He’s Multiple-Scale Solution for the Three-dimensional Nonlinear KH Instability of Rotating Magnetic Fluids

  • Yusry Osman El-Dib Department of Mathematics, Faculty of Education, Ain Shams University
  • Amal A Mady Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt


This paper elucidates a trend in solving nonlinear oscillators of the rotating Kelvin-Helmholtz instability. The system is constituted by the vertical flux or the horizontal flux. He’s multiple-scales perturbation methodology has been applied and therefore the system is represented by a generalized homotopy equation. This approach ends up in a periodic answer to a nonlinear oscillator with high nonlinearity. The cubic-quintic nonlinear Duffing equation is obligatory as a condition to uniformly answer. This equation is employed to derive the stability criteria. The transition curves are plotted to investigate the stability image. It's shown that the angular velocity suppresses the instability. The tangential flux plays a helpful role, whereas the vertical field encompasses a destabilizing influence. Within the existence of the rotation, the velocity ratio reduces stability configuration.

Keywords: He’s-Multiple-Scale Method, Kelvin-Helmholtz Instability, Nonlinear Stability, Rotating Fluids, Magnetic Fluids.


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How to Cite
Y. El-Dib and A. Mady, “He’s Multiple-Scale Solution for the Three-dimensional Nonlinear KH Instability of Rotating Magnetic Fluids”, Int. Ann. Sci., vol. 9, no. 1, pp. 52-69, Dec. 2019.
Research Article