Nobumitsu Yokoi

Statistical analysis of the effects of helicity in inhomogeneous turbulence

Effects of helicity in three‐dimensional incompressible inhomogeneous turbulence are examined with the aid of a two‐scale direct‐interaction approximation (DIA). The turbulent helicity gives a measure of the reflectional asymmetry in a turbulent flow and its inhomogeneity contributes to the sustainment of large‐scale vorticity field in a three‐dimensional mean flow. The importance of helicity effects is discussed in the context of flows in a rotating system and swirling flows in a pipe. A three‐equation model with the turbulent helicity incorporated is proposed using the theoretical results. The validity of the model is confirmed quantitatively through the application to a decaying swirling flow in a pipe.

Turbulent magnetohydrodynamic dynamo for accretion disks using the cross-helicity effect

Accretion disks are studied using the concept of the turbulent magnetohydrodynamic (MHD) dynamo. Under this concept, the effect of cross helicity (magnetic-field/velocity correlation function) plays a key role as does the effect of turbulent viscosity and anomalous resistivity. In the presence of the cross helicity, the rotational motion of the disk can generate the toroidal magnetic field. The magnetic field produces the thrust for launching the jet which, in turn, induces the poloidal magnetic field under the cross-helicity effect. The close relationship between the magnetic field and the plasma velocity is a primary feature of the cross-helicity dynamo

Turbulence theories and modelling of fluids and plasmas

Theoretical and heuristic modelling methods are reviewed for studying turbulence phenomena of fluids and plasmas. Emphasis is placed on understanding of effects on turbulence characteristics due to inhomogeneities of field and plasma parameters. The similarity and dissimilarity between the methods for fluids and plasmas are sought in order to shed light on the properties that are shared or not by fluid and plasma turbulence.

Cross helicity and related dynamo

The turbulent cross helicity is directly related to the coupling coefficients for the mean vorticity in the electromotive force and for the mean magnetic-field strain in the Reynolds stress tensor. This suggests that the cross-helicity effects are important in the cases where global inhomogeneous flow and magnetic-field structures are present. Since such large-scale structures are ubiquitous in geo/astrophysical phenomena, the cross-helicity effect is expected to play an important role in geo/astrophysical flows. In the presence of turbulent cross helicity, the mean vortical motion contributes to the turbulent electromotive force. Magnetic-field generation due to this effect is called the cross-helicity dynamo. Several features of the cross-helicity dynamo are introduced. Alignment of the mean electric-current density J with the mean vorticity Ω , as well as the alignment between the mean magnetic field B and velocity U , is supposed to be one of the characteristic features of the dynamo. Unlike the case in the helicity or α effect, where J is aligned with B in the turbulent electromotive force, we in general have a finite mean-field Lorentz force J  ×  B in the cross-helicity dynamo. This gives a distinguished feature of the cross-helicity effect. By considering the effects of cross helicity in the momentum equation, we see several interesting consequences of the effect. Turbulent cross helicity coupled with the mean magnetic shear reduces the effect of turbulent or eddy viscosity. Flow induction is an important consequence of this effect. One key issue in the cross-helicity dynamo is to examine how and how much cross helicity can be present in turbulence. On the basis of the cross-helicity transport equation, its production mechanisms are discussed. Some recent developments in numerical validation of the basic notion of the cross-helicity dynamo are also presented.

Explosive turbulent magnetic reconnection.

We report simulation results for turbulent magnetic reconnection obtained using a newly developed Reynolds-averaged magnetohydrodynamics model. We find that the initial Harris current sheet develops in three ways, depending on the strength of turbulence: laminar reconnection, turbulent reconnection, and turbulent diffusion. The turbulent reconnection explosively converts the magnetic field energy into both kinetic and thermal energy of plasmas, and generates open fast reconnection jets. This fast turbulent reconnection is achieved by the localization of turbulent diffusion. Additionally, localized structure forms through the interaction of the mean field and turbulence.

