Abstract
A model of the spreading of an oil spill based on ordinary differential equations (ODE) of the balance of forces acting on an axially symmetric slick is proposed. The proposed model differs from similar models due to the special choice of coefficients of enforcement members in the ODE. These coefficients are chosen according to the following condition: the Fay relation is obtained from the main equation of the model by equating force pairs at each spreading stage; at each stage, the prevailing (according to the Fay approach) force pair is selected for it. An advantage of the proposed model is the more consistent and natural passage from the finite Fay relations containing constants determined by the experimental data to the more general ODE describing the spreading. Additionally, the model considers the main weathering processes, using the method of pseudocomponents and the general posing of the problem in the form of the Cauchy problem for a set of differential equations and additional relationships. The simulation of the transformation of an oil spill for various parameters and a comparison with observations are implemented.
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