2014/07/31 by Jian-Zhou Zhu, Zhu, Jian-Zhou · 5 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Amplitude #Classical mechanics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Geomagnetism and Paleomagnetism Studies #Geophysics (physics.geo-ph) #Magnetic field #Magnetohydrodynamic drive #Magnetohydrodynamics #Mechanics #Nonlinear system #Physics #Plasma Physics (physics.plasm-ph) #Quantum mechanics #Solar and Space Plasma Dynamics #Solar and Stellar Astrophysics (astro-ph.SR) #Superposition principle #Turbulence #Vortex #Vorticity #astro-ph.SR #physics.flu-dyn #physics.geo-ph #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.1407.8404
published in arXiv (Cornell University) (Cornell University)
arxiv created 2014/07/31 · openalex publication_date 2014/07/31 · arxiv updated 2014/08/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.