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Evolution of stochastically homogeneous magnetic field advected by incompressible turbulent flow with large magnetic Prandtl numbers is considered at the scales less than Kolmogorov viscous scale. It is shown that, despite unlimited growth of the magnetic field, its feedback on the fluids dynamics remains negligibly small.
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We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal non-dissipative case is studied up to the equivalent of 2048^3 grid points for one of these flows. The temporal evolution of the logarithmic decrements, delta, of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of delta, the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind.
Magnetohydrodynamical (MHD) dynamos emerge in many different astrophysical situations where turbulence is present, but the interaction between large-scale (LSD) and small-scale dynamos (SSD) is not fully understood. We performed a systematic study of turbulent dynamos driven by isotropic forcing in isothermal MHD with magnetic Prandtl number of unity, focusing on the exponential growth stage. Both helical and non-helical forcing was employed to separate the effects of LSD and SSD in a periodic domain. Reynolds numbers (Rm) up to $approx 250$ were examined and multiple resolutions used for convergence checks. We ran our simulations with the Astaroth code, designed to accelerate 3D stencil computations on graphics processing units (GPUs) and to employ multiple GPUs with peer-to-peer communication. We observed a speedup of $approx 35$ in single-node performance compared to the widely used multi-CPU MHD solver Pencil Code. We estimated the growth rates both from the averaged magnetic fields and their power spectra. At low Rm, LSD growth dominates, but at high Rm SSD appears to dominate in both helically and non-helically forced cases. Pure SSD growth rates follow a logarithmic scaling as a function of Rm. Probability density functions of the magnetic field from the growth stage exhibit SSD behaviour in helically forced cases even at intermediate Rm. We estimated mean-field turbulence transport coefficients using closures like the second-order correlation approximation (SOCA). They yield growth rates similar to the directly measured ones and provide evidence of $alpha$ quenching. Our results are consistent with the SSD inhibiting the growth of the LSD at moderate Rm, while the dynamo growth is enhanced at higher Rm.
We explore the role of gravitational settling on inertial particle concentrations in a wall-bounded turbulent flow. While it may be thought that settling can be ignored when the settling parameter $Svequiv v_s/u_tau$ is small ($v_s$ - Stokes settling velocity, $u_tau$ - fluid friction velocity), we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined, not by the size of $v_s$ compared with $u_tau$ or any other fluid velocity scale, but by the size of $v_s$ relative to the other mechanisms that control the vertical particle velocity and concentration profile. We explain this in the context of the particle mean-momentum equation, and show that in general, there always exists a region in the boundary layer where settling cannot be neglected, no matter how small $Sv$ is (provided it is finite). Direct numerical simulations confirm the arguments, and show that the near-wall concentration is highly dependent on $Sv$ even when $Svll 1$, and can reduce by an order of magnitude when $Sv$ is increased from $O(10^{-4})$ and $O(10^{-2})$. The results also show that the preferential sampling of ejection events in the boundary layer by inertial particles when $Sv=0$ is profoundly altered as $Sv$ is increased, and is replaced by a preferential sampling of sweep events due to the onset of the preferential sweeping mechanism.
We use DNS to study inter-scale and inter-space energy exchanges in the near-field of a turbulent wake of a square prism in terms of the KHMH equation written for a triple decomposition of the velocity field accounting for the quasi-periodic vortex shedding. Orientation-averaged terms of the KHMH are computed on the plane of the mean flow and on the geometric centreline. We consider locations between $2$ and $8$ times the width $d$ of the prism. The mean flow produces kinetic energy which feeds the vortex shedding coherent structures. In turn, these structures transfer energy to the stochastic fluctuations over all length-scales $r$ from the Taylor length $lambda$ to $d$ and dominate spatial turbulent transport of two-point stochastic turbulent fluctuations. The orientation-averaged non-linear inter-scale transfer rate $Pi^{a}$ which was found to be approximately independent of $r$ by Alves Portela et. al. (2017) in the range $lambdale r le 0.3d$ at a distance $x_{1}=2d$ from the square prism requires an inter-scale transfer contribution of coherent structures for this approximate constancy. However, the near-constancy of $Pi^a$ at $x_1=8d$ which was also found by Alves Portela et. al. (2017) is mostly due to stochastic fluctuations. Even so, the proximity of $-Pi^a$ to the turbulence dissipation rate $varepsilon$ in the range $lambdale rle d$ at $x_1=8d$ requires contributions of the coherent structures. Spatial inhomogeneity also makes a direct and distinct contribution to $Pi^a$, and the constancy of $-Pi^a/varepsilon$ close to 1 would not have been possible without it either in this near-field flow. Finally, the pressure-velocity term is also an important contributor to the KHMH, particularly at scales r larger than about $0.4d$, and appears to correlate with the purely stochastic non-linear inter-scale transfer rate when the orientation average is lifted.
Magnetic fields in galaxies and galaxy clusters are amplified from a very weak seed value to the observed $mu{rm G}$ strengths by the turbulent dynamo. The seed magnetic field can be of primordial or astrophysical origin. The strength and structure of the seed field, on the galaxy or galaxy cluster scale, can be very different, depending on the seed-field generation mechanism. The seed field first encounters the small-scale dynamo, thus we investigate the effects of the strength and structure of the seed field on the small-scale dynamo action. Using numerical simulations of driven turbulence and considering three different seed-field configurations: 1) uniform field, 2) random field with a power-law spectrum, and 3) random field with a parabolic spectrum, we show that the strength and statistical properties of the dynamo-generated magnetic fields are independent of the details of the seed field. We demonstrate that, even when the small-scale dynamo is not active, small-scale magnetic fields can be generated and amplified linearly due to the tangling of the large-scale field. In the presence of the small-scale dynamo action, we find that any memory of the seed field for the non-linear small-scale dynamo generated magnetic fields is lost and thus, it is not possible to trace back seed-field information from the evolved magnetic fields in a turbulent medium.
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