A STUDY OF THE DYNAMO TRANSITION IN A SELF-CONSISTENT NONLINEAR DYNAMO MODEL

We develop a nonlinear dynamo model that couples the evolution of a large-scale magnetic field with the turbulent dynamics of a magnetofluid system in the small scale by electromotive force. Because the dynamo effect takes place in astrophysical objects characterized by a range of dynamical parameters (Reynolds numbers, Prandtl number, etc.) which is beyond the current possibilities of direct numerical simulations, we describe the nonlinear behavior of the system at small scales by using a shell model. Under specific conditions of the turbulent state, the field fluctuations at small scales are able to trigger the dynamo instability. The stability curve derived from our simulations allows us to gain some insight not only into the regime of parameters analyzed up to this point but also for very large Prandtl numbers. Moreover, from our analysis, it is shown that the large-scale dynamo transition displays a hysteretic behavior revealing its subcritical nature. The system, undergoing dynamo transition, can reach different dynamo regimes depending on the Reynolds numbers of the magnetic flow. This points out the critical role that turbulence plays in the dynamo phenomenon. Moreover, in this Letter, we show the presence of the natural ordering of dynamo regimes (oscillatory-reversing-steady dynamos) observed in the large-scale magnetic field for increasing magnetic Reynolds numbers. However, the signature of these regimes is also found in the small-scale dynamo by looking at the scaling properties of magnetic fluctuation energy as a function of magnetic Reynolds number.