Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence (original) (raw)
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Incompressible Homogeneous Anisotropic Turbulence: Magnetohydrodynamic Turbulence
Homogeneous Turbulence Dynamics, 2018
Magnetohydrodynamic (MHD) turbulence is present in electrically-conducting fluids, both in industrial devices and in the core of the earth, and is ubiquitous in heliophysics and astrophysics. MHD is also the first step to address the physics of plasmas, with recent studies motivated by the ITER project. Interactions of velocity and magnetic (or induction) fields yield new coupled effects. These effects can be mainly described and modelled in our context of homogeneous turbulence, because the Lorentz (or Laplace) force is a body force, as are the Coriolis force (Chap. 7) and the buoyancy force (Chap. 10). Limits of our incompressible and "homogenized" approach are touched upon at the end of this chapter. Incompressibility is not questioned in a turbulent liquid metal, but it is not suited in many astrophysical situations, so that we will explore the limits of this approximation as well, and look at some extensions using the anelastic approximation, or magnetosonic modes. Analogies and differences with the "hydro" (hydrodynamic hereinafter) case can be first discussed in the presence of a mean magnetic field, which can appear as a mean Alfvén velocity using a simple rescaling. Without strong diffusion and in the presence of a dominant mean field B 0 , Alfvén waves are easily identified from background coupled equations, observations, experiments and numerical simulations. With respect to the other wave régimes presented in this book in the "hydro" case, these plane waves are not dispersive (sometime called semi-dispersive), the dispersion law displays a typical mean-velocity-scale (the Alfvén velocity) and not a typical frequency (Coriolis parameter, stratification frequency). In contrast with the Coriolis force and the buoyancy force (at least within the Boussinesq approximation), that are linear, the Lorentz force is quadratic, so that it yields cubic correlations in the equations for kinetic energy and total energy, as for nonlinear transfer terms. Accordingly, Alfvén waves are well identified in the presence of a dominant external magnetic field, when the Lorentz force is linearized, but they do exist without mean magnetic field.
Interplay between Alfvén and magnetosonic waves in compressible magnetohydrodynamics turbulence
Physics of Plasmas, 2017
Using spatio-temporal spectra, we show direct evidence of excitation of magnetosonic and Alfvén waves in three-dimensional compressible magnetohydrodynamic turbulence at small Mach numbers. For the plasma pressure dominated regime, or the high β regime (with β the ratio between fluid and magnetic pressure), and for the magnetic pressure dominated regime, or the low β regime, we study magnetic field fluctuations parallel and perpendicular to a guide magnetic field B0. In the low β case, we find excitation of compressible and incompressible fluctuations, with a transfer of energy towards Alfvénic modes and to a lesser extent towards magnetosonic modes. In particular, we find signatures of the presence of fast magnetosonic waves in a scenario compatible with that of weak turbulence. In the high β case, fast and slow magnetosonic waves are present, with no clear trace of Alfvén waves, and a significant part of the energy is carried by two-dimensional turbulent eddies.
The influence of a mean magnetic field on three-dimensional magnetohydrodynamic turbulence
Journal of Fluid Mechanics, 1994
Building on results from two-dimensional magnetohydrodynamic (MHD) turbulence (Shebalin, Matthaeus & Montgomery 1983), the development of anisotropic states from initially isotropic ones is investigated numerically for fully three-dimensional incompressible MHD turbulence. It is found that when an external d.c. magnetic field (B0) is imposed on viscous and resistive MHD systems, excitations are preferentially transferred to modes with wavevectors perpendicular to B0). The anisotropy increases with increasing mechanical and magnetic Reynolds numbers, and also with increasing wavenumber. The tendency of B0 to inhibit development of turbulence is also examined.
The Anisotropy of Magnetohydrodynamic Alfvenic Turbulence
The Astrophysical Journal, 2000
We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2π threaded by strong uniform magnetic fields. We use a pseudo-spectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale-independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along local magnetic field lines. The results are consistent with the scaling lawk ∼k 2/3 ⊥ proposed by Sridhar (1995, 1997). Herek (andk ⊥ ) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations which may be a sign of limitations to the model, or our inability to fully resolve the inertial range of turbulence in our simulations.
Physical Review Fluids
We studied the anisotropization of homogeneous magnetohydrodynamic turbulence at low magnetic Reynolds numbers. Flows of this type are not only important for different engineering applications, but also provide an appealing framework for studies of quasi-two-dimensional turbulence with strongly modified transport properties. The results of large-scale forced, direct numerical simulations are presented and compared with those obtained with the quasi-normal scale elimination theory. For a weak magnetic field, the simulations validated the theoretical predictions, including the generation of the k −7/3 range of the energy spectra and its propagation toward higher wave numbers with increasing magnetic field strength. In a strong magnetic field, the turbulence attains a quasi-two-dimensional state with an enstrophy cascade inertial range of the normal flow components in the normal plane and a passive scalar inertial-convective range of the parallel component. The corresponding energy spectra are in a good agreement with logarithmically corrected k −3 and k −1 theoretical predictions. With increasing Reynolds number at constant magnetic field the enstrophy cascade becomes unstable and is replaced by helicity cascade with k −7/3 energy spectrum. The enstrophy cascade is restored with an increasing magnetic field. An investigation of the mechanism of energy injection into the parallel component in a strong magnetic field revealed that the energy is supplied directly by an external force. The spectrum of the parallel component depends on the isotropy of external forcing and is, thus, not universal.
