Mathematical Model of a Flooding Process in the Don Delta during Extreme Surges

A. L. Chikin1, ✉, L. G. Chikina2

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

2 South Federal University, Rostov-on-Don, Russian Federation

✉ e-mail: chikin1956@gmail.com

Abstract

Purpose. The work consists in developing a mathematical model to study the flooding processes in the Don delta during the extreme surges.

Methods and Results. The level fluctuations in the Taganrog Bay are calculated based on solving a system of equations for long waves in a homogeneous incompressible fluid in the Coriolis force field. The problem is solved by the finite-difference methods on high-performance computing systems. The algorithm for determining the area of the Don delta flooding in the process of a surge is given. It is based on comparing the heights of the delta area to the water level and on taking a decision whether to flood or drain a computational cell. The calculation results are compared to the water level values observed at the gauging station, and are also displayed as a map diagram of the flooded area.

Conclusions. The proposed model should be applied in case of the extreme surges when a significant delta area is flooded. The model makes it possible to calculate accurately the hydrodynamic parameters of a flow including the magnitude of water level difference. The proposed algorithm determining whether flooding or draining is required for a computational domain, permits to reveal the areas in the Don delta where flooding depends on the wind conditions.

Keywords

shallow water equations, surge oscillations, computational experiment, flooding

Acknowledgements

The paper was prepared within the framework of state assignment of the Southern Scientific Center of RAS, state registration number of the project is 122011900153-9. The calculations were performed at the cluster in CCU “High-Performance Computing” of Southern Federal University.

Original russian text

Original Russian Text © A. L. Chikin, L. G. Chikina, 2024, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 40, Iss. 1, pp. 146–159 (2024)

For citation

Chikin, A.L. and Chikina, L.G., 2024. Mathematical Model of a Flooding Process in the Don Delta during Extreme Surges. Physical Oceanography, 31(1), pp. 135-147.

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