TY - JOUR

T1 - Dynamical effects of a magnetic field versus the nonlinear wave regime of a rotating layer of liquid

AU - Перегудин, Сергей Иванович

AU - Перегудина, Элина Сергеевна

AU - Холодова, Светлана Евгеньевна

N1 - 1. Kholodova, S.E.: Quasi-geostrophic motions in a rotating layer of an electrically conducting fluid. Journal of Applied Mechanics and Technical Physics 50, no. 1., pp. 25- 34 (2009). 2. Kholodova, S.E., Peregudin, S.I.: Modeling and Analysis of Streams and Waves in Liquid and Granular Mediums. St. Peterb. Gos. Univ., St. Petersburg (2009) [in Russian]. 3. Needler, G.T.: A model for thermocline circulation in an ocean of finite depth. J. Marine Res. 25, pp. 329-342 (1967) 4. Landau, L. D., Lifshitz, E. M., Pitaevskii, L.P.: Electrodynamics of Continuous Media. Vol. 8 (2nd ed.). Butterworth-Heinemann (1984) 5. Pedlosky J. Geophysical Fluid Dynamics. New York, Springer (1987)

PY - 2018/9/30

Y1 - 2018/9/30

N2 - The present paper is concerned with the dynamics of a magnetic field consequent on three-dimensional large-scale motions of an inviscid incompressible homogeneous perfectly conducting rotating fluid concentrated in a spherical layer. The proposed mathematical model of the above physical process is a closed system of partial differential equations consisting of hydrodynamic equations with due account of the rotation, the Lorentz force, and the corresponding equations of magnetic dynamics with required boundary conditions. We analyze the mathematical model which can be used for calculation of three-dimensional motions with large time scale and when the space horizontal scale is comparable to the layer radius. The principal idea of our approach is in the construction of a scheme of successive approximation, in which the geostrophic approximation is the first step. Our approach allows one to go beyond the heuristic arguments and derive general geostrophic equations describing the motion of both homogeneous and inhomogeneous electrically conducting rotating fluid. We obtain an analytic solution of the system of nonlinear partial differential equations that model the geostrophic motion in the spherical layer of perfect electrically conducting inhomogeneous rotating fluid. The analysis of the structure of the above fields of magnetohydrodynamic quantities allows one to justify the existence of strong changes in the thing layer adjacent to the outer boundary.

AB - The present paper is concerned with the dynamics of a magnetic field consequent on three-dimensional large-scale motions of an inviscid incompressible homogeneous perfectly conducting rotating fluid concentrated in a spherical layer. The proposed mathematical model of the above physical process is a closed system of partial differential equations consisting of hydrodynamic equations with due account of the rotation, the Lorentz force, and the corresponding equations of magnetic dynamics with required boundary conditions. We analyze the mathematical model which can be used for calculation of three-dimensional motions with large time scale and when the space horizontal scale is comparable to the layer radius. The principal idea of our approach is in the construction of a scheme of successive approximation, in which the geostrophic approximation is the first step. Our approach allows one to go beyond the heuristic arguments and derive general geostrophic equations describing the motion of both homogeneous and inhomogeneous electrically conducting rotating fluid. We obtain an analytic solution of the system of nonlinear partial differential equations that model the geostrophic motion in the spherical layer of perfect electrically conducting inhomogeneous rotating fluid. The analysis of the structure of the above fields of magnetohydrodynamic quantities allows one to justify the existence of strong changes in the thing layer adjacent to the outer boundary.

KW - quasi-geostrophic motion, rotating fluid, magnetic field diffusion, magnetohydrodynamic processes

M3 - Conference article

VL - 3

SP - 177

EP - 183

JO - Journal of Computational Technologies

JF - Journal of Computational Technologies

SN - 1560-7534

T2 - 9th International Conference on Computational and Information Technologies in Science, Engineering and Education, CITech 2018

Y2 - 25 September 2018 through 28 September 2018

ER -