An approximate model of de Saint-Venant equations is proposed to study the motion of a flood wave down a channel. Its validity is not restricted to mild bottom slopes and the resulting parabolic equation can be integrated even if the variation of the wave speed with the flow rate is taken into account.
@article{RLINA_1978_8_64_6_594_0, author = {Enrico Marchi}, title = {La propagazione delle onde di piena}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti}, volume = {64}, year = {1978}, pages = {594-602}, zbl = {0424.76014}, language = {it}, url = {http://dml.mathdoc.fr/item/RLINA_1978_8_64_6_594_0} }
Marchi, Enrico. La propagazione delle onde di piena. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 64 (1978) pp. 594-602. http://gdmltest.u-ga.fr/item/RLINA_1978_8_64_6_594_0/
[1] 73, n. 3, 147-154, n. 4, 237-240.
(1871) - «Compte Rendu de l'Ac. des Sciences». Paris,[2]
(1971) - Open Channel Flow. The MacMillan Co. Chap. 9.[3]
e (1977) - Mathematical Models for Surface Water Hydrology. J. Wiley and Sons, 169-179.[4]
(1951) - «Bull. No. 1». Disaster Prevention Research Institute, Kyoto University, Japan, Dec.[5]
e (1977) - Mathematical Models for Surface Water Hydrology. J. Wiley and Sons, 109-147.[6]
(1965) - Le reti idrauliche. Pàtron, Cap. V.[7] L'Energia Elettrica, n. 8, 783-791.
(1956) - (1974) - Linear and Nonlinear Waves. J. Wiley and Sons. Cap. 2, 3, 4.