Showing papers by "Uriel Frisch published in 1975"
TL;DR: In this article, the authors investigated the consequences of the conservation of magnetic helicity for incompressible three-dimensional turbulent MHD flows and obtained absolute equilibrium spectra for inviscid infinitely conducting flows truncated at lower and upper wavenumbers kmin and kmax.
Abstract: Some of the consequences of the conservation of magnetic helicity for incompressible three-dimensional turbulent MHD flows are investigated. Absolute equilibrium spectra for inviscid infinitely conducting flows truncated at lower and upper wavenumbers kmin and kmax are obtained. When the total magnetic helicity approaches an upper limit given by the total energy (kinetic plus magnetic) divided by kmin, the spectra of magnetic energy and helicity are strongly peaked near kmin; in addition, when the cross-correlations between the velocity and magnetic fields are small, the magnetic energy density near kmin greatly exceeds the kinetic energy density. Several arguments are presented in favour of the existence of inverse cascades of magnetic helicity towards small wavenumbers leading to the generation of large-scale magnetic energy.
526 citations
TL;DR: In this paper, it was shown that the three-dimensional (two-dimensional) energy inertial range, if it exists, cannot have an energy spectrum steeper than $k − √ 8 − 3 − 4 (k − 4 )$.
Abstract: For incompressible three-dimensional (two-dimensional) turbulence of finite energy, bounds are obtained on energy (enstrophy) flux. To estimate the nonlinear terms, we use a decomposition of the Fourier space into shells of exponentially increasing radii and the property of boundedness in position space of square-integrable functions with Fourier transforms of compact support. In the limit of zero viscosity, it is shown that the three-dimensional (two-dimensional) energy (enstrophy) inertial range, if it exists, cannot have an energy spectrum steeper than $k^{-\frac{8}{3}} (k^{-4})$ . Similar results are obtained for the advection of a passive scalar. The connexion with the problem of homogeneous turbulence and intermittency is briefly discussed.
43 citations
32 citations
TL;DR: In this article, Steenbeck et al. showed that turbulent flows that are not statistically invariant under plane reflections may be important for the generation of magnetic fields, and the equation for the mean magnetic field may then be written as follows:
Abstract: It is known that turbulent flows that are not statistically invariant under plane reflections may be important for the generation of magnetic fields. Within the framework of the kinematic dynamo problem (prescribed velocity fields), Steenbeck et a1.l have shown that in helical flows, that is, flows in which velocity and vorticity are statistically correlated, a mean magnetic field may be amplified by the so-called (Y effect. The equation for the mean magnetic field may then be written as follows:
9 citations