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1.

Rheinhardt, Matthias

et al.

KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.

Devlen, Ebru

KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.

Rädler, Karl-Heinz

KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.

Brandenburg, Axel

KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.

Mean-field dynamo action from delayed transport2014In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 441, no 1, p. 116-126Article in journal (Refereed)

Abstract [en]

We analyse the nature of dynamo action that enables growing horizontally averaged magnetic fields in two particular flows that were studied by Roberts in 1972, namely his flows II and III. They have zero kinetic helicity either pointwise (flow II), or on average (flow III). Using direct numerical simulations, we determine the onset conditions for dynamo action at moderate values of the magnetic Reynolds number. Using the test-field method, we show that the turbulent magnetic diffusivity is then positive for both flows. However, we demonstrate that for both flows large-scale dynamo action occurs through delayed transport. Mathematically speaking, the magnetic field at earlier times contributes to the electromotive force through the off-diagonal components of the a tensor such that a zero mean magnetic field becomes unstable to dynamo action. This represents a qualitatively new mean-field dynamo mechanism not previously described.

Direct numerical simulations (DNSs) of isotropically forced homogeneous stationary turbulence with an imposed passive scalar concentration gradient are compared with an analytical closure model which provides evolution equations for the mean passive scalar flux and variance. Triple correlations of fluctuations appearing in these equations are described in terms of relaxation terms proportional to the quadratic correlations. Three methods are used to extract the relaxation timescales tau(i) from DNSs. Firstly, we insert the closure ansatz into our equations, assume stationarity and solve for tau(i). Secondly, we use only the closure ansatz itself and obtain tau(i) from the ratio of quadratic and triple correlations. Thirdly, we remove the imposed passive scalar gradient and fit an exponential law to the decaying solution. We vary the Reynolds (Re) and Peclet numbers (while fixing their ratio at unity) and the degree of scale separation and find for large Re a fair correspondence between the different methods. The ratio of the turbulent relaxation time of the passive scalar flux to the turnover time of the turbulent eddies is of the order of 3, which is in remarkable agreement with earlier work. Finally, we make an effort to extract the relaxation timescales relevant for the viscous and diffusive effects. We find two regimes that are valid for small and large Re, respectively, but the dependence of the parameters on scale separation suggests that they are not universal.