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Non-equilibrium property of turbulence modifies characteristics of turbulent transport. With the aid of response-function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the turbulent energy ($K$) and its dissipation rate ($\varepsilon$) along the mean stream through the advective derivatives of $K$ and $\varepsilon$. Applications of this effect to the turbulent convection with plumes are considered for the first time in this work. The non-equilibrium transport effects associated with plumes are addressed in two aspects. Firstly, the effect associated with a single plume is evaluated using data measured in the recent plume/jet experiments. The second argument is developed for the collective turbulent transport associated with multiple plumes mimicking the stellar convection zone. In this second case, for the purpose of capturing the plume motions into the advective derivatives, use has to be made of the time--space double averaging procedure, where the turbulent fluctuations are divided into the coherent or dispersion component (which represents plume motions) and incoherent or random component. With the aid of the transport equations of the coherent velocity stress and the incoherent counterpart, the interaction between the dispersion and random fluctuations are also discussed in the context of convective turbulent flows with plumes. It is shown from these analyses that the non-equilibrium effect associated with plume motions is of a great deal of relevance in the convective turbulence modelling., Comment: 22 pages, 6 figures, 2 tables, submitted to Atmosphere. Turbulence from Earth to Planets, Stars and Galaxies - Commemorative Issue Dedicated to the Memory of Jackson Rae Herring

Kinetic helicity (hereafter helicity) is defined by the correlation between the velocity and the flow-aligned vorticity. Helicity, as well as energy, is an inviscid invariant of the hydrodynamic equations. In contrast to energy, a measure of the turbulent intensity, turbulent helicity, representing right- and left-handed twist associated with a fluctuating motion, provides a measure of the structural or topological property of the fluctuation. The helicity effect on the turbulent transport can be analytically obtained in the framework of the multiple-scale renormalized perturbation expansion theory through the inclusion of the non-reflectionally-symmetric part for the lowest-order (homogeneous and isotropic) velocity correlation. The physical significance of the helicity-related contribution to the momentum transport is explained. By utilizing the analytical expression of the Reynolds stress, a turbulence model with helicity effect incorporated (helicity model) is constructed. This helicity model is applied to a swirling flow to show its validity in describing the prominent properties of the flow. In addition to the transport suppression, inhomogeneous helicity coupled with a rotation can induce a large-scale flow. The results of direct numerical simulations (DNSs) confirming the global flow generation by helicity will be also reviewed, followed by several possible applications in geo- and astro-physical flow phenomena., Comment: 66 pages 15 figures, Chapter 3 in Helicities in Geophysics, Astrophysics and Beyond (AGU Books, Wiley, 2023)

The cross helicity (velocity--magnetic-field correlation) effects in the magnetic-field induction and momentum transport in the magnetohydrodynamic (MHD) turbulence are investigated with the aid of the multiple-scale renormalized perturbation expansion analysis. The outline of the theory is presented with reference to the role of the cross-interaction response functions between the velocity and magnetic field. In this formulation, the expressions of the turbulent fluxes: the turbulent electromotive force (EMF) in the mean induction equation and the Reynolds and turbulent Maxwell stresses in the momentum equation are obtained. Related to the expression of EMF, the physical origin of the cross-helicity effect in dynamos, as well as other dynamo effects, is discussed. In order to understand the actual role of the turbulent cross helicity, its transport equations is considered. Several generation mechanisms of cross helicity are discussed with illustrative examples. On the basis of the cross-helicity production mechanisms, its effect in stellar dynamos is discussed. The role of cross helicity in the momentum transport and global flow generation is also argued. Characteristic features of turbulence effects in fast reconnection are reviewed with special emphasis on the role of cross helicity in localizing the effective resistivity. Finally, a remark is addressed on an approach that elucidates the structure generation and sustainment in extremely strong turbulence. An appropriate formulation for the anti-diffusion effect, which acts against the usual diffusion effect, is needed. Turbulence modeling approach based on such an analytical formulation is also argued in comparison with the conventional heuristic modeling. The importance of the self-consistent framework treating the non-linear interaction between the mean field and turbulence is stressed as well., Comment: 95 pages, 37 figures

