（磁）流体动力系统的精确解及非线性螺旋波的叠加原理
On the exact solutions of (magneto)hydrodynamic systems and the superposition principles of nonlinear helical waves
摘要：
本文用统一意义上的螺旋表象系统地阐述了几种流体力学模型的任意振幅圆偏振波的限制叠加原理。结果表明，只有单波长同手征Beltrami模和一维二分量分层涡模（我们称之为XYz流/波）满足任意振幅叠加以消除一般非线性的一般模式;同时，对于某些特定情况，还有其他特殊的叠加原理。我们试图评论与地球和/或天体物理流体和磁流体动力学湍流问题的可能联系，如旋转湍流，发电机和太阳大气湍流，特别是与引入局部冻结在一些（随机分布）时空区域的无序。最近关于霍尔和完全双流体磁流体力学的精确解的分歧也解决了这样的治疗。这项工作的补充，通过研究模式，完全杀死三元相互作用或非线性，以前的研究热化纯粹从三元相互作用，反过来又提供了替代的视角的非线性。
英文摘要：
The principles of restricted superposition of circularly polarized arbitrary-amplitude waves for several hydrodynamic type models are illustrated systematically with helical representation in a unified sense. It is shown that the only general modes satisfying arbitrary-amplitude superposition to kill the generic nonlinearity are the mono-wavelength homochiral Beltrami mode and the one-dimensional-two-component stratified vorticity mode, which we call the XYz flow/wave; while, there are other special superposition principles for some specific cases. We try to remark on the possible connections with the geo- and/or astro-physical fluid and magnetohydrodynamic turbulence issues, such as the rotating turbulence, dynamo and solar atmosphere turbulence, especially with the introduction of disorder locally frozen in some (randomly distributed) space-time regions. Recent disagreements about exact solutions of Hall and fully two-fluid magnetohydrodynamics are also settled down by such a treatment. This work complements, by studying the modes which completely kill the triadic interactions or the nonlinearities, previous studies on the thermalization purely from the triadic interactions, and in turn offers alternative perspectives of the nonlinearities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
