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ABSTRACT We present numerical simulation results for the propagation of Alfvén waves in the charge starvation regime. This is the regime where the plasma density is below the critical value required to supply the current for the wave. We analyse a conservative scenario where Alfvén waves pick up charges from the region where the charge density exceeds the critical value and advect them along at a high Lorentz factor. The system consisting of the Alfvén wave and charges being carried with it, which we call charge-carrying Alfvén wave (CC-AW), moves through a medium with small, but non-zero, plasma density. We find that the interaction between CC-AW and the stationary medium has a two-stream like instability which leads to the emergence of a strong electric field along the direction of the unperturbed magnetic field. The growth rate of this instability is of the order of the plasma frequency of the medium encountered by the CC-AW. Our numerical code follows the system for hundreds of wave periods. The numerical calculations suggest that the final strength of the electric field is of the order of a few per cent of the AW amplitude. Little radiation is produced by the sinusoidally oscillating currents associated with the instability during the linear growth phase. However, in the non-linear phase, the fluctuating current density produces strong EM radiation near the plasma frequency and limits the growth of the instability.
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Two-dimensional stability analysis of finite-amplitude interfacial gravity waves in a two-layer fluid
We explore basic mechanisms for the instability of finite-amplitude interfacial gravity waves through a two-dimensional linear stability analysis of the periodic and irrotational plane motion of the interface between two unbounded homogeneous fluids of different density in the absence of background currents. The flow domains are conformally mapped into two half-planes, where the time-varying interface is always mapped onto the real axis. This unsteady conformal mapping technique with a suitable representation of the interface reduces the linear stability problem to a generalized eigenvalue problem, and allows us to accurately compute the growth rates of unstable disturbances superimposed on steady waves for a wide range of parameters. Numerical results show that the wave-induced Kelvin–Helmholtz (KH) instability due to the tangential velocity jump across the interface produced by the steady waves is the major instability mechanism. Any disturbances whose dominant wavenumbers are greater than a critical value grow exponentially. This critical wavenumber that depends on the steady wave steepness and the density ratio can be approximated by a local KH stability analysis, where the spatial variation of the wave-induced currents is neglected. It is shown, however, that the growth rates need to be found numerically with care and the successive collisions of eigenvalues result in the wave-induced KH instability. In addition, the present study extends the previous results for the small-wavenumber instability, such as modulational instability, of relatively small-amplitude steady waves to finite-amplitude ones.
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- Award ID(s):
- 2108524
- PAR ID:
- 10345098
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 938
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.145
