Magnetic field generation by intermittent convection

Abstract

Magnetic field generation in three-dimensional Rayleigh-Bénard convection of an electrically conducting fluid is studied numerically by fixing the Prandtl number at P = 0.3 and varying the Rayleigh number (Ra) as a control parameter. A recently reported route to hyperchaos involving quasiperiodic regimes, crises and chaotic intermittent attractors is followed, and the critical magnetic Prandtl number (P c m ) for dynamo action is determined as a function of Ra. A mechanism for the onset of intermittency in the magnetic energy is described, the most beneficial convective regimes for dynamo action in this transition to weak turbulence are identified, and the impact of intermittency on the dependence of P c m on Ra is discussed.

Magnetic field generation by pointwise zero-helicity three-dimensional steady flow of an incompressible electrically conducting fluid

“…Will magnetic field generation continue and will magnetic field persist? Simulations of various nonlinear small-scale convective dynamos attest that most different scenarios are possible: upon modification by the Lorentz force due to the growing magnetic field, the flow can settle to a non-generating hydrodynamic attractor, and in such a "self-extinguishing dynamo" magnetic field decays to zero [10]; alternatively, the MHD regime can saturate to a stable MHD steady or periodic state [6]; or it may consist of a chaotic sequence of visits to formerly attracting hydrodynamic states, some of which can generate magnetic field, and other ones cannot, thus exhibiting intermittent upsurges and decays of magnetic field [7]; or the evolution can consist of a chaotic sequence of visits to unstable but identifiable MHD states -a scenario [33] for development of magnetic field reversals is an example; or it can be just an unstructured chaotic trajectory in the phase space. In any case, when the overcriticality is not too small, the initial flow is abandoned, rendering inapplicable our analysis.…”

“…As above for the α-effect tensor, we first consider the limit of small local magnetic Reynolds numbers realised as a repeated limit ε → 0 and η → ∞. The evolutionary versions of (7) and (20) imply…”

“…The nature of this phenomenon is the same for both mechanisms of large-scale generation, as we will now briefly discuss. Let us consider a first auxiliary problem (7) in the form of the left equation for a zero-mean solenoidal field S k . Generically, the magnetic induction operator L has a three-dimensional kernel spanned by the fields e k + S k , thus being invertible in the functional subspace of our interest.…”

“…We expand, for a given η, the unknown field and the r.h.s. of the left equation (7) in the basis of solenoidal zero-mean eigenfunctions f n (η) of the magnetic induction operator, Lf n (η) = µ n (η)f n (η):…”

“…The first limit, in ε, yields the asymptotic expansions (6); we just need to calculate the second one, in η. From (7), the neutral modes have the asymptotics…”