Инд. авторы:	Fedotova Z.I., Khakimzyanov Gayaz S., Dutykh D.
Заглавие:	Energy equation for certain approximate models of long-wave hydrodynamics
Библ. ссылка:	Fedotova Z.I., Khakimzyanov Gayaz S., Dutykh D. Energy equation for certain approximate models of long-wave hydrodynamics // Russian Journal of Numerical Analysis and Mathematical Modelling. - 2014. - Vol.29. - Iss. 3. - P.167-178. - ISSN 0927-6467. - EISSN 1569-3988.
Внешние системы:	DOI: 10.1515/rnam-2014-0013; РИНЦ: 24055646; SCOPUS: 2-s2.0-84902299205; WoS: 000337174200003;
Реферат:	eng: A new derivation of completely nonlinear weakly-dispersive shallow water equations is given without assumption of flow potentiality. Boussinesq type equations are derived for weakly nonlinear waves above a moving bottom. It is established that the total energy balance condition holds for all nonlinear dispersion models obtained here.
Ключевые слова:	Surface waves.; Nonlinear dispersion equations; Ideal incompressible fluid; Conservative laws;
Издано:	2014
Физ. характеристика:	с.167-178
Цитирование:	1. S. V. Bazenkov, N. N. Morozov, and O. P. Pogutse, Dispersive effects in two-dimensional hydrodynamics. Doklady Akad. Nauk SSSR 293 (1987), No. 4, 818-822 (in Russian). 2. J. L. Bona, T. Colin, and D. Lannes, Long wave approximations for water waves. Arch. Rational Mech. Anal. 178 (2005), 373-410. 3. J. D. Carter and R. Cienfuegos, The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations. Eur. J. Mech. B/Fluids 30 (2011), 259-268. 4. D. Clamond and D. Dutykh, Practical use of variational principles for modelling water waves. Physica D 241 (2012), No. 1, 25-36. 5. F. Dias and P. Milewski, On the fully-nonlinear shallow-water generalized Serre equations. Physics Letters A 374 (2010), No. 8, 1049-1053. 6. A. A. Dorfman and G. I. Yagovdik, The equations of approximate nonlinear-dispersive theory of long gravitational waves caused by a moving bottom and propagating in a basin of variable depth. Chisl. Metody Mekhan. Sploshn. Sredy 8 (1977), No. 1, 36-48 (in Russian). 7. D. Dutykh and F. Dias, Energy of tsunami waves generated by bottom motion. Proc. R. Soc. A. 465 (2009), 725-744. 8. R. C. Ertekin, W. C. Webster, and J. V. Wehausen, Waves caused by a moving disturbance in a shallow channel of finite width. J. Fluid Mech. 169 (1986), 275-292. 9. Z. I. Fedotova and E. D. Karepova, Variational principle for approximate models of wave hydrodynamics. Russ. J. Numer. Anal. Math. Modelling 11 (1996), No. 3, 183-204. 10. Z. I. Fedotova and G. S. Khakimzyanov, Shallow water equations on a movable bottom. Russ. J. Numer. Anal. Math. Modelling 24 (2009), No. 1, 31-41. 11. Z. I. Fedotova and G. S. Khakimzyanov, Full nonlinear dispersion model of shallow water equations on a rotating sphere. J. Appl. Mech. and Tech. Phys. 52 (2011), No. 6, 865-876. 12. A. E. Green and P. M. Naghdi, A derivation of equations for wave propagation in water of variable depth. J. Fluid Mech. 78 (1976), No. 2, 237-246. 13. D. Lannes and P. Bonneton, Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation. Phys. Fluids 21 (2009), 16601-16609. 14. Y. A. Li, Hamiltonian structure and linear stability of solitary waves of the Green-Naghdi equations. J. Nonlin. Math. Phys. 9 (2002), No. 1, 99-105. 15. L. V. Ovsyannikov, N. I. Makarenko, V. I. Nalimov, et al., Nonlinear Problems in the Theory of Surface and Internal Waves. Nauka, Novosibirsk, 1985 (in Russian). 16. D. H. Peregrine, Long waves on a beach. J. Fluid. Mech. 27 (1967), No. 4, 815-827. 17. N. E. Voltzinger, K. A. Klevanny, and E. N. Pelinovsky, Long-Wave Dynamics of the Coastal Zone. Gidrometeoizdat, Leningrad, 1989 (in Russian). 18. N. E. Voltsinger and R. V. Pyaskovskii, The Theory of Shallow Water, Gidrometeoizdat, Leningrad, 1977 (in Russian). 19. G. B. Whitham, Linear and Nonlinear Waves. John Wiley&Sons, Inc., New York, 1974. 20. M. I. Zheleznyak and E. N. Pelinovsky, Physico-mathematical models of the tsunami climbing a beach. In: Tsunami Climbing a Beach (Ed. E. N. Pelinovsky). IAP Akad. Sci. USSR, Gorky, 1985, pp. 8-33 (in Russian).