Herault, Johann and Rincon, François and Cossu, Carlo and Lesur, Geoffroy and Ogilvie, Gordon I. and Longaretti, Pierre-Yves Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows. (2011) Physical Review E, vol. 84 (n° 3). pp. 036321(1)-036321(9). ISSN 1539-3755
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Official URL: http://link.aps.org/doi/10.1103/PhysRevE.84.036321
The nature of dynamo action in shear ﬂows prone to magnetohydrodynamc instabilities is investigated using the magnetorotational dynamo in Keplerian shear ﬂow as a prototype problem. Using direct numerical simulations and Newton’s method, we compute an exact time-periodic magnetorotational dynamo solution to three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic ﬁeld and nonaxisymmetric perturbations ampliﬁed by the magnetorotational instability. We demonstrate that this large-scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-ﬁeld dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic ﬁelds in shear ﬂows and call for new theoretical dynamo models. These ﬁndings may offer important clues to understanding the transitional and statistical properties of subcritical magnetorotational turbulence.
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