Cross-helicity dynamo effect in magnetohydrodynamic turbulent channel flow

The inter-relationships between magnetic helicity, magnetic reconnection, and dynamo effects are discussed. In laboratory experiments, where two plasmas are driven to merge, the helicity content of each plasma strongly affects the reconnection rate, as well as the shape of the diffusion region. Conversely, magnetic reconnection events also strongly affect the global helicity, resulting in efficient helicity cancellation (but not dissipation) during counter-helicity reconnection and a finite helicity increase or decrease (but less efficiently than dissipation of magnetic energy) during co-helicity reconnection. Close relationships also exist between magnetic helicity and dynamo effects. The turbulent electromotive force along the mean magnetic field (alpha-effect), due to either electrostatic turbulence or the electron diamagnetic effect, transports mean-field helicity across space without dissipation. This has been supported by direct measurements of helicity flux in a laboratory plasma. When the dynamo effect is driven by electromagnetic turbulence, helicity in the turbulent field is converted to mean-field helicity. In all cases, however, dynamo processes conserve total helicity except for a small battery effect, consistent with the observation that the helicity is approximately conserved during magnetic relaxation.

The inter-relationships between magnetic helicity, magnetic reconnection, and dynamo effects are discussed. In laboratory experiments, where two plasmas are driven to merge, the helicity content of each plasma strongly affects the reconnection rate, as well as the shape of the diffusion region. Conversely, magnetic reconnection events also strongly affect the global helicity, resulting in efficient helicity cancellation (but not dissipation) during counter-helicity reconnection and a finite helicity increase or decrease (but less efficiently than dissipation of magnetic energy) during co-helicity reconnection. Close relationships also exist between magnetic helicity and dynamo effects. The turbulent electromotive force along the mean magnetic field (alpha-effect), due to either electrostatic turbulence or the electron diamagnetic effect, transports mean-field helicity across space without dissipation. This has been supported by direct measurements of helicity flux in a laboratory plasma. When the dynamo effect is driven by electromagnetic turbulence, helicity in the turbulent field is converted to mean-field helicity. In all cases, however, dynamo processes conserve total helicity except for a small battery effect, consistent with the observation that the helicity is approximately conserved during magnetic relaxation.

Large eddy simulation (LES) of transient magnetohydrodynamic (MHD) turbulent flow under a single-ruler electromagnetic brake (EMBr) in a laboratory-scale, continuous-casting mold is presented. The influence of different electrically-conductive boundary conditions on the MHD flow and electromagnetic field was studied, considering two different wall boundary conditions: insulating and conducting. Both the transient and time-averaged horizontal velocities predicted by the LES model agree well with the measurements of the ultrasound Doppler velocimetry (UDV) probes. Q-criterion was used to visualize the characteristics of the three-dimensional turbulent eddy structure in the mold. The turbulent flow can be suppressed by both configurations of the experiment’s wall (electrically-insulated and conducting walls). The shedding of small-scale vortices due to the Kelvin–Helmholtz instability from the shear at the jet boundary was observed. For the electrically-insulated walls, the flow was more unstable and changed with low-frequency oscillations. However, the time interval of the changeover was flexible. For the electrically-conducting walls, the low-frequency oscillations of the jets were well suppressed; a stable double-roll flow pattern was generated. Electrically-conducting walls can dramatically increase the induced current density and electromagnetic force; hence they contribute to stabilizing the MHD turbulent flow.

Turbulent dynamo modeling in a rotating frame is performed to enable studies of reversed field pinches of fusion plasma and planetary magnetic fields. The Reynolds stresses, turbulent electromotive force, and other important correlation functions, which appear in the equations for the mean velocity and magnetic field, are modeled using the mean fields and four bulk turbulence quantities (the magnetohydrodynamic turbulent energy, its dissipation rate, the cross helicity, and the residual helicity). Four equations for those bulk quantities are combined with the mean-field equations to lead to a self-consistent dynamo model. Specifically, the importance of the cross-helicity effect is pointed out. This model shows that the equilibrium state of reversed field pinches of plasma is a neutral state under the condition of vanishing cross helicity. The relevance to the study of the Earth’s and other planetary magnetic fields is discussed.

