We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 1024 3 collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number Pr M over a large range, namely, 0.01 ≤ Pr M ≤ 10. We obtain data for a wide variety of statistical measures such as probability distribution functions (PDFs) of moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterise intermittency, isosurfaces of quantities such as the moduli of the vorticity and current, and joint PDFs such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from larger intermittency in the magnetic field than in the velocity field, at large Pr M , to smaller intermittency in the magnetic field than in the velocity field, at low Pr M . Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of Pr M , multiscaling exponent ratios agree, at least within our errorbars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.

Inviscid invariants of flow equations are crucial in determining the direction of the turbulent energy cascade. In this work we investigate a variant of the three-dimensional Navier-Stokes equations that shares exactly the same ideal invariants (energy and helicity) and the same symmetries (under rotations, reflections, and scale transforms) as the original equations. It is demonstrated that the examined system displays a change in the direction of the energy cascade when varying the value of a free parameter which controls the relative weights of the triadic interactions between different helical Fourier modes. The transition from a forward to inverse cascade is shown to occur at a critical point in a discontinuous manner with diverging fluctuations close to criticality. Our work thus supports the observation that purely isotropic and three-dimensional flow configurations can support inverse energy transfer when interactions are altered and that inside all turbulent flows there is a competition among forward and backward transfer mechanisms which might lead to multiple energy-containing turbulent states.

The effects of the helicity on the dynamics of turbulent flows are investigated. The aim is to disentangle the role of helicity in fixing the direction, the intensity, and the fluctuations of the energy transfer across the inertial range of scales. We introduce an external parameter α that controls the mismatch between the number of positive and negative helically polarized Fourier modes. We present direct numerical simulations of Navier-Stokes equations from the fully symmetrical case, α=0, to the fully asymmetrical case, α=1, when only helical modes of one sign survive. We found a singular dependency of the direction of the energy cascade on α, measuring a positive forward flux as soon as only a few modes with different helical polarities are present. Small-scale fluctuations are also strongly sensitive to the degree of mode reduction, leading to a vanishing intermittency already for values of α∼0.1. If the analysis is restricted to sets of modes with the same helicity sign, intermittency is vanishing for the modes belonging to the minority set, and it is close to that measured on the original Navier-Stokes equations for the other set.

We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small-and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achieved for the magnetic component with the same helicity of the flow, in agreement with the Stretch-Twist-Fold mechanism. Vice versa, in presence of a Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite sign, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows.

The large scale turbulent statistics of mechanically driven superfluid 4 He was shown experimentally to follow the classical counterpart. In this paper we use direct numerical simulations to study the whole range of scales in a range of temperatures T ∈ [1.3, 2.1] K. The numerics employ selfconsistent and non-linearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well-correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particulary efficient in the temperature range between 1.8 K and 2 K, leading to enhancement of small scales intermittency for these temperatures. (iii) At low T and close to T λ the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.