Abstract
The problem of the stability of the sandy bottom of a rectangular channel with respect to spatially onedimensional perturbations is formulated. The channel stability problem is solved using the sediment discharge formula modified by taking into account the effect of free-surface perturbations on sediment transport. Analytic dependences of the propagation velocity of bottom perturbations on time are obtained for small Froude numbers. Wavelengths for the most rapidly growing bottom perturbations are obtained analytically, and the problem of the evolution of a single bottom perturbation is solved.
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References
P. G. Petrov, “Motion of a bed load,” J. Appl. Mech. Tech. Phys., 32, No. 5, 717–721 (1991).
A. G. Petrov and P. G. Petrov, “Sediment discharge vector in a turbulent flow above an eroded bottom,” J. Appl. Mech. Tech. Phys., 41, No. 2, 298–308 (2000).
V. M. Lokhtin, On the Mechanism of the River Channel [in Russian], Tip. Dombrovskogo, Kazan’ (1895).
E. C. Bingham, Fluidity and Plasticity, McGraw Hill, New York (1923).
F. I. Frankl, “Motion of sandy waves,” Dokl. Akad. Nauk SSSR, 89, No. 1, 29–32 (1953).
N. I. Makkaveev, River Channel and Erosion in Its Basin [in Russian], Izd. Akad. Nauk SSSR, Moscow (1955).
J. F. Kennedy, “The mechanics of dunes and antidunes in erodible-bed channels,” J. Fluid Mech., 16, No. 4, 521–544 (1963).
T. Hayashi, “Formation of dunes and antidunes in open channels,” J. Hydraul. Div. Proc. Amer. Soc. Civ. Eng., 96, No. 6, 357–366 (1970).
F. Engelund and J. Fredsoe, “Sediment ripples and dunes,” Annu. Rev. Fluid Mech., No. 14, 13–37 (1982).
V. M. Katolikov and Z. D. Kopaliani, “Point bars in river channels: formation conditions and their dynamics,” Vod. Res., 28, No. 5, 579–586 (2001).
K. Taki and G. Parker, “Transportational cyclic steps created by flow over an erodible bed,” J. Hydrodyn. Res., 132, No. 4, 437–438 (2006).
K. V. Grishanin, Stability of River Beds and Channels [in Russian], Gidrometeoizdat, Leningrad (1974).
N. E. Kochin, I. A. Kibel’, and N. V. Roze, Theoretical Hydrodynamics [in Russian], Vols. 1 and 2, Fizmatgiz, Moscow (1963)
K. V. Grishanin, Theory of Channel Process [in Russian], Transport, Moscow (1972).
B. A. Shulyak, Physics of Waves on the Surface of a Granular Medium and Fluid [in Russian], Nauka, Moscow (1971).
R. A. Bagnold, “An approach to the sediment transport problem from general physics,” U.S. Geolog. Survey Prof. Paper No. 422-I (1966).
I. I. Potapov, “On the closing of the equations of channel deformations for a cohesionless bottom,” Preprint No. 117, Computer Center, Far East Division, Russian Academy of Sciences, Khabarovsk (2008).
A. N. Butakov, Hydraulics of Development of River Channel Mesoforms [in Russian], RUND, Moscow (1999).
Yu. M. Korchokha, “Dune movement of sediments on the Polomet’ River,” Tr. Gos. Gidrol. Inst., No. 161, 98–122 (1968).
V. F. Pushkarev, “Movement of entrained sediments,” Tr. Gos. Gidrol. Inst., No. 8, 93–110 (1948).
V. I. Nikora, “Spectra of sandy waves in forward flow,” Meteorolog. Gidrolog., No. 5, 92–102 (1983).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 51, No. 1, pp. 62–74, January–February, 2010.
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Petrov, A.G., Potapov, I.I. Formulation and solution of the problem of the stability of a cohesionless channel bottom. J Appl Mech Tech Phy 51, 51–61 (2010). https://doi.org/10.1007/s10808-010-0008-z
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DOI: https://doi.org/10.1007/s10808-010-0008-z