Solar and stellar dynamos shed small-scale and large-scale magnetic helicity of opposite signs. However, solar wind observations and simulations have shown that some distance above the dynamo both the small-scale and large-scale magnetic helicities have reversed signs. With realistic simulations of the solar corona above an active region now being available, we have access to the magnetic field and current density along coronal loops. We show that a sign reversal in the horizontal averages of the magnetic helicity occurs when the local maximum of the plasma beta drops below unity and the field becomes nearly fully force free. Hence, this reversal is expected to occur well within the solar corona and would not directly be accessible to in situ measurements with the Parker Solar Probe or SolarOrbiter. We also show that the reversal is associated with subtle changes in the relative dominance of structures with positive and negative magnetic helicity.

Appealing to an analytical result from mean-field theory, we show, using a generic galaxy model, that galactic dynamo action can be suppressed by small-scale magnetic fluctuations. This is caused by the magnetic analogue of the Radler or Omega x J effect, where rotation-induced corrections to the mean-field turbulent transport result in what we interpret to be an effective reduction of the standard a effect in the presence of small-scale magnetic fields.

We present exact solutions of the incompressible Navier-Stokes equations in a background linear shear flow. The method of construction is based on Kelvin's investigations into linearized disturbances in an unbounded Couette flow. We obtain explicit formulae for all three components of a Kelvin mode in terms of elementary functions. We then prove that Kelvin modes with parallel (though time-dependent) wave vectors can be superposed to construct the most general plane transverse shearing wave. An explicit solution is given, with any specified initial orientation, profile and polarization structure, with either unbounded or shear-periodic boundary conditions.

We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancellation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three dimensional a effect-type dynamo-generated magnetic field, with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161-2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at approximate to 0.06 Mm(-1) (scales around 100 Mm). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven a effect-type dynamos.

We report a systematic strengthening of the local solar surface or fundamental f- mode one to two days prior to the emergence of an active region (AR) in the same (corotating) location. Except for a possibly related increase in the kurtosis of the magnetic field, no indication can be seen in the magnetograms at that time. Our study is motivated by earlier numerical findings of Singh et al., which showed that, in the presence of a nonuniform magnetic field that is concentrated a few scale heights below the surface, the f- mode fans out in the diagnostic kw diagram at high wavenumbers. Here we explore this possibility using data from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and show for six isolated ARs, 11130, 11158, 11242, 11105, 11072, and 11768, that at large latitudinal wavenumbers (corresponding to horizontal scales of around 3000 km), the f- mode displays strengthening about two days prior to AR formation and thus provides a new precursor for AR formation. Furthermore, we study two ARs, 12051 and 11678, apart from a magnetically quiet patch lying next to AR. 12529, to demonstrate the challenges in extracting such a precursor signal when a newly forming AR emerges in a patch that lies in close proximity to. one or several already existing ARs, which are expected to pollute neighboring patches. We then discuss plausible procedures for extracting precursor signals from regions with crowded environments. The idea that the f- mode is perturbed days before any visible magnetic activity occurs at the surface can be important in constraining dynamo models aimed at understanding the global magnetic activity of the Sun.

We present a theory of large-scale dynamo action in a turbulent flow that has stochastic, zero-mean fluctuations of the a parameter. Particularly interesting is the possibility of the growth of the mean magnetic field due to Moffatt drift, which is expected to he finite in a statistically anisotropic turbulence. We extend the Kraichnan Moffatt model to explore effects of finite memory of a fluctuations, in a spirit similar to that of Sridhar & Singh (Mon. Not. R. Astron. Soc., vol. 445, 2014, pp. 3770-3787). Using the first-order smoothing approximation, we derive a linear integro-differential equation governing the dynamics of the large-scale magnetic field, which is non-perturbative in the alpha-correlation time tau(alpha), We recover earlier results in the exactly solvable white-noise limit where the Moffatt drift does not contribute to the dynamo growth/decay. To study finite-memory effects, we reduce the integro-differential equation to a partial differential equation by assuming that tau(alpha). be small but non-zero and the large-scale magnetic field is slowly varying. We derive the dispersion relation and provide an explicit expression for the growth rate as a function of four independent parameters. When tau(alpha) not equal 0, we find that: (i) in the absence of the Moffatt drift, but with finite Kraichnan diffusivity, only strong a fluctuations can enable alpha mean-field dynamo (this is qualitatively similar to the white-noise case); (ii) in the general case when also the Moffatt drift is non-zero, both weak and strong a fluctuations can lead to a large-scale dynamo; and (iii) there always exists a wavenumber (k) cutoff at sonic large k beyond which the growth rate turns negative, irrespective of weak or strong a fluctuations. Thus we show that a finite Moffatt drift can always facilitate large-scale dynamo action if sufficiently strong, even in the case of weak alpha fluctuations, and the maximum growth occurs at intermediate wavenumbers.

