Dependence of the internal wave energy flux on the parameters of a two­layer hydrodynamic system

Authors

DOI:

https://doi.org/10.15587/1729-4061.2020.210263

Keywords:

energy flux, internal progressive waves, two-layer hydrodynamic system, anomalous dispersion

Abstract

The study was performed to analyze the flux of energy of internal gravitational-capillary waves in a two-layer hydrodynamic liquid system with finite layer thicknesses. The problem was considered for an ideal incompressible fluid in the field of gravity as well as taking into account the forces of surface tension. The problem was formulated in a dimensionless form for small values of the coefficient of nonlinearity. The dispersion of the gravitational-capillary progressive waves was studied in detail depending on the coefficient of surface tension and the ratio of layer densities. It was proved that with the increase in the wavenumber, the group velocity begins to pass ahead of the phase velocity and their equality occurs at the minimum of the phase velocity. Dependence of the total average energy flux on the wavenumber (wavelength) and thickness of the liquid layers was calculated and graphically analyzed for different values of physical quantities, in particular, density and the coefficient of surface tension. It follows from the analysis that the energy flux of gravitational internal waves increases to a certain maximum value with an increase in the thickness of the lower layer and then approaches a certain limit value. For capillary waves, the energy flux of internal waves is almost independent of the thickness of the lower layer. It was also shown that the average energy flux for gravitational waves at a stable amplitude is almost independent of the wavelength. On the contrary, for capillary waves, the energy flux increases sharply with an increase in the wavenumber.

The results of the analysis of the energy flux of internal progressive waves make it possible to qualitatively assess physical characteristics in the development of environmental technologies that use internal undulatory motions in various aquatic environments as a source of energy

Author Biographies

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

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

PhD, Associate Professor

Department of Applied Mathematics, Statistics and Economics

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

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Published

2020-08-31

How to Cite

Naradovyi, V., Hurtovyi, Y., & Avramenko, O. (2020). Dependence of the internal wave energy flux on the parameters of a two­layer hydrodynamic system. Eastern-European Journal of Enterprise Technologies, 4(8 (106), 28–36. https://doi.org/10.15587/1729-4061.2020.210263

Issue

Vol. 4 No. 8 (106) (2020): Energy-saving technologies and equipment

Section

Energy-saving technologies and equipment

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Copyright (c) 2020 Volodymyr Naradovyi, Yurii Hurtovyi, Olga Avramenko

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