IUCAA Preprints
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Item Strong mean field dynamos require supercritical helicity fluxes(2006-01-10) Brandenburg, Axel; Subramanian, KandaswamySeveral one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vishniac & Cho (2001, ApJ 550, 752). Only above this threshold is the current helicity flux also able to alleviate catastrophic quenching. The fact that certain turbulence simulations have now shown apparently non-resistively limited mean field saturation amplitudes may be suggestive of the current helicity flux having exceeded this critical value. Even below this critical value the field still reaches appreciable strength at the end of the kinematic phase, which is in qualitative agreement with dynamos in periodic domains. However, for large magnetic Reynolds numbers the field undergoes subsequent variations on a resistive time scale when, for long periods, the field can be extremely weak.Item Kinetic and magnetic alpha effects in nonlinear dynamo theory(2007-01-19) Sur, Sharanya; Subramanian, Kandaswamy; Brandenburg, AxelThe backreaction of the Lorentz force on the α-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The nonlinear α-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On the one hand, one can express α completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic α-effect and an oppositely signed term proportional to the helical part of the small scale magnetic field. These results hold for both steady and time dependent forcing at arbitrary strength of the mean field. In addition, the τ-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the τ closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net α-effect. However for delta-correlated time-dependent forcing, this force–field correlation vanishes, enabling one to write α exactly as the sum of kinetic and magnetic α-effects, similar to what one obtains also in the large Reynolds number regime in theτ-approximation closure hypothesis. In the limit of strong imposed fields, B0, we find α ∝ B−2 0 for delta-correlated forcing, in contrast to the well-known α ∝ B−3 0 behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows.Item Role of the Yoshizawa effect in the Archontis dynamo(2009-05-01) Sur, Sharanya; Brandenburg, AxelThe generation of mean magnetic fields is studied for a simple non-helical flow where a net cross helicity of either sign can emerge. This flow, which is also known as the Archontis flow, is a generalization of the Arnold–Beltrami–Childress flow, but with the cosine terms omitted. The presence of cross helicity leads to a mean-field dynamo effect that is known as the Yoshizawa effect. Direct numerical simulations of such flows demonstrate the presence of magnetic fields on scales larger than the scale of the flow. Contrary to earlier expectations, the Yoshizawa effect is found to be proportional to the mean magnetic field and can therefore lead to its exponential instead of just linear amplification for magnetic Reynolds numbers that exceed a certain critical value. Unlike α effect dynamos, it is found that the Yoshizawa effect is not noticeably constrained by the presence of a conservation law. It is argued that this is due to the presence of a forcing term in the momentum equation which leads to a nonzero correlation with the magnetic field. Finally, the application to energy convergence in solar wind turbulence is discussed.Item Kinematic alpha effect in isotropic turbulence simulations(2008-01) Sur, Sharanya; Brandenburg, Axel; Subramanian, KandaswamyUsing numerical simulations at moderate magnetic Reynolds numbers up to 220 it is shown that in the kinematic regime, isotropic helical turbulence leads to an alpha effect and a turbulent diffusivitywhose values are independent of the magnetic Reynolds number,Rm, provided Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first order smoothing approximation. For small values of Rm, alpha and turbulent diffusivity are proportional to Rm. Over finite time intervals meaningful values of alpha and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that small-scale dynamo-generated fields do not make a correlated contribution to the mean electromotive force.