Dissipative structures in a nonlinear dynamo
Gilbert, Andrew D.
Geophysical and Astrophysical Fluid Dynamics
Taylor & Francis
© 2011 Taylor & Francis
This paper considers magnetic ﬁeld generation by a ﬂuid ﬂow in a system referred to as the Archontis dynamo: a steady nonlinear magnetohydrodynamic (MHD) state is driven by a prescribed body force. The ﬁeld and ﬂow become almost equal and dissipation is concentrated in cigar-like structures centred on straight-line separatrices. Numerical scaling laws for energy and dissipation are given that extend previous calculations to smaller diﬀusivities. The symmetries of the dynamo are set out, together with their implications for the structure of ﬁeld and ﬂow along the separatrices. The scaling of the cigar-like dissipative regions, as the square root of the diﬀusivities, is explained by approximations near the separatrices. Rigorous results on the existence and smoothness of solutions to the steady, forced MHD equations are given.
Agence Nationale de la Recherche, France
Russian foundation for basic research
This paper gives new results concerning magnetic field generation leading to a steady equilibrated state, the so-called Archontis dynamo. A combination of numerical work, analysis of PDEs and functional analysis is used to derive information on scaling laws for dissipative structures in the dynamo.
This is an Accepted Manuscript of an article published by Taylor & Francis in Geophysical and Astrophysical Fluid Dynamics, Volume 105, Issue 6, 2011, available online on 2 Dec 2010: http://wwww.tandfonline.com/10.1080/03091929.2010.513332.
Author's accepted manuscript
Volume 105, Issue 6, 2011, pp. 629-653