dx.doi.org/10.1080/00221686.2009.9522028