Numerical Study of Resonant Oscillations of Water Level in the Sea of Azov under the Impact of Weak External Forces

А. L. Chikin

Federal Research Center the Southern Scientific Center, Russian Academy of Sciences, Rostov-on-Don, Russian Federation

e-mail: chikin1956@gmail.com

Abstract

Purpose. The study is aimed at determining the frequencies of resonant oscillations of water surface level in the Sea of Azov.

Methods and Results. The computational experiments were performed using a mathematical model based on a system of equations for long waves in a homogeneous fluid. The wind of variable direction or strength and atmospheric pressure oscillations were considered to be an external force. The problem was solved by the finite-difference methods using the implicit difference schemes. The values of period lengths at which the resonant effect arises were obtained. The oscillation frequency values were determined by calculating the total energy of oscillations as a sum of potential and kinetic energy. Agreement between the values of resonant frequency (or periods) of sea level oscillations under conditions of variable wind load and changing atmospheric impact has been revealed. It has been established that stable resonant oscillations emerge after four to seven periods of external periodic forcing, after which the oscillatory motion stabilizes.

Conclusions. The applied mathematical model permits to conduct computational experiments for studying the process of formation of resonant oscillations of the Azov Sea water level. The results of investigation describe adequately the periodic external influence on the water surface of the Sea of Azov. The calculated resonance frequencies are consistent with the results obtained by other authors.

Keywords

shallow water equations, resonance, resonant oscillations, seiche, computational experiment

Acknowledgements

The article was prepared as part of the state assignment of SSC, RAS for 2025 (state registration No. 125012100503-4). The calculations were performed on the High-Performance Computing cluster (CCU) at the Southern Federal University.

Original russian text

Original Russian Text © А. L. Chikin, 2025, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 41, Iss. 4, pp. 557–567 (2025)

For citation

Chikin, A.L., 2025. Numerical Study of Resonant Oscillations of Water Level in the Sea of Azov under the Impact of Weak External Forces. Physical Oceanography, 32(4), pp. 577-586.

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