Dynamos and MHD theory of turbulence suppression

Characteristics of electrically conducting media are reviewed from the macroscopic viewpoint based on mean-field magnetohydrodynamics, while being compared using the methodology and knowledge in fluid mechanics. The themes covered in this review range from the mechanism of generating stellar magnetic fields (dynamo) to transport properties in fusion. The primary concern here is to see the characteristics common to these apparently different phenomena, within the framework of the mean-field theory. Owing to the intrinsic limitation of the approach, the present discussions are limited more or less to specific aspects of phenomena. They are supplemented with reference to theoretical, numerical, and observational approaches intrinsic to each theme. In the description of dynamo phenomena, emphasis is laid on the cross helicity dynamo. Features common to stellar magnetic-field generation and the rotational-motion drive in toroidal plasmas are illustrated on this basis.

A turbulence model for magnetohydrodynamic plasmas

The statistical theory of inhomogeneous turbulence is applied to develop a system of model equations for magnetohydrodynamic (MHD) turbulence. The statistical descriptors of MHD turbulence are taken to be the turbulent MHD energy, its dissipation rate, the turbulent cross helicity (velocity-magnetic field correlation), turbulent MHD residual energy (difference between the kinetic and magnetic energies), and turbulent residual helicity (difference between the kinetic and current helicities). Evolution equations for these statistical quantities are coupled to the mean-field dynamics. The model is applied to two MHD-plasma phenomena: turbulence evolution with prescribed mean velocity and magnetic fields in the solar wind, and mean flow generation in the presence of a mean magnetic field and cross helicity in tokamak plasmas. These applications support the validity of the turbulence model. In the presence of a mean magnetic field, turbulence dynamics should be subject to combined effects of nonlinearity and Alfvén waves; consequences for the dissipation rate of MHD residual energy are discussed.

Stationary large‐scale magnetic fields generated by turbulent motion in a spherical region

Stationary large‐scale magnetic fields generated by an electrically conducting fluid in a spherical region are examined analytically, using the concept of the turbulent dynamo based on helicity and cross‐helicity effects. Under this concept, the toroidal magnetic field is induced through the combination of a rotational motion and the turbulent cross‐helicity effect. This field generates the poloidal one through the turbulent residual‐helicity (alpha) effect. A new magnetic‐field generation mechanism in the vicinity of the poles is also described. These findings are discussed in the context of the dimension of the convection part of a stellar object.

An application of the turbulent magnetohydrodynamic residual-energy equation model to the solar wind

A magnetohydrodynamic (MHD) turbulence model incorporating the turbulent MHD residual energy (difference between the kinetic and magnetic energies) is applied to solar-wind turbulence. In the model, the dynamics of the turbulent cross-helicity (cross-correlation between the velocity and magnetic field) and the turbulent MHD residual energy, which are considered to describe the degree of Alfvenicity of the MHD turbulence, are solved simultaneously with the dynamics of the turbulent MHD energy and its dissipation rate. The transition of solar-wind turbulence from the Alfven-wave-like fluctuations near the Sun in the inner heliosphere to the fully developed MHD turbulence in the outer heliosphere is discussed. Magnetic dominance in the solar-wind fluctuations is addressed from the dynamics of the evolution equation of the residual energy. An interpretation of the observed Alfven ratio (ratio of the kinetic to magnetic energies) of ∼0.5 is proposed from the viewpoint of a stationary solution of the turbulence...

Mean Field Theory Interpretation of Solar Polarity Reversal

A mechanism of the polarity reversal of the solar magnetic field is explored on the basis of the mean field or turbulent dynamo theory. In the low-latitude region of the convective zone, the toroidal magnetic field, which is the origin of sunspots, is generated by the rotational motion of fluids, with the turbulent cross helicity as the intermediary. This field generates the poloidal field of dipole type through the alpha or turbulent helicity effect. The latter, in turn, contributes to the annihilation of the turbulent cross helicity, resulting in the decay of the toroidal magnetic field. This process indicates less room for the occurrence of the fully developed poloidal field in the low-latitude region and paves the way for the polarity reversal through the change of the sign of the turbulent cross helicity. A simple model mimicking the periodic polarity reversal is presented, and the relationship of the reversal period to the ratio of the poloidal to toroidal fields is given. The meridional-flow velocity at the solar surface is estimated, giving a result consistent with observations.