26a-L-9 Turbulent electromotive force and cross helicity in MHD flows

Progress in lattice Boltzmann methods for magnetohydrodynamic flows relevant to fusion applications

Large-scale coherent magnetic fields observed in the nearby galaxies are thought to originate by a mean-field dynamo. This is governed via the turbulent electromotive force (EMF, $\overline{{\boldsymbol {\cal E}} {}}$) generated by the helical turbulence driven by supernova (SN) explosions in the differentially rotating interstellar medium (ISM). In this paper, we aim to investigate the possibility of dynamo action by the virtue of buoyancy due to a cosmic ray (CR) component injected through the SN explosions. We do this by analysing the magnetohydrodynamic simulations of local shearing box of ISM in which the turbulence is driven via random SN explosions and the energy of the explosion is distributed in the CR and/or thermal energy components. We use the magnetic field aligned diffusion prescription for the propagation of CR. We compare the evolution of magnetic fields in the models with the CR component to our previous models that did not involve the CR. We demonstrate that the inclusion of CR component enhances the growth of dynamo slightly. We further compute the underlying dynamo coefficients using the test-field method and argue that the entire evolution of the large-scale mean magnetic field can be reproduced with an α − Ω dynamo model. We also show that the inclusion of CR component leads to an unbalanced turbulent pumping between magnetic field components and additional dynamo action by the Rädler effect.

The excellent drag reduction effect of the bubble drag reduction technique has been proved through many experiments since it was proposed. In this paper, the authors investigate the bubble-turbulence interaction and the corresponding drag reduction effect with a two-way coupled Euler–Lagrange code. The liquid phase is simulated by using a large eddy simulation method with the immersed bubbles treated using a nonlinear collision model to accurately simulate the bubble–wall interaction. A Gaussian distributed method is adopted to obtain the void fraction and interphase forces in the two-way coupled algorithm. Two typical wall-bounded turbulent flow problems (turbulent channel flow and boundary layer flow) are simulated to validate the accuracy and stability in bubbly flows and investigate the drag reduction mechanism. First, the effect of bubbles on the turbulent flow is studied in the channel flow cases in which the bubbles are observed attaching to the upper plate and swaying in the spanwise direction. In this case, Reynolds stress near the wall is decreased, which contributes to the drag reduction. Moreover, drag reduction of a turbulent boundary layer flow with bubble injection is studied in which the drag reduction under different air flow rates is in good agreement with experimental results. The contribution of turbulence and different liquid forces to the migration of bubbles away from the wall is investigated. The bubble trajectory in the turbulent boundary layer is divided into three distinct stages and discussed in detail finally.

Pressure drops and velocity distributions of liquid metal MHD flow in pipes are closely related to the geometry of the cross-section. Liquid metal flows in two types of electrically conducting circular pipes under a uniform magnetic field applied transversely to the flow are investigated numerically using large eddy simulation with a coherent structure model developed in the OpenFOAM environment. One pipe has a typical circular cross-section (N-pipe), whereas the other has four V-shaped strips at the wall parallel and perpendicular to the magnetic field (F-pipe). The increasing transverse magnetic field causes a turbulent MHD flow evolves into a single-sided turbulent flow and a laminar flow in the N-pipe. The V-shaped strips on the Hartmann wall generate a low-velocity belt along the magnetic field direction in the center of the pipe and weak high-velocity jets near the V-shaped strips. Furthermore, the inflection points in the velocity profile improve instability and turbulence. The root mean square of the velocity fluctuation, in particular, the transverse components increase with the Hartmann number increasing along the magnetic field direction in the F-pipe. The V-shaped strips delay the MHD turbulent-laminar transition. However, the skin friction coefficient is slightly higher in the F-pipe than in the N-pipe, with the same dimensionless parameters. The research results can be applied to the turbulence promoter in the MHD pipe flow. Key words: Magnetohydrodynamic turbulent flow, large eddy simulation, pipe, V-shaped strips. Tables 5, Figs 9, Refs 23.

Magnetohydrodynamic (MHD) turbulent flows are found in the solar wind, the magnetosheath and the magnetotail plasma sheet. In this paper, we review both observational and theoretical evidence for turbulent flow in the magnetotail. MHD simulations of the global magnetosphere for southward interplanetary magnetic field (IMF) exhibit nested vortices in the earthward outflow from magnetic reconnection that are consistent with turbulence. Similar simulations for northward IMF also exhibit enhanced vorticity consistent with turbulence. These result from Kelvin-Helmholtz (KH) instabilities. However, the turbulent flows association with reconnection fill much of the magnetotail while the turbulent flows associated with the KH instability are limited to a smaller region near the magnetopause. Analyzing turbulent flows in the magnetotail is difficult because of the limited extent of the tail and because the flows there are usually sub-magnetosonic. Observational analysis of turbulent flows in the magnetotail usually assume that the Taylor frozen-in-flow hypothesis is valid and compare power spectral density vs. frequency with spectral indices derived for fluid turbulence by Kolmogorov in 1941. Global simulations carried out for actual magnetospheric substorms in the tail enable the results of the simulations to be compared directly with observed power spectra. The agreement between the two techniques provides confidence that the plasma sheet plasma is actually turbulent. The MHD results also allow us to calculate the power vs. wave number; results that also support the idea that the tail is turbulent.

