Carbone, Vincenzo; Veltri, Pierluigi Discrete scalar cascade models and manetohydrodynamic turbulence. (English) Zbl 0661.76040 Phys. Fluids, A 1, No. 2, 420-421 (1989). 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. Cited in 1 Document MSC: 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 76F99 Turbulence 76W05 Magnetohydrodynamics and electrohydrodynamics Keywords:discrete scalar models; magnetohydrodynamic turbulence; Alfvén wave; statistical techniques; Markovian approximation; random phase approximation PDFBibTeX XMLCite \textit{V. Carbone} and \textit{P. Veltri}, Phys. Fluids, A 1, No. 2, 420--421 (1989; Zbl 0661.76040) Full Text: DOI References: [1] Deniansky V. N., Prikl. Mat. Mekh. 38 pp 507– (1974) [2] DOI: 10.1063/1.861896 · Zbl 0369.76052 · doi:10.1063/1.861896 [3] DOI: 10.1063/1.861896 · Zbl 0369.76052 · doi:10.1063/1.861896 [4] DOI: 10.1007/BF01011698 · doi:10.1007/BF01011698 [5] DOI: 10.1017/S0022112080001693 · Zbl 0465.76046 · doi:10.1017/S0022112080001693 [6] DOI: 10.1016/0167-2789(85)90002-8 · Zbl 0577.76109 · doi:10.1016/0167-2789(85)90002-8 [7] Carbone V., Astron. Astrophys. 188 pp 239– (1987) [8] Grappin R., Astron. Astrophys. 105 pp 6– (1982) [9] DOI: 10.1007/BF02890146 · doi:10.1007/BF02890146 [10] DOI: 10.1017/S0022112076002140 · Zbl 0336.76019 · doi:10.1017/S0022112076002140 [11] DOI: 10.1103/PhysRev.109.1407 · doi:10.1103/PhysRev.109.1407 [12] DOI: 10.1017/S0022112059000362 · Zbl 0093.41202 · doi:10.1017/S0022112059000362 [13] DOI: 10.1063/1.1762201 · Zbl 0166.22901 · doi:10.1063/1.1762201 [14] DOI: 10.1017/S0022112071001204 · Zbl 0219.76064 · doi:10.1017/S0022112071001204 [15] DOI: 10.1017/S0022112077000962 · Zbl 0363.76014 · doi:10.1017/S0022112077000962 [16] DOI: 10.1017/S0022112074001303 · Zbl 0285.76021 · doi:10.1017/S0022112074001303 [17] DOI: 10.1063/1.1691777 · Zbl 0155.55801 · doi:10.1063/1.1691777 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.