Astrophysical magnetic fields and nonlinear dynamo theory

A review of the present status of the theory of magnetic reconnection is given. In strongly collisional plasmas reconnection proceeds via resistive current sheets, i.e. quasi-stationary macroscopic Sweet-Parker sheets at intermediate values of the magnetic Reynolds number R m , or mirco-current sheets in MHD turbulence, which develops at high R m . In hot, dilute plasmas the reconnection dynamics is dominated by nondissipative effects, mainly the Hall term and electron inertia. Reconnection rates are found to depend only on the ion mass, being independent of the electron inertia and the residual dissipation coefficients. Small-scale whistler turbulence is readily excited giving rise to an anomalous electron viscosity. Hence reconnection may be much more rapid than predicted by conventional resistive theory.

Magnetic reconnection in plasmas

Direct numerical simulations of turbulent flows over riblet-mounted surfaces are performed to educe the mechanism of drag reduction by riblets. The computed drag on the riblet surfaces is in good agreement with the existing experimental data. The mean-velocity profiles show upward and downward shifts in the log–law for drag-decreasing and drag-increasing cases, respectively. Turbulence statistics above the riblets are computed and compared with those above a flat plate. Differences in the mean-velocity profile and turbulence quantities are found to be limited to the inner region of the boundary layer. Velocity and vorticity fluctuations as well as the Reynolds shear stresses above the riblets are reduced in drag-reducing configurations. Quadrant analysis indicates that riblets mitigate the positive Reynolds-shear-stress-producing events in drag-reducing configurations. From examination of the instantaneous flow fields, a drag reduction mechanism by riblets is proposed: riblets with small spacings reduce viscous drag by restricting the location of the streamwise vortices above the wetted surface such that only a limited area of the riblets is exposed to the downwash of high-speed fluid that the vortices induce.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112093002575

Direct numerical simulation of turbulent flow over riblets

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence Our study covers both gas-pressure-dominated (high β) and magnetic-pressure-dominated (low β) plasmas at different Mach numbers In addition, we present results for super-Alfvenic turbulence and discuss in what way it is similar to sub-Alfvenic turbulence We describe a technique of separating different magnetohydrodynamic modes (slow, fast and Alfven) and apply it to our simulations We show that, for both high- and low-β cases, Alfven and slow modes reveal a Kolmogorov k - 5 / 3 spectrum and scale-dependent Goldreich-Sridhar anisotropy, while fast modes exhibit a k - 3 / 2 spectrum and isotropy We discuss the statistics of density fluctuations arising from MHD turbulence in different regimes Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence In addition, we show that magnetic field enhancements and density enhancements are marginally correlated Addressing the density structure of partially ionized interstellar gas on astronomical-unit scales, we show that the viscosity-damped regime of MHD turbulence that we reported earlier for incompressible flows persists for compressible turbulence and therefore may provide an explanation for these mysterious structures

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Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications

We report the results of an extensive numerical study of the small-scale turbulent dynamo. The primary focus is on the case of large magnetic Prandtl numbers Prm, which is relevant for hot low-density astrophysical plasmas. A Prm parameter scan is given for the model case of viscosity-dominated (low Reynolds number) turbulence. We concentrate on three topics: magnetic energy spectra and saturation levels, the structure of the magnetic field lines, and intermittency of the field strength distribution. The main results are as follows: (1) the folded structure of the field (direction reversals at the resistive scale, field lines curved at the scale of the flow) persists from the kinematic to the nonlinear regime; (2) the field distribution is self-similar and appears to be lognormal during the kinematic regime and exponential in the saturated state; and (3) the bulk of the magnetic energy is at the resistive scale in the kinematic regime and remains there after saturation, although the magnetic energy spectrum becomes much shallower. We propose an analytical model of saturation based on the idea of partial two-dimensionalization of the velocity gradients with respect to the local direction of the magnetic folds. The model-predicted saturated spectra are in excellent agreement with numerical results. Comparisons with large-Re, moderate-Prm runs are carried out to confirm the relevance of these results and to test heuristic scenarios of dynamo saturation. New features at large Re are elongation of the folds in the nonlinear regime from the viscous scale to the box scale and the presence of an intermediate nonlinear stage of slower than exponential magnetic energy growth accompanied by an increase of the resistive scale and partial suppression of the kinetic energy spectrum in the inertial range. Numerical results for the saturated state do not support scale-by-scale equipartition between magnetic and kinetic energies, with a definite excess of magnetic energy at small scales. A physical picture of the saturated state is proposed. Subject heading gs: magnetic fields — methods: numerical — MHD — plasmas — turbulence

https://iopscience.iop.org/article/10.1086/422547/pdf

Simulations of the Small-Scale Turbulent Dynamo

http://iopscience.iop.org/article/10.1016/0169-5983(89)90021-X/pdf

Dual solutions of the flow through a curved tube

https://iopscience.iop.org/article/10.1016/S0169-5983(02)00103-X/pdf

Laminar flows through a curved rectangular duct over a wide range of the aspect ratio

https://iopscience.iop.org/article/10.1016/0169-5983(94)90035-3/pdf

Torsion effect on the flow in a helical pipe

Statistical properties of MHD turbulence and the mechanism of turbulent dynamo are investigated by direct numerical simulations of three‐dimensional MHD equations. It is assumed that the turbulent field has a high symmetry and that the fluid has hyperviscosity and hypermagnetic diffusivity. An external force is exerted on the fluid as kinetic energy and helicity sources. The main concern of the present study is whether magnetic fields of scales comparable to the dominant fluid motions can be generated or not. It is shown that the turbulent dynamo is effective if hypermagnetic diffusivity is smaller than a critical value. The total energy spectrum is close to the k−5/3 power law in the inertial range. The energy transfer between kinetic and magnetic fields is discussed.

Shinichiro Yanase

Papers

Dual solutions of the flow through a curved tube

Laminar flows through a curved rectangular duct over a wide range of the aspect ratio

Torsion effect on the flow in a helical pipe

Statistical properties of MHD turbulence and turbulent dynamo

Numerical study of non-isothermal flow with convective heat transfer in a curved rectangular duct