Alpha effect and turbulent diffusion from convection

Abstract

Aims. We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods. We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations. Results. The results for the α-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos θ latitude profile for moderate rotation. Turbulent diffusivity, η t , is proportional to the square of the turbulent vertical velocity in all cases. Whereas η t decreases approximately inversely proportional to the wavenumber of the field, the α-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak α-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small α-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent α-shear dynamo may also act in the simulations. If both rotation and shear are present, the α-effect is more pronounced. At the same time, the combination of the shear-current and Ω × J-effects is also stronger than in the case of shear alone, but subdominant to the α-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.

Advances in Theory and Simulations of Large-Scale Dynamos

“…For unstratified convection with an imposed field Cattaneo & Hughes (2006) find that α diminishes for large magnetic Reynolds numbers, even for kinematically weak magnetic fields. With stratification, on the other hand, Käpylä et al (2008b) find val-ues of α that are compatible with those from simple estimates. They used the test-field method while Cattaneo & Hughes (2006) used an imposed field and estimate α as the ratio between the resulting field-aligned electromotive force and the imposed field.…”

“…Another example is the case of rigidly rotating convection. Using the test-field method, Käpylä et al (2008b) noticed that with increasing rotation rate α increases and η t decreases. This led to the prediction that there should be α 2 dynamo action (i.e.…”

Dynamo action and magnetic buoyancy in convection simulations with vertical shear

“…This value is above the critical Rm for dynamo excitation. Previous studies have shown that the turbulent transport coefficients for convection are independent of the magnetic Reynolds number provided that Rm is sufficiently larger than unity (Käpylä et al 2009a). Thus the results of this run can be considered representative of the present setup.…”

“…Normalized profiles of the kinetic helicity, and the turbulent transport coefficients α xx , α yy , η t , η , γ and γ (from top to bottom) computed with the test-field method. also been found from convection with horizontal shear (Käpylä et al 2009a). In the case with vertical shear presented here, the relevant coefficient for this effect is not captured by the current version of the test-field method with only z-dependent test fields.…”

An efficient method for computing the eigenfunctions of the dynamo equation

“…Often the coefficients are approximated by simple analytical functions of position, and their tensorial character is disregarded. Recently, the test-field method, developed by Schrinner et al (2005Schrinner et al ( , 2007) (see also Ossendrijver et al 2001Ossendrijver et al , 2002, allows one to determine all tensorial components of α and β directly from self-consistent numerical simulations (Brandenburg et al 2008;Käpylä et al 2009). These coefficients are sometimes strongly varying functions of position.…”