Wave propagation in a three-layer semi-infinite hydrodynamic system with a rigid lid

Authors

DOI:

https://doi.org/10.15587/1729-4061.2017.111941

Keywords:

interaction of waves, three-layer hydrodynamic system, amplitude of waves, ratio of amplitudes

Abstract

Research into propagation and interaction of waves in a three-layer hydrodynamic system is one of the relevant problems of modern theoretical and experimental hydrodynamics. The authors studied propagation and interaction of waves along contact surfaces of the three-layer hydrodynamic system "liquid half-space – layer – layer with a rigid lid". By applying a method of large-scale approximations, the first three linear approximations of the correspondent weakly nonlinear problem were obtained. The structure of wave motions on contact surfaces was explored. Dependence of amplitudes of waves-responses on contact surfaces at various geometrical and physical parameters was analyzed. In particular, for large values of thickness of the upper layer, it was found that a change in value of the wave number leads to rapid convergence of amplitudes of waves-responses to the common limited value. The authors showed the need for a detailed study of the limited case in the absence of density jump, in which one of the solutions of dispersion equation tends to zero. Results of the present research can be used in the design of algorithms for detection of wave motions in various liquid media. 

Author Biographies

Olga Avramenko, Volodymyr Vynnychenko Central Ukrainian State Pedagogical University Shevchenka str., 1, Kropyvnytskyi, Ukraine, 25006

Doctor of Physical and Mathematical Sciences, Professor, Head of Department

Department of Applied Mathematics, Statistics and Economics

Maria Lunyova, Volodymyr Vynnychenko Central Ukrainian State Pedagogical University Shevchenka str., 1, Kropyvnytskyi, Ukraine, 25006

Postgraduate student

Department of Applied Mathematics, Statistics and Economics

Volodymyr Naradovyi, Volodymyr Vynnychenko Central Ukrainian State Pedagogical University Shevchenka str., 1, Kropyvnytskyi, Ukraine, 25006

PhD, Senior Lecturer

Department of Applied Mathematics, Statistics and Economics

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Published

2017-10-30

How to Cite

Avramenko, O., Lunyova, M., & Naradovyi, V. (2017). Wave propagation in a three-layer semi-infinite hydrodynamic system with a rigid lid. Eastern-European Journal of Enterprise Technologies, 5(5 (89), 58–66. https://doi.org/10.15587/1729-4061.2017.111941

Issue

Vol. 5 No. 5 (89) (2017): APPLIED PHYSICS

Section

Applied physics

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Copyright (c) 2017 Olga Avramenko, Maria Lunyova, Volodymyr Naradovyi

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