In Chapter 9, we examined turbulence effects on the global or mean components of magnetic fields and fluid motion. They are characterized by the turbulent electromotive force E M and the Reynolds stress R ij . These two quantities are related to the mean components and the turbulence characteristics, and the construction of the transport equations for the latter leads to a closed system of turbulent dynamo. In the approach, attention is focused on the analytical insight into the global magnetic-field generation processes that are common to various types of turbulent motion of electrically conducting fluids. Therefore the highly time-dependent properties of turbulence associated with small-scale components are beyond the reach of turbulent dynamo.

Chapter 9 The turbulent electromotive force in the case of rotational mean motion

We derive an exact equation for homogeneous isotropic magnetohydrodynamic (MHD) turbulent flows with nonzero helicity; this result is of the same nature as the classical von Kármán-Howarth (VKH-HM) formulation for the kinetic energy of turbulent fluids. Helical MHD is relevant to the astrophysical flows such as in the solar corona, or the interstellar medium, and in the dynamo problem. The derivation involves the new writing of the general form of tensors for that case, for either vectors or (pseudo)axial vectors. It is shown that, for general third-order tensors, four generating functions are needed when taking into account the nonmirror invariance of helical fluids, instead of two as in the fully isotropic case. The new equation obtained, denoted by VKH-HM, links the dissipation of magnetic helicity to the third-order correlations involving combinations of the components of the velocity, the magnetic field, and the magnetic potential. Finally, in the long-time and nonresistive limit, this relationship leads to a linear scaling with separation of the third-order tensor, correlating the two normal components of the electromotive force and of the magnetic potential.

In the present work we study potential applicability of large eddy simulation (LES) method for prediction of flatness and skewness of compressible magnetohydrodynamic (MHD) turbulence. The knowledge of these quantities characterizes non-Gaussian properties of turbulence and can be used for verification of hypothesis on Gaussianity for the turbulent flow under consideration. Prediction accuracy of these quantities by means of LES method directly determines efficiency of reconstruction of probability density function (PDF) that depends on used subgrid-scale (SGS) parameterizations. Applicability of LES approach for studying of PDF properties of turbulent compressible magnetic fluid flow is investigated and potential feasibilities of five SGS parameterizations by means of comparison with direct numerical simulation results are explored. The skewness and the flatness of the velocity and the magnetic field components under various hydrodynamic Reynolds numbers, sonic Mach numbers, and magnetic Reynolds numbers are studied. It is shown that various SGS closures demonstrate the best results depending on change of similarity numbers of turbulent MHD flow. The case without any subgrid modeling yields sufficiently good results as well. This indicates that the energy pile-up at the small scales that is characteristic for the model without any subgrid closure, does not significantly influence on determination of PDF. It is shown that, among the subgrid models, the best results for studying of the flatness and the skewness of velocity and magnetic field components are demonstrated by the Smagorinsky model for MHD turbulence and the model based on cross-helicity for MHD case. It is visible from the numerical results that the influence of a choice subgrid parametrization for the flatness and the skewness of velocity is more essential than for the same characteristics of magnetic field.

Steady turbulent viscous incompressible fluid flow in a plane channel is calculated for the case of uniform blowing and suction through opposite walls. There are no experimental data for flows of this type. The flows were calculated by two methods: a direct numerical simulation method and using a three-parameter turbulence model. Direct numerical simulation was carried out using the same (apart from the boundary conditions) algorithm for numerical solution of the Navier-Stokes equations as that used earlier for calculating flows in pipes and channels with impermeable walls. In the second group of calculations the version of the model published in 1978 was used. The results obtained by the two methods are in good agreement. The difference is within the spread of the experimental data used for determining the parameters of the model. The agreement obtained makes it possible to assert that the turbulence direct numerical simulation algorithm developed can be used for the analysis of flows with quite different boundary conditions, including cases where there are no corresponding experimental data.