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Discrete scalar cascade models and manetohydrodynamic turbulence. (English) Zbl 0661.76040

The role of discrete scalar models in modeling the magnetohydrodynamic turbulence is discussed using the hypothesis that Alfvén wave propagation dominates in comparison to turbulent eddy effects. It is shown that standard statistical techniques (direct interaction closure, Markovian approximation, and random phase approximation) performed on discrete nonlinear cascade models give rise to a set of equations that can also be obtained independently. This is done by using either basic principles or introducing discrete shells in the wavenumber space into a statistical set derived directly from MHD equations. This result permits discussion of the role of discrete models in understanding the behavior of MHD turbulence.

MSC:

76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76F99 Turbulence
76W05 Magnetohydrodynamics and electrohydrodynamics
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References:

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