Turbulence is typically not in equilibrium, i.e. mean quantities such as the mean energy and helicity are typically time-dependent. The effect of non-stationarity on the turbulent hydromagnetic dynamo process is studied here with the use of the two-scale direct-interaction approximation (TSDIA), which allows to explicitly relate the mean turbulent Reynolds and Maxwell stresses and the mean electromotive force (EMF) to the spectral characteristics of turbulence, such as e.g. the mean energy, as well as kinetic and cross-helicity. It is demonstrated, that the non-equilibrium effects can enhance the dynamo process when the magnetohydrodynamic (MHD) turbulence is both helical and cross-helical. This effect is based on the turbulent infinitesimal-impulse cross-response functions, which do not affect turbulent flows in equilibrium. The evolution and sources of the cross-helicity in MHD turbulence is also discussed., Comment: 23 pages, 3 figures

In strongly compressible magnetohydrodynamic turbulence, obliqueness between the large-scale density gradient and magnetic field gives an electromotive force mediated by density variance (intensity of density fluctuation). This effect is named ``magnetoclinicity'', and is expected to play an important role in large-scale magnetic-field generation in astrophysical compressible turbulent flows. Analysis of large-scale instability due to the magnetoclinicity effect shows that the mean magnetic-field perturbation is destabilised at large scales in the vicinity of strong mean density gradient in the presence of density variance., Comment: 8 pages, 2 figures, iTi (interdisciplinary Turbulence initiative) 2021

Plumes in a convective flow are considered to be relevant to the turbulent transport in convection. The effective mass, momentum, and heat transports in the convective turbulence are investigated in the framework of time--space double averaging procedure, where a field quantity is decomposed into three parts: the spatiotemporal mean (spatial average of the time-averaged) field, the dispersion or coherent fluctuation, and the random or incoherent fluctuation. With this framework, turbulent correlations in the mean-field equations are divided into the dispersion/coherent and random/incoherent correlation part. By reckoning the plume as the coherent fluctuation, a transport model for the convective turbulence is constructed with the aid of the non-equilibrium effect, in which the change of turbulence characteristics along the mean stream is taken into account for the modelling of the turbulent transport coefficients. In this work, for the first time, change of turbulence properties along plume motions is incorporated into the expression of the turbulent transport coefficients. This non-equilibrium model is applied to a stellar convective flow. One of the prominent characteristics of a surface cooling-driven convection, the enhanced and localised turbulent mass flux below the surface layer, which cannot be reproduced at all by the usual eddy-diffusivity model with mixing length theory (MLT), is well reproduced by the present model. Our results show that the incorporation of plume motion into turbulent transport model is an important and very relevant extension of mean-field theory beyond the heuristic gradient transport model with MLT., Comment: 18 pages, 8 figures

Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main features, both new and old, as the discovery of bi-directional cascades or the role of helical vortices in the enhancement of large-scale magnetic fields in the dynamo problem. The dynamical contribution in magnetohydrodynamic (MHD) of the cross-correlation between velocity and induction is discussed as well. We consider next how turbulent transport is affected by helical constraints, in particular in the context of magnetic reconnection and fusion plasmas {under one- and two-fluid approximations}. Central issues on how to construct turbulence models for non-reflectionally symmetric helical flows are reviewed, including in the presence of shear, and we finally briefly mention the possible role of helicity in the development of strongly localized quasi-singular structures {at small scale)., Comment: 14 pages, 0 figure 0 table

We present results of Reynolds-averaged turbulence model simulation on the problem of magnetic reconnection. In the model, in addition to the mean density, momentum, magnetic field, and energy equations, the evolution equations of the turbulent cross-helicity $W$, turbulent energy $K$ and its dissipation rate $\varepsilon$ are simultaneously solved to calculate the rate of magnetic reconnection for a Harris-type current sheet. In contrast to previous works based on algebraic modeling, the turbulence timescale is self-determined by the nonlinear evolutions of $K$ and $\varepsilon$, their ratio being a timescale. We compare the reconnection rate produced by our mean-field model to the resistive non-turbulent MHD rate. To test whether different regimes of reconnection are produced, we vary the initial strength of turbulent energy and study the effect on the amount of magnetic flux reconnected in time., Comment: 10 pages, 7 figures

Mean-field dynamo equations are addressed with the aid of the path-integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener integral over all the trajectories of fluid particle. The form of the equations is just the same as the conventional mean-field equations, but the present equations are derived with the velocity-field realization affected by the magnetic-field force. In this sense, the present ones are nonlinear dynamo equations., Comment: 6 pages, 0 figures; submitted to Journal of Plasma Physics

