Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotropic plasmas for a cylindrical equilibrium model. The equilibrium magnetic field lines are unidirectional and parallel with the z axis. The nonlinear governing equations for resonant slow magnetoacoustic (SMA) waves are derived. Using the method of matched asymptotic expansions inside and outside the narrow dissipative layer, we generalize the connection formulae for the Eulerian perturbation of the total pressure and for the normal component of the velocity.ududThese nonlinear connection formulae in dissipative cylindrical MHD are an important extention of the connection formulae obtained in linear ideal MHD [Sakurai et al., Solar Phys. 133, 227 (1991)], linear dissipative MHD [Goossens et al., Solar Phys. 175, 75 (1995); Erdélyi, Solar Phys. 171, 49 (1997)] and in nonlinear dissipative MHD derived in slab geometry [Ruderman et al., Phys. Plasmas4, 75 (1997)]. These generalized connection formulae enable us to connect the solutions at both sides of the dissipative layer without solving the MHD equations in the dissipative layer. We also show that the nonlinear interaction of harmonics in the dissipative layer is responsible for generating a parallel mean flow outside the dissipative layer.
展开▼
机译:在圆柱体平衡模型的弱耗散各向同性等离子体中研究了非线性共振慢磁流体动力学(MHD)波。平衡磁场线是单向的并且平行于z轴。推导了共振慢磁声(SMA)波的非线性控制方程。使用狭窄的耗散层内外的匹配渐近展开法,我们推导了总压力的欧拉扰动和速度的法向分量的连接公式。 ud ud这些耗散圆柱MHD的非线性连接公式是线性理想MHD中获得的连接公式的重要扩展[Sakurai等,Solar Phys。 133,227(1991)],线性耗散MHD [Goossens等,Solar Phys。 175,75(1995); Erdélyi,太阳物理学。 171,49(1997)]和非线性耗散MHD来源于平板几何[Ruderman et al。,Phys。 Plasmas4,75(1997)]。这些通用的连接公式使我们可以在耗散层的两侧连接解决方案,而无需在耗散层中求解MHD方程。我们还表明,耗散层中谐波的非线性相互作用是导致在耗散层外部产生平行平均流的原因。
展开▼