Abstract
The nonlinear stage of development of perturbations at a tangential magnetohydrodynamic discontinuity is investigated in the weakly subcritical and supercritical regimes. It is assumed that the fluid is incompressible and that the density and magnetic field, as well as the velocity, suffer a discontinuity. An equation describing the evolution of low-amplitude nonlinear perturbations is obtained. For periodic perturbations this equation reduces to an infinite system of ordinary differential equations for the amplitudes of the Fourier harmonics. The system is reduced to finite form by truncation and then integrated numerically. Calculations show that the evolution of an initially sinusoidal perturbation always ends with the appearance in the wave profile of an infinite derivative. This can take the form of either an infinitely sharp peak (knife-edge) or wave breaking.
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S. I. Syrovatskii, “Magnetohydrodynamics,” Usp. Fiz. Nauk,62, 247 (1957).
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford (1961).
A. Miura, “Nonlinear evolution of the magnetohydrodynamic Kelvin-Helmholtz instability,” Phys. Rev. Lett.,49, 779 (1982).
M. S. Ruderman, “Propagation of nonlinear Alfvén surface waves along a tangential magnetohydrodynamic discontinuity in an incompressible fluid,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 98 (1985).
O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics [in Russian], Nauka, Moscow (1975).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 30–39, May–June, 1988.
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Ruderman, M.S. Effect of nonlinearity on the development of oscillatory magnetohydrodynamic Kelvin-Helmholtz instability in the weakly supercritical regime. Fluid Dyn 23, 348–355 (1988). https://doi.org/10.1007/BF01054739
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DOI: https://doi.org/10.1007/BF01054739