zbMATH — the first resource for mathematics

Concerning the description of long nonlinear waves in channels. (English. Russian original) Zbl 0888.76007
Fluid Dyn. 31, No. 5, 739-746 (1996); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza. 1996, No. 5, 136-145 (1996).
Summary: A method of deriving the equations that describe long nonlinear waves in channels of arbitrary cross-section, taking the transverse acceleration of fluid particles into account (the Boussinesq approximation), is proposed. For channels of certain cross-sections the equations are written in explicit form. In the case of narrow channels, the Boussinesq equations and those of the next approximation are written in explicit form for arbitrary cross-sections.

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Full Text: DOI
[1] D. H. Peregrine, ”Long waves in a uniform channel of arbitrary cross section,”J. Fluid. Mech.,32, Pt. 2, 353 (1968). · Zbl 0162.57504
[2] D. H. Peregrine, ”Solitary waves in trapezoidal channels,”J. Fluid. Mech.,47, Pt. 1, 1 (1969).
[3] M. D. Groves, ”Hamiltonian long wave theory for water waves in a channel,”Quart. J. Mech. and Appl. Math.,47, Pt. 3, 367 (1994). · Zbl 0868.76013
[4] M. H. Teng and T. Y. Wu, ”Nonlinear water waves in channels of arbitrary shape,”J. Fluid. Mech.,242, 211 (1992). · Zbl 0756.76013
[5] H. Lamb,Hydrodynamics, Cambridge University Press, New York (1957).
[6] M. E. Eglit,Nonstationary Motions in River Beds and on Slopes [in Russian], MGU Press, Moscow (1986).
[7] G. B. Whitham,Linear and Nonlinear Waves, Wiley, New York (1974). · Zbl 0373.76001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.