Nearly incompressible fluids. II: Magnetohydrodynamics, turbulence, and waves. (English) Zbl 0785.76100
This is a continuation of the authors’ work [Phys. Fluids, A 3, No. 1, 69-82 (1991; Zbl 0718.76049)] on the theory of nearly incompressible fluid to magnetohydrodynamics in all three possible plasma \(\beta\) limits \((\beta\ll 1\), \(\beta\sim 1\), \(\beta\gg 1)\), where \(\beta\) is the ratio of thermal to magnetic pressure. The authors derive the equations of nearly incompressible fluid dynamics and then provide a detailed analysis of the spectral properties of the density or any other fluctuations. It is shown that, for a \(\beta\ll 1\) magnetofluid, quasi-one-dimensional long-wavelength acoustic wave propagate parallel to the applied magnetic field. For a \(\beta\sim 1\) plasma, Alfvén waves propagate parallel to the applied magnetic field. The \(\beta\gg 1\) case is fully three- dimensional. In this case, the MHD model gives rise to essentially isotropic behavior in the fluctuations. This model is fully three- dimensional in the incompressible flow field variables and fully three- dimensional in terms of the compressible and acoustic corrections. The high frequency waves correspond to sound waves. The detailed mathematical analysis is presented for each of the three \(\beta\) limits-cases. The authors claim that observations support their theory which has applications to solar wind.
Reviewer: L.Debnath (Orlando)
MSC:
76W05 | Magnetohydrodynamics and electrohydrodynamics |
76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
76F99 | Turbulence |
85A30 | Hydrodynamic and hydromagnetic problems in astronomy and astrophysics |
Keywords:
spectral properties; quasi-one-dimensional long-wavelength acoustic wave; Alfvén waves; high frequency waves; solar windCitations:
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