The plasmoid instability may lead to fast magnetic reconnection through long current sheets(CS). It is well known that large-Reynolds-number plasmas easily become turbulent. We address the question whether turbulence enhances the energy conversion rate of plasmoid-unstable current sheets. We carry out appropriate numerical MHD simulations, but resolving simultaneously the relevant large-scale (mean-) fields and the corresponding small-scale, turbulent, quantities by means of direct numerical simulations (DNS) is not possible. Hence we investigate the influence of small scale turbulence on large scale MHD processes by utilizing a subgrid-scale (SGS) turbulence model. We verify the applicability of our SGS model and then use it to investigate the influence of turbulence on the plasmoid instability. We start the simulations with Harris-type and force-free CS equilibria in the presence of a finite guide field in the direction perpendicular to the reconnection plane. We use the DNS results to investigate the growth of the plasmoid instability. The energy and cross-helicity due to turbulence are obtained in terms of the mean fields by a Gaussian filtering formulation from a Reynolds averaging turbulence model. The influence of turbulence on the reconnection rate of the plasmoid instability is investigated. To verify the predictions of the SGS-model, the electromotive force (${\bf\cal{E}}$) is calculated for the coarse data obtained by filtering and compared to the SGS-model. The symmetry breakage with respect to the guide field direction causes a turbulent helicity which reduces the influence of the apparent turbulent resistivity. The reduced reconnection rate of guide field plasmoid reconnection is attributed to a balancing between the different physical effects related to turbulence., Comment: 10 pages, 13 figures

Transport equation of the dissipation rate of turbulent helicity is derived with the aid of a statistical analytical closure theory of inhomogeneous turbulence. It is shown that an assumption on the helicity scaling with an algebraic relationship between the helicity and its dissipation rate leads to the transport equation of the turbulent helicity dissipation rate without resorting to a heuristic modeling., Comment: 6 pages, 0 figures, Progress in Turbulence VI

A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous mean flow effect on turbulence, it is shown that turbulent cross helicity (velocity--magnetic-field correlation) should enter the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. The inclusion of the cross-helicity effect makes the present model different from the current $\alpha$--$\Omega$-type models mainly in two points. First, in addition to the usual $\alpha$ (helicity effect) and $\beta$ (turbulent magnetic diffusivity), we consider the $\gamma$ coefficient (cross-helicity effect) as a key ingredient of the dynamo process. Second, unlike the $\alpha$ and $\beta$ coefficients, which are often treated as an adjustable parameter in the current studies, the spatiotemporal evolution of $\gamma$ coefficient is solved simultaneously with the mean magnetic-field equations. The basic scenario is as follows: In the presence of turbulent cross helicity, the toroidal field is induced by the toroidal rotation in mediation by the turbulent cross helicity. The $\alpha$ effect generates the poloidal field from the toroidal one. This poloidal field produces a turbulent cross helicity whose sign is opposite to the original one. Then a cycle of reversal completes. Eigenvalue analyses of the simplest possible present model give a butterfly diagram, which confirms the above scenario as well as the equator-ward migrations, the phase relationship between the cross helicity and magnetic fields, etc. These results suggest that the oscillation of the turbulent cross helicity is a key for the activity cycle. The reversal of the turbulent cross helicity is not the result of the magnetic-field reversal, but the cause of the latter. This new model is expected to open up the possibility of the mean-field or turbulence closure dynamo approaches., Comment: 15 pages, 6 figures

The effect of kinetic helicity (velocity--vorticity correlation) on turbulent momentum transport is investigated. The turbulent kinetic helicity (pseudoscalar) enters the Reynolds stress (mirrorsymmetric tensor) expression in the form of a helicity gradient as the coupling coefficient for the mean vorticity and/or the angular velocity (axial vector), which suggests the possibility of mean-flow generation in the presence of inhomogeneous helicity. This inhomogeneous helicity effect, which was previously confirmed at the level of a turbulence- or closure-model simulation, is examined with the aid of direct numerical simulations of rotating turbulence with non-uniform helicity sustained by an external forcing. The numerical simulations show that the spatial distribution of the Reynolds stress is in agreement with the helicity-related term coupled with the angular velocity, and that a large-scale flow is generated in the direction of angular velocity. Such a large-scale flow is not induced in the case of homogeneous turbulent helicity. This result confirms the validity of the inhomogeneous helicity effect in large-scale flow generation and suggests that a vortex dynamo is possible even in incompressible turbulence where there is no baroclinicity effect., Comment: 15pages, 11 figures

