Model of steady river flow motion in the cross section of a curved natural channel

Model of steady river flow motion in the cross section of a curved natural channel

Koroliova K.S. (CC FEB RAS, Khabarovsk , Russia)
Potapov I.I. (CC FEB RAS, Khabarovsk , Russia)
Potapov D.I. (CC FEB RAS, Khabarovsk , Russia)

Abstract

At present, the study of secondary flows using three-dimensional modeling is possible only for channels of small size and a relatively simple bed shape. Reduced-order hydraulic models are still required for modeling natural river flows. In this paper, a reduced mathematical model described the turbulent hydrodynamic flow along a river channel of the natural shape and took into account the secondary flows formed at channel bends is proposed. The reduction of the three-dimensional model to a two-dimensional one in the cross-section of the channel is carried out by hypothesizing the quasi-stationarity of the considered hydrodynamic flow and its asymptotic behavior along the flow coordinate of the channel. The model is formulated in a mixed “velocity-vortex-stream function” statement. An additional requirement for the problem reduction is the definition of boundary conditions on the flow free surface for the velocity fields determined in the normal and tangential directions to the channel axis. It is assumed that the values of these velocities should be determined from the solution of auxiliary problems or obtained from the data of natural or experimental measurements. The finite element method in the Petrov-Galerkin formulation is used as a numerical method for solving the mathematical model equations; an algorithm for the problem solving is proposed on its basis. To validate the proposed mathematical model and the algorithm, numerical modeling of the hydrodynamic flow in the Desna River cross-sections is implemented. Good agreement between the calculations by the proposed model and the results of the field measurements is obtained. It is shown that the proposed model describes the quiet turbulent flow in a bend channel with natural morphology adequately and with good accuracy, it correctly predicts the behavior of both the main and secondary flows.

Keywords

iver flow, natural morphology; pen channel; river bend; cross-section; finite element method.

Edition

Proceedings of the Institute for System Programming, vol. 38, issue 2, 2026, pp. 207-226

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

DOI: 10.15514/ISPRAS-2026-38(2)-14

For citation

Koroliova K.S., Potapov I.I., Potapov D.I. Model of steady river flow motion in the cross section of a curved natural channel. Proceedings of the Institute for System Programming, vol. 38, issue 2, 2026, pp. 207-226 DOI: 10.15514/ISPRAS-2026-38(2)-14.

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