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| Content Provider | Springer Nature Link |
|---|---|
| Author | Sa, T. Matsuoka, C. Nishihara, K. |
| Copyright Year | 2016 |
| Abstract | A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer–Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows. |
| Ending Page | 572 |
| Page Count | 42 |
| Starting Page | 531 |
| File Format | |
| ISSN | 09388974 |
| e-ISSN | 14321467 |
| Journal | Journal of Nonlinear Science |
| Issue Number | 2 |
| Volume Number | 27 |
| Language | English |
| Publisher | Springer US |
| Publisher Date | 2016-10-21 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics Classical Mechanics Economic Theory/Quantitative Economics/Mathematical Methods Richtmyer–Meshkov instability Vortex flows MHD interfacial instability Non-uniform current-vortex sheet Alfvén number Surface Alfvén wave Analysis Magnetohydrodynamics and electrohydrodynamics Interfacial stability and instability Nonlinear effects |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Engineering Modeling and Simulation |
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