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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 1437-1452 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A computational investigation of magnetic helicity of the fluctuating magnetic field Hm in ideal and freely decaying three-dimensional (3-D) magnetohydrodynamics (MHD) in the presence of a uniform mean magnetic field is performed. It is shown that for ideal 3-D MHD Hm, which is a rugged invariant in the absence of a mean magnetic field [Frisch et al., J. Fluid Mech. 77, 796 (1975)], decays from its initial value and proceeds to oscillate about zero. The decay of Hm is shown to result from the presence of a new "generalized'' helicity invariant, which includes contributions from the uniform magnetic field. The loss of invariance of Hm will diminish the effects of inverse transfer of Hm on freely decaying turbulence. This is demonstrated in a discussion of the selective decay relaxation process. © 1995 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 1850-1867 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Lattice gas and lattice Boltzmann methods are recently developed numerical schemes for simulating a variety of physical systems. In this paper a new lattice Boltzmann model for modeling two-dimensional (2-D) incompressible magnetohydrodynamics (MHD) is presented. The current model fully utilizes the flexibility of the lattice Boltzmann method in comparison with previous lattice gas and lattice Boltzmann MHD models, reducing the number of moving directions from 36 in other models to 12 only. To increase computational efficiency, a simple single time relaxation rule is used for collisions, which directly controls the transport coefficients. The bidirectional streaming process of the particle distribution function in this paper is similar to the original model [H. Chen and W. H. Matthaeus, Phys. Rev. Lett. 58, 1845 (1987), S. Chen et al., Phys. Rev. Lett. 67, 3776 (1991)], but has been greatly simplified, affording simpler implementation of boundary conditions and increasing the feasibility of extension into a workable three-dimensional (3-D) model. Analytical expressions for the transport coefficients are presented. Also, as example cases, numerical calculation for the Hartmann flow is performed, showing a good agreement between the theoretical prediction and numerical simulation, and a sheet-pinch simulation is performed and compared with the results obtained with a spectral method.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2207-2216 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier–Stokes fluid to a "most probable,'' or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1848-1864 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The selective decay and dynamic alignment relaxation theories are used to interpret the time asymptotic behavior of a Galerkin model of three-dimensional (3-D) magnetohydrodynamics (MHD). A large number of simulations are performed that scan a parameter space defined by the rugged ideal invariants: energy, cross helicity, and magnetic helicity. Ranges of the initial parameters are found where one or both of the relaxation theories are needed to describe the time asymptotic properties of the system, as previously found in analogous studies of two-dimensional (2-D) MHD [Ting et al., Phys. Fluids 29, 3261 (1986)]. In many cases, the time asymptotic state can be interpreted as a relaxation to minimum energy. For certain parameter ranges spectral back transfer of cross helicity can lead to growth in velocity-magnetic field correlation [Stribling and Matthaeus, Phys. Fluids B 2, 1979 (1990)]. A simple decay model, based on absolute equilibrium theory, predicts a mapping of initial onto time asymptotic states, and accurately describes the long time behavior of the runs when magnetic helicity is present. We also discuss two processes, operating on time scales shorter than selective decay and dynamic alignment, in which the ratio of kinetic to magnetic energy relaxes to values O(1). The faster of the two takes states initially dominant in magnetic energy to a state of near-equipartition between kinetic and magnetic energy through power law growth of kinetic energy. The other process takes states initially dominant in kinetic energy to the near-equipartitioned state through exponential growth of magnetic energy.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1929-1931 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan [Phys. Fluids 8, 1385 (1965)]. The role of Alfvén wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22–1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented "golden rules'' for relating the spectral transfer time scale to the Alfvén and eddy-turnover time scales.
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1235-1237 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Cellular automata modeling of the advection of a passive scalar in a two-dimensional flow is examined in the context of discrete lattice kinetic theory. It is shown that if the passive scalar is represented by tagging or "coloring'' automation particles a passive advection–diffusion equation emerges without use of perturbation expansions. For the specific case of the hydrodynamic lattice gas model of Frisch, Hasslacher, and Pomeau [Phys. Rev. Lett. 56, 1505 (1986)] the diffusion coefficient is calculated by perturbation.
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 2886-2904 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We evaluate a number of simple, one-point phenomenological models for the decay of energy-containing eddies in magnetohydrodynamic (MHD) and hydrodynamic turbulence. The MHD models include effects of cross helicity and Alfvénic couplings associated with a constant mean magnetic field, based on physical effects well-described in the literature. The analytic structure of three separate MHD models is discussed. The single hydrodynamic model and several MHD models are compared against results from spectral-method simulations. The hydrodynamic model phenomenology has been previously verified against experiments in wind tunnels, and certain experimentally determined parameters in the model are satisfactorily reproduced by the present simulation. This agreement supports the suitability of our numerical calculations for examining MHD turbulence, where practical difficulties make it more difficult to study physical examples. When the triple-decorrelation time and effects of spectral anisotropy are properly taken into account, particular MHD models give decay rates that remain correct to within a factor of 2 for several energy-halving times. A simple model of this type is likely to be useful in a number of applications in space physics, astrophysics, and laboratory plasma physics where the approximate effects of turbulence need to be included. © 1995 American Institute of Physics.
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 1237-1237 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 657-657 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The results of Drake et al.1 on conversion of a periodic array of Navier-Stokes vortices into shear flow are interpreted in an alternate context. Reservations are expressed concerning the computation. (AIP)
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 3634-3644 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The dynamics of a compressible magnetofluid plasma with a polytropic equation of state are considered in the limit of low plasma frame acoustic Mach number. The relationship between the equations describing the low Mach number flow and the equations of idealized incompressible magnetohydrodynamics is investigated using a multiple time scale asymptotic expansion procedure, which is justified by appealing to several rigorous theorems concerning both hydrodynamics and magnetohydrodynamics. When appropriate assumptions are adopted concerning the degree of departure from incompressibility, the lowest-order behavior is that of incompressible magnetohydrodynamics, associated with order Mach number-squared "pseudosound'' density fluctuations. The first corrections to incompressible flow take the form of magnetoacoustic fluctuations, with associated pressure fluctuations at the same order as the pseudosound pressure. Resumming the asymptotic series gives rise to a simple set of equations that describes "nearly incompressible magnetohydrodynamics.'' The theory provides a justification for the turbulent density spectrum theory of Montgomery, Brown, and Matthaeus [J. Geophys. Res. 92, 282 (1987)] and clarifies several issues pertaining to Alfvén wave turbulence in the solar wind. The nearly incompressible description may also be useful in other theoretical contexts, particularly in extensions of incompressible magnetohydrodynamic turbulence theory, since it is expected to be valid for finite times (until possible shock structures form) when the global Mach number is sufficiently small.
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