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Инд. авторы: Fedotova Z.I., Khakimzyanov G.S.
Заглавие: Nonlinear-dispersive shallow water equations on a rotating sphere and conservation laws
Библ. ссылка: Fedotova Z.I., Khakimzyanov G.S. Nonlinear-dispersive shallow water equations on a rotating sphere and conservation laws // Journal of Applied Mechanics and Technical Physics. - 2014. - Vol.55. - Iss. 3. - P.404-416. - ISSN 0021-8944. - EISSN 1573-8620.
Внешние системы: DOI: 10.1134/S0021894414030043; РИНЦ: 24062057; SCOPUS: 2-s2.0-84903381991; WoS: 000338493100004;
Реферат: eng: Nonlinear dispersive shallow water equations on a sphere are obtained without using the potential flow assumption. Boussinesq-type equations for weakly nonlinear waves over a moving bottom are derived. It is found that the total energy balance holds for all obtained nonlinear dispersive equations on a sphere.
Ключевые слова: energy conservation law; Boussinesq type equations; surface waves; shallow water equations on a sphere; nonlinear dispersive equations;
Издано: 2014
Физ. характеристика: с.404-416
Цитирование:
1. E. Terrile, M. Brocchini, K. H. Christensen, and J. T. Kirby, "Dispersive Effects on Wave-Current Interaction and Vorticity Transport in Nearshore Flows," Phys. Fluids 20, 036602 (2008).
2. Y. Zhang, A. B. Kennedy, N. Panda, et al., "Boussinesq-Green-Naghdi Rotational Water Wave Theory," Coastal Eng. 73, 13-27 (2013).
3. J. T. Kirby, F. Shi, B. Tehranirad, et al., "Dispersive Tsunami Waves in the Ocean: Model Equations and Sensitivity to Dispersive and Co Riolis Effects," Ocean Model. 62, 39-55 (2013).
4. J. L. Bona, T. Colin, and D. Lannes, "Long Wave Approximations for Water Waves," Arch. Rational Mech. Anal. 178, 373-410 (2005).
5. I. V. Lyubashevskaya and A. N. Chupakhin, "Basis of Differential Invariants of the Symmetry Group of the Green-Naghdi Equations," Vestn. Udmurt. Univ., Ser. 1: Mat. Mekh. Komput. Nauki, No. 2, 52-62 (2009).
6. A. A. Cherevko and A. P. Chupakhin, "Equations of the Shallow Water Model on a Rotating Attracting Sphere. 1. Derivation and General Properties," Prikl. Mekh. Tekh. Fiz. 50(2), 24-36 (2009) [J. Appl. Mech. Tech. Phys. 50 (2), 188-198 (2009)].
7. A. A. Cherevko and A. P. Chupakhin, "Shallow Water Equations on a Rotating Sphere. 2. Simple Stationary Waves and Sound Sharacteristics," Prikl. Mekh. Tekh. Fiz. 50(3), 82-96 (2009) [J. Appl. Mech. Tech. Phys. 50 (3), 428-440 (2009)].
8. D. H. Peregrine, "Long Waves on a Beach," J. Fluid Mech. 27(4), 815-827 (1967).
9. J. Miles and R. Salmon, "Weakly Dispersive Nonlinear Gravity Waves," J. Fluid Mech. 157, 519-531 (1985).
10. S. V. Bazdenkov, N. N. Morozov, and O. P. Pogutse, "Dispersive Effects in Two-Dimensional Hydrodynamics," Dokl. Akad. Nauk SSSR 293(4), 818-822 (1987).
11. Z. I. Fedotova and G. S. Khakimzyanov, "Analysis of the Conditions of Derivation of Nonlinear Dispersive Equations," Vychisl. Tekhnol. 17(5), 94-108 (2012).
12. 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. 16(9), 275-292 (1986).
13. Z. I. Fedotova and G. S. Khakimzyanov, "Full Nonlinear Dispersive Model of Shallow Water Equations on a Rotating Sphere," Prikl. Mekh. Tekh. Fiz. 52(6), 22-35 (2011) [J. Appl. Mech. Tech. Phys. 52 (6), 22-35 (2011)].
14. G. S. Khakimzyanov, Yu. I. Shokin, V. B. Barakhnin, and N. Yu. Shokina, Numerical Simulation of Fluid Flows with Surface Waves (Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2001) [in Russian].
15. A. A. Dorfman and G. I. Yagovdik, "Approximate Nonlinear Dispersive Equations of Long GravitationalWaves Caused by Movements of the Bottom and Propagating in a Tank of Variable Depth, " in Numerical Methods of Continuum Mechanics (Inst. of Theor. and Appl. Mech., Sib. Branch, Acad. of Sci. of the USSR, 1977), Vol. 8, No. 1, pp. 36-48.