论文标题
浅水磁流体动力剪切流的关键层不稳定性
Critical-layer instability of shallow water magnetohydrodynamic shear flows
论文作者
论文摘要
在本文中，研究了带有剪切平行磁场的浅水剪切流的不稳定性。在这样的磁性剪切流中传播的波遇到了关键水平，在这种速度相对于基本流量$ c-u（y）$匹配的alfvén波速度$ \ pm b（y）/\ sqrt {μρ} $，基于本地磁场$ b（y）$，$ b（y）$，$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $。结果表明，当两个临界级别彼此接近时，临界层会产生不稳定性。解决了不稳定性问题，将大型波数和数值溶液的渐近溶液结合在一起，并使用动量保护来解释不稳定性的机理。对于浅水MHD系统，本文给出了局部微分方程的一般形式，该方程是为任何通用场和流量曲线的临界层的临界层的一般形式，并确定磁场如何根据临界层中的电势涡度来修改纯流体动力稳定性标准。磁场轮廓的曲率或等效的电流梯度，临界层中的$ j'= -b''/μ$在不稳定性中起着互补作用。
In this paper, the instability of shallow water shear flow with a sheared parallel magnetic field is studied. Waves propagating in such magnetic shear flows encounter critical levels where the phase velocity relative to the basic flow $c-U(y)$ matches the Alfvén wave velocities $\pm B(y)/\sqrt{μρ}$, based on the local magnetic field $B(y)$, the magnetic permeability $μ$ and the mass density of the fluid $ρ$. It is shown that when the two critical levels are close to each other, the critical layer can generate an instability. The instability problem is solved, combining asymptotic solutions at large wavenumbers and numerical solutions, and the mechanism of instability explained using the conservation of momentum. For the shallow water MHD system, the paper gives the general form of the local differential equation governing such coalescing critical layers for any generic field and flow profiles, and determines precisely how the magnetic field modifies the purely hydrodynamic stability criterion based on the potential vorticity gradient in the critical layer. The curvature of the magnetic field profile, or equivalently the electric current gradient, $J' = - B''/μ$ in the critical layer is found to play a complementary role in the instability.