The Generation of Magnetic Fields through Driven Turbulence
The Astrophysical Journal, 2000
We have tested the ability of driven turbulence to generate magnetic field structure from a weak uniform field using three dimensional numerical simulations of incompressible turbulence. We used a pseudo-spectral code with a numerical resolution of up to 144 3 collocation points. We find that the magnetic fields are amplified through field line stretching at a rate proportional to the difference between the velocity and the magnetic field strength times a constant. Equipartition between the kinetic and magnetic energy densities occurs at a scale somewhat smaller than the kinetic energy peak. Above the equipartition scale the velocity structure is, as expected, nearly isotropic. The magnetic field structure at these scales is uncertain, but the field correlation function is very weak. At the equipartition scale the magnetic fields show only a moderate degree of anisotropy, so that the typical radius of curvature of field lines is comparable to the typical perpendicular scale for field reversal. In other words, there are few field reversals within eddies at the equipartition scale, and no fine-grained series of reversals at smaller scales. At scales below the equipartition scale, both velocity and magnetic structures are anisotropic; the eddies are stretched along the local magnetic field lines, and the magnetic energy dominates the kinetic energy on the same scale by a factor which increases at higher wavenumbers. We do not show a scale-free inertial range, but the power spectra are a function of resolution and/or the imposed viscosity and resistivity. Our results are consistent with the emergence of a scale-free inertial range at higher Reynolds numbers.
Probing Physics of Magnetohydrodynamic Turbulence Using Direct Numerical Simulation
1998
The energy spectrum and the nolinear cascade rates of MHD turbulence is not clearly understood. We have addressed this problem using direct numerical simulation and analytical calculations. Our numerical simulations indicate that Kolmogorov-like phenomenology with k −5/3 energy spectrum, rather than Kraichnan's k −3/2 , appears to be applicable in MHD turbulence. Here, we also construct a self-consistent renomalization group procedure in which the mean magnetic field gets renormalized, which in turns yields k −5/3 energy spectrum. The numerical simulations also show that the fluid energy is transferred to magnetic energy. This result could shed light on the generation magnetic field as in dynamo mechanism.
Characterization of Flow-Magnetic Field Interactions in Magneto-Hydrodynamic Turbulence
Journal of Computational and Nonlinear Dynamics, 2013
We examine the complex nonlinear flow-magnetic field dynamics in magneto-hydrodynamic (MHD) turbulence. Using direct numerical simulations (DNS), we investigate the dynamical interactions subject to the influence of a uniform applied background magnetic field. The initial magnetic and kinetic Reynolds numbers (based on Taylor microscale) are 45 and there are no initial magnetic field fluctuations. The sum total of turbulent magnetic and kinetic energies decays monotonically. With time, the turbulent magnetic fluctuations grow by extracting energy from velocity fluctuations. Expectedly, the distribution of energy between kinetic and magnetic fluctuations exhibits large periodic oscillations from the equipartition state due to Alfvén waves. We perform a detailed analysis of the flow-magnetic field coupling and posit a simple model for the energy interchange. Such dynamical analysis can provide the insight required for turbulence control and closure modeling strategies.
Spectral study of anisotropic magnetohydrodynamic turbulence
2009
A spectral analysis of anisotropic magneto-hydrodynamic turbulence, in presence of a constant magnetic field, is presented using direct numerical simulations. A method of decomposing the spectral space into ring structures is presented and the energy transfers between such rings are studied. This decomposition method takes into account the angular dependency of transfer functions in anisotropic systems, while it allows to recover easily the known shell-to-shell transfers in the limit of isotropic turbulence. For large values of the constant magnetic field, the dominant energy transfers appear to be in the direction perpendicular to the mean magnetic field. The linear transfer due to the constant magnetic also appear to be important in redistributing the energy between the velocity and the magnetic fields.
Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence
Reports on progress in physics. Physical Society (Great Britain), 2017
In this review we summarise the current status of the quasi-static magnetohydrodynamic turbulence. The energy spectrum is steeper than Kolmogorov's k (-5/3) spectrum due to the decrease of the kinetic energy flux with wavenumber k as a result of Joule dissipation. The spectral index decreases with the increase of interaction parameter. The flow is quasi two-dimensional with strong [Formula: see text] at small k and weak [Formula: see text] at large k, where [Formula: see text] and [Formula: see text] are the perpendicular and parallel components of velocity relative to the external magnetic field. For small k, the energy flux of [Formula: see text] is negative, but for large k, the energy flux of [Formula: see text] is positive. Pressure mediates the energy transfer from [Formula: see text] to [Formula: see text].