Helical fluid and (Hall)-MHD turbulence: a brief review.

Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main features, both new and old, such as the discovery of bi-directional cascades or the role of helical vortices in the enhancement of large-scale magnetic fields in the dynamo problem. The dynamical contribution in magnetohydrodynamic of the cross-correlation between velocity and induction is discussed as well.

Small-scale behavior of Hall magnetohydrodynamic turbulence.

Decaying Hall magnetohydrodynamic (HMHD) turbulence is studied using three-dimensional (3D) direct numerical simulations with grids up to 768(3) points and two different types of initial conditions. Results are compared to analogous magnetohydrodynamic (MHD) runs and both Laplacian and Laplacian-squared dissipative operators are examined. At scales below the ion inertial length, the ratio of magnetic to kinetic energy as a function of wave number transitions to a magnetically dominated state.

Rotating turbulence under "precession-like" perturbation.

The effects of changing the orientation of the rotation axis on homogeneous turbulence is considered. We perform direct numerical simulations on a periodic box of 1024(3) grid points, where the orientation of the rotation axis is changed (a) at a fixed time instant (b) regularly at time intervals commensurate with the rotation time scale. The former is characterized by a dominant inverse energy cascade whereas in the latter, the inverse cascade is stymied due to the recurrent changes in the rotation axis resulting in a strong forward energy transfer and large-scale structures that resemble those of isotropic turbulence.

Anisotropy and nonuniversality in scaling laws of the large-scale energy spectrum in rotating turbulence.

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two-dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale Lf, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the inverse cascade range at a small but fixed Rossby number, Rof≈0.

Long-time properties of magnetohydrodynamic turbulence and the role of symmetries.

Using direct numerical simulations with grids of up to 512(3) points, we investigate long-time properties of three-dimensional magnetohydrodynamic turbulence in the absence of forcing and examine in particular the roles played by the quadratic invariants of the system and the symmetries of the initial configurations. We observe that when sufficient accuracy is used, initial conditions with a high degree of symmetries, as in the absence of helicity, do not travel through parameter space over time, whereas by perturbing these solutions either explicitly or implicitly using, for example, single precision for long times, the flows depart from their original behavior and can either become strongly helical or have a strong alignment between the velocity and the magnetic field. When the symmetries are broken, the flows evolve towards different end states, as already predicted by statistical arguments for nondissipative systems with the addition of an energy minimization principle.

Not much helicity is needed to drive large-scale dynamos.

Understanding the in situ amplification of large-scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large-scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity f(h,C) has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that f(h,C) decreases as the ratio of forcing to large-scale wave numbers k(F)/k(min) increases.

Alfvén waves and ideal two-dimensional Galerkin truncated magnetohydrodynamics.

We investigate numerically the dynamics of two-dimensional Euler and ideal magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up to 4096(2), for which several quadratic invariants are preserved by the truncation and the statistical equilibria are known. Initial conditions are the Orszag-Tang vortex with a neutral X point centered on a stagnation point of the velocity field in the large scales. In MHD, we observe that the total energy spectra at intermediate times and intermediate scales correspond to the interactions of eddies and waves, E(T)(k)~k(-3/2).

Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks.

We demonstrate that, for the case of quasiequipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics (LAMHD) alpha model reproduces well both the large-scale and the small-scale properties of turbulent flows; in particular, it displays no increased (superfilter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the subfilter scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of superfilter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally nonlocal energy transfer (associated with Alfvén waves), it is responsible for the absence of a viscous bottleneck in magnetohydrodynamics (MHD), as compared to the fluid case.

Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes alpha model and their large-eddy-simulation potential.

We compute solutions of the Lagrangian-averaged Navier-Stokes alpha - (LANS alpha ) model for significantly higher Reynolds numbers (up to Re approximately 8300 ) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes inertial range followed by a second inertial range specific to the LANS alpha model. Both fully helical and nonhelical flows are examined, up to Reynolds numbers of approximately 1300.

Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo.

We study the transfer of energy between different scales for forced three-dimensional magnetohydrodynamics turbulent flows in the kinematic dynamo regime. Two different forces are examined: a nonhelical Taylor-Green flow with magnetic Prandtl number P(M) = 0.4 and a helical ABC flow with P(M) = 1.

Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence.

We investigate the transfer of energy from large scales to small scales in fully developed forced three-dimensional magnetohydrodynamics (MHD) turbulence by analyzing the results of direct numerical simulations in the absence of an externally imposed uniform magnetic field. Our results show that the transfer of kinetic energy from large scales to kinetic energy at smaller scales and the transfer of magnetic energy from large scales to magnetic energy at smaller scales are local, as is also found in the case of neutral fluids and in a way that is compatible with the Kolmogorov theory of turbulence. However, the transfer of energy from the velocity field to the magnetic field is a highly nonlocal process in Fourier space.

Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling.

We present direct numerical simulations and Lagrangian averaged (also known as alpha model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations.

Numerical solutions of the three-dimensional magnetohydrodynamic alpha model.

We present direct numerical simulations and alpha -model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical dynamo effect. The MHD alpha model is shown to capture the long-wavelength spectra in all these problems, allowing for a significant reduction of computer time and memory at the same kinetic and magnetic Reynolds numbers. In the helical dynamo, not only does the alpha model correctly reproduce the growth rate of magnetic energy during the kinematic regime, it also captures the nonlinear saturation level and the late generation of a large scale magnetic field by the helical turbulence.

Continuum analysis of an avalanche model for solar flares.

We investigate the continuum limit of a class of self-organized critical lattice models for solar flares. Such models differ from the classical numerical sandpile model in their formulation of stability criteria in terms of the curvature of the nodal field, and are known to belong to a different universality class. A fourth-order nonlinear hyperdiffusion equation is reverse engineered from the discrete model's redistribution rule.