Published online by Cambridge University Press: 11 May 2010
Fast dynamo saturation is explored numerically using a simplified model. The magnetic field has many degrees of freedom and allows the generation of fine structure at large Rm. The velocity field is constrained, containing two Fourier modes and so eight degrees of freedom; the Lorentz force is projected onto these modes. Numerical simulations at varying Rm are discussed.
Fast dynamo instabilities are the subject of intense research (reviewed in Childress 1992), through numerical simulations and analytical studies of simple models. However little is known about how a fast dynamo instability might saturate and what the resulting spatial structure and temporal behaviour of the field might be. Does a fast dynamo saturate by suppressing the flow field until the effective magnetic Reynolds number is reduced to a value of order unity or by modifying transport effects of the flow (Vainshtein et al. 1993)? Is the saturated magnetic energy in equipartition with the kinetic energy and how is the magnetic energy distributed; in particular how much energy is stored in large-scale field components (Vainshtein & Cattaneo 1992)? Does the field contain the fine structure typical of kinematic fast dynamo instabilities and is it intermittent in time? The difficulty in answering these questions is that dynamo action only allows growth of 3-d magnetic fields and through the Lorentz force this leads to all the complexities of 3-d MHD turbulence. Numerical studies are computationally expensive and only moderate values of Rm have been achieved (see, for example, Gilman 1983, Glatzmaier 1985, Meneguzzi & Pouquet 1989, Nordlund et al 1991 and Galanti et al 1992).
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