Title | Mathematical modeling of dynamic processes in a continuous electrically conductive medium |
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Authors | S. K. Kazankov^{1}, S. I. Peregudin^{2}, S. E. Kholodova^{1}^{1}University IFMO ^{2}Saint-Petersburg State University |

Annotation | A mathematical model describing the dynamics of geophysical processes in an electrically conductive incompressible fluid bounded by free and solid impermeable surfaces is presented, taking into account the effects of magnetic field diffusion, gravity and Coriolis force. The mathematical model is based on the solution of the boundary magnetohydrodynamic problem for partial differential equations, taking into account the effects of long waves of small amplitude. By means of appropriate transformations, the system of differential equations of vector type and partial derivatives can be reduced to one scalar equation for the modified function perturbation of the free surface of the ocean. The mathematical analysis of the presented model used to study magnetohydrodynamic processes in the ocean of the northern hemisphere demonstrates the occurrence of the phenomenon of inversion of the induced magnetic field. |

Keywords | magnetic hydrodynamics, geophysics, ocean, electrically conductive fluid, incompressible fluid, mathematical modeling, magnetic field inversion |

Citation | Kazankov S. K., Peregudin S. I., Kholodova S. E. ''Mathematical modeling of dynamic processes in a continuous electrically conductive medium'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 73-78. Available at: https://conf.svmo.ru/files/2023/papers/paper10.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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