We perform numerical experiments to study the shear dynamo problem where we look for the growth of a large-scale magnetic field due to non-helical stirring at small scales in a background linear shear flow in previously unexplored parameter regimes. We demonstrate the large-scale dynamo action in the limit where the fluid Reynolds number (Re) is below unity while the magnetic Reynolds number (Rm) is above unity; the exponential growth rate scales linearly with shear, which is consistent with earlier numerical works. The limit of low Re is particularly interesting, as seeing the dynamo action in this limit would provide enough motivation for further theoretical investigations, which may focus attention on this analytically more tractable limit of Re < 1 compared to the more formidable limit of Re > 1. We also perform simulations in the regimes where (i) both (Re, Rm) < 1, and (ii) Re > 1 and Rm < 1, and compute all of the components of the turbulent transport coefficients (alpha(ij) and alpha(ij)) using the test-field method. A reasonably good agreement is observed between our results and the results of earlier analytical works in similar parameter regimes.

With the ultimate aim of using the fundamental or f mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfven-to-sound speed ratio of about 0.1, a 5 per cent frequency increase of the f mode can be measured when k(x)H(p) = 3-4, where k(x) is the horizontal wavenumber and H-p is the pressure scaleheight at the surface. Since the solar radius is about 2000 times larger than H-p, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a k(x)-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for k(x)H(p) approximate to 4, but decreased relative to its nonmagnetic value for k(x)H(p) approximate to 9.

We show that in the presence of a magnetic field that is varying harmonically in space, the fundamental mode, or f-mode, in a stratified layer is altered in such a way that it fans out in the diagnostic k omega diagram, with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014), where a uniform magnetic field was considered, here we employ a non-uniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic field. The expansion of the f-mode is stronger for fields confined to the layer below the surface. In some of those cases, the k omega diagram also reveals a new class of low-frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the f-mode expansion might be a new and sensitive tool to determine subsurface magnetic fields with azimuthal or other horizontal periodicity.

We present a model of large-scale dynamo action in a shear flow that has stochastic, zero-mean fluctuations of the a parameter. This is based on a minimal extension of the Kraichnan Moffatt model, to include a background linear shear and Galilean-invariant alpha-statistics. Using the firstorder smoothing approximation we derive a linear integro-differential equation for the largescale magnetic field, which is non-perturbative in the shearing rate S, and the alpha-correlation time r. The white-noise case, tau(alpha) = 0, is solved exactly, and it is concluded that the necessary condition for dynamo action is identical to the Kraichnan Moffatt model without shear; this is because white-noise does not allow for memory effects, whereas shear needs time to act. To explore memory effects we reduce the integro-differential equation to a partial differential equation, valid for slowly varying fields when is small but non-zero. Seeking exponential modal solutions, we solve the modal dispersion relation and obtain an explicit expression for the growth rate as a function of the six independent parameters of the problem. A non-zero r, gives rise to new physical scales, and dynamo action is completely different from the white-noise case; e.g. even weak a fluctuations can give rise to a dynamo. We argue that, at any wavenumber, both Moffatt drift and Shear always contribute to increasing the growth rate. Two examples are presented: (a) a Moffatt drift dynamo in the absence of shear and (b) a Shear dynamo in the absence of Moffatt drift.