This article presents a mathematical model describing the dynamics of bank erosion and horizontal deformations in the lower reaches of the Amu Darya River. The study focuses on the development of the erosion boundary along straight and curved riverbank sections. The process is analyzed as a time-dependent phenomenon characterized by varying intensities and stabilization phases. Empirical coefficients were introduced to express the relationship between the length and width of the erosion zone, enabling the determination of its geometric and temporal parameters. The model provides analytical expressions that characterize the shape and development rate of the eroded area, incorporating the asynchronous onset of stabilization for both longitudinal and transverse dimensions. The proposed theoretical formulations were verified using field data collected from the lower Amu Darya, showing an accuracy of 5–10%, which confirms the adequacy of the developed model for engineering applications.  

Riverbank erosion, deformation intensity, erosion boundary, curved riverbank

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