Magnetic reconnection requires, at least locally, a non-ideal plasma response. In collisionless space and astrophysical plasmas, turbulence could permit this instead of the too rare binary collisions. We investigated the influence of turbulence on the reconnection rate in the framework of a single fluid compressible MHD approach. The goal is to find out, whether unresolved, sub-grid for MHD simulations, turbulence can enhance the reconnection process in high Reynolds number astrophysical plasma. We solve, simultaneously with the grid-scale MHD equations, evolution equations for the sub-grid turbulent energy and cross helicity according to Yokoi's model (Yokoi (2013)) where turbulence is self-generated and -sustained through the inhomogeneities of the mean fields. Simulations of Harris and force free sheets confirm the results of Higashimori et al. (2013) and new results are obtained about the dependence on resistivity for large Reynolds number as well as guide field effects. The amount of energy transferred from large to the small scales is enhanced in case of fast turbulent reconnection and energy spectra are used to interpret the obtained regime of reconnection controlled by the turbulence timescale $\tau_t$. The overall process is even faster for larger Reynolds numbers controlled by the background molecular resistivity $\eta$, as long as the initial level of turbulence is not too large. This implies that turbulence plays an important role on fast reconnection at situation of large Reynolds number while the amplitude of turbulence can still be small., Comment: 11 pages, 17 figures, will be submitted to Physics of Plasmas (PoP)

Through the enhancement of transport, turbulence is expected to contribute to the fast reconnection. However the effects of turbulence are not so straightforward. In addition to the enhancement of transport, turbulence under some environment shows effects that suppress the transport. In the presence of turbulent cross helicity, such a dynamic balance between the transport enhancement and suppression occurs. As this result of dynamic balance, the region of effective enhanced magnetic diffusivity is confined to a narrow region, leading to the fast reconnection. In order to confirm this idea, a self-consistent turbulence model for the magnetic reconnection is proposed. With the aid of numerical simulations where turbulence effects are incorporated in a consistent manner through the turbulence model, the dynamic balance in the turbulence magnetic reconnection is confirmed., Comment: 18 pages, 7 figures

A maintenance mechanism of an approximately linear velocity profile of the Venus zonal flow or superrotation is explored, with the aid of a Reynolds-averaged turbulence modeling approach. The basic framework is similar to that of Gierasch (1975) in the sense that the mechanism is examined under a given meridional circulation. The profile mimicking the observations of the flow is initially assumed, and its maintenance mechanism in the presence of turbulence effects is investigated from a viewpoint of the suppression of energy cascade. In the present work, the turbulent viscosity is regarded as an indicator of the intensity of the cascade. A novelty of this formalism is the use of the isotropic turbulent viscosity based on a nonlocal time scale linked to a large-scale flow structure. The mechanism is first discussed qualitatively. On the basis of these discussions, the two-dimensional numerical simulation of the proposed model is performed, with an initially assumed superrotation, and the fast zonal flow is shown to be maintained, compared with the turbulent viscosity lacking the nonlocal time scale. The relationship of the present model with the current general-circulation-model simulation is discussed in light of a crucial role of the vertical viscosity., Comment: 12 figures, Geophysical and Astrophysical Fluid Dynamics, Vol. 107, Issue 4 (2013), http://www.tandfonline.com/doi/full/10.1080/03091929.2013.803546

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. Unlike the case in the helicity or $\alpha$ effect, where ${\bf{J}}$ is aligned with ${\bf{B}}$ in the turbulent electromotive force, we in general have a finite mean-field Lorentz force ${\bf{J}} \times {\bf{B}}$ 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., Comment: Open Access: http://www.tandfonline.com/doi/abs/10.1080/03091929.2012.754022

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., Comment: 4 pages, 4 figures, accepted by PRL

In the presence of large-scale vortical motions and/or magnetic-field strains, the turbulent cross helicity (velocity--magnetic-field correlation in fluctuations) may contribute to the turbulent electromotive force and the Reynolds stress. These effects of cross helicity are considered to balance the primary effects of turbulence such as the turbulent magnetic diffusivity in magnetic-field evolution and the eddy viscosity in the momentum transport. The cross-helicity effects may suppress the enhanced transports due to turbulence. Physical interpretation of the effects is presented with special emphasis on the difference between the cross-helicity effect and the usual $\alpha$ or helicity effect in the dynamo action. The relative importance of the cross-helicity effect in dynamo action is validated with the aid of a direct numerical simulation (DNS) of the Kolmogorov flow with an imposed magnetic field. Several mechanisms that provide turbulence with the cross helicity are also discussed., Comment: 10 pages, 6 figures, Journal of Physics Conference Series: 13th European Turbulence Conference (ETC13)

Roles of turbulence in