Abstract
Much effort has gone into identifying and classifying systems that might be capable of dynamo action, i.e. capable of generating and sustaining magnetic field indefinitely against dissipative effects in a conducting fluid. However, it is difficult, if not almost technically impossible, to derive a method of determining in both an absolutely conclusive and a pragmatic manner whether a system is a dynamo or not in the nonlinear regime. This problem has generally been examined only for closed systems, despite the fact that most realistic situations of interest are not strictly closed. Here we examine the even more complex problem of whether a known nondynamo closed system can be distinguished pragmatically from a true dynamo when a small input of magnetic field to the system is allowed. We call such systems ‘stoked nondynamos’ owing to the ‘stoking’ or augmentation of the magnetic field in the system. It may seem obvious that magnetic energy can be sustained in such systems since there is an external source, but crucial questions remain regarding what level is maintained and whether such nondynamo systems can be distinguished from a true dynamo. In this paper, we perform 3D nonlinear numerical simulations with time-dependent ABC forcing possessing known dynamo properties. We find that magnetic field can indeed be maintained at a significant stationary level when stoking a system that is a nondynamo when not stoked. The maintained state results generally from an eventual rough balance of the rates of input and decay of magnetic field. We find that the relevance of this state is dictated by a parameter κ representing the correlation of the resultant field with the stoking forcing function. The interesting regime is where κ is small but non-zero, as this represents a middle ground between a state where the stoking has no effect on the pre-existing nondynamo properties and a state where the effect of stoking is easily detectable. We find that in this regime, (a) the saturated state is somewhat unexpectedly enhanced by a bias resulting from the random fluctuating statistics of the decay process, and (b) the state is indistinguishable from a true dynamo except via κ itself. Such results make the pragmatic identification of dynamos in real situations even more difficult than had previously been thought.
Highlights
Dynamo theory is ubiquitously invoked to explain the presence of long-lived magnetic fields in many, if not most, astrophysical and geophysical situations, from the Earths magnetic field through stars including our Sun and on to galaxies and other cosmological bodies
We examine four stoked cases at Ω = 2.5, in which the stoking amplitude B0 is varied through the values (10−1, 10−2, 10−3, 10−6); the wavenumber of the magnetic forcing k is set to unity
Each simulation goes though an initial amplification phase that is nearly identical to that in the unstoked case. We stress that these initial phenomena are not of real interest in the current problem; it may even have been more perspicacious merely to have switched on stoking in the established nonlinear regime of the BCT cases
Summary
Dynamo theory is ubiquitously invoked to explain the presence of long-lived magnetic fields in many, if not most, astrophysical and geophysical situations, from the Earths magnetic field through stars including our Sun and on to galaxies and other cosmological bodies. The MHD systems adopted for dynamo calculations are typically magnetically closed, having no imposed source of magnetic energy apart from the initial field This is true of both analytical and numerical work, in which idealized boundary conditions are conveniently imposed. We study systems that are intrinsically nondynamos in isolation, and examine whether a weak magnetic source can support the system in a nonlinear state that mimics a true dynamo. If in practice such false dynamos cannot be separated from true dynamos without independent knowledge of the existence of an external source, new and potentially interesting avenues of exploration may be opened In this first paper, we work with systems, previously studied in detail by Brummell, Cattaneo and Tobias (BCT) [5], which are well known for their kinematic dynamo properties and which are integrated into the nonlinear regime. The issues outlined above apply to all dynamos, in this paper we work with examples of smallscale dynamos, where the magnetic field is created at scales comparable to those of the velocity field (and smaller) rather than with large-scale dynamos that generate fields at scales significantly larger those of the velocity
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