The numerical simulation of Faraday waves on the basis of hydrodynamic equations in the shallow-water approximation

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• 作者：T. G. Elizarova (1)
  D. S. Saburin (2)
  
  1. Keldysh Institute of Applied Mathematics ; Russian Academy of Sciences ; Miusskaya sq. 4 ; Moscow ; 125047 ; Russia
  2. Lomonosov Moscow State University ; Moscow ; 119991 ; Russia
  
• 关键词：Faraday waves ; shallow ; water equations ; numerical modeling
• 刊名：Moscow University Physics Bulletin
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：70
• 期：1
• 页码：1-6
• 全文大小：275 KB
• 参考文献：1. Kalinichenko, V A, Nesterov, S V, Sekerzh-Zen鈥檏ovich, S Ya, Chaikovskii, A A (1995) Experimental study of surface waves with Faraday resonance excitation. Fluid Dynamics 30: pp. 101-106 CrossRef
  2. Kalinichenko, V A (2009) Breaking of Faraday waves and jet launch formation. Fluid Dynamics 44: pp. 577-586 CrossRef
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  4. P茅rinet, N, Juric, D, Tuckerman, L S (2009) Numerical simulation of Faraday waves. J. Fluid Mech. 635: pp. 1-26 CrossRef
  5. Wright, J, Yon, S, Pozrikidis, C (2000) Numerical studies of two-dimensional Faraday oscillations of inviscid fluids. J. Fluid Mech. 402: pp. 1-32 CrossRef
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  7. Moiseev, N N (1953) Mat. Sb. 32: pp. 61-96
  8. Ibrahim, R A (2005) Liquid Sloshing Dynamics: Theory and Applications. Cambridge Univ., Cambridge CrossRef
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  10. Kulikovskii, A G, Pogorelov, N V, Semenov, A Yu (2001) Mathematical Questions of Digital Solution of Hyperbolic Equation Systems.
  11. Bulatov, O V, Elizarova, T G (2011) Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows. Compt. Mathem. Mathem. Phys. 51: pp. 160-173 CrossRef
  12. Elizarova, T G, Saburin, D A (2013) Numerical simulation of fluid oscillations in fuel tanks. Mathem. Models Compt. Simul. 5: pp. 470-478 CrossRef
  13. Elizarova, T G (2009) Quasi-Gas Dynamic Equations. CrossRef
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-8460

文摘

Faraday waves were numerically simulated in the shallow-water approximation. The algorithm is based on the regularized shallow-water equations. The results correspond to the existing theoretical and experimental data. In particular, the parametric resonance is found for the first and second wave modes, in which regular and irregular waves with respect to the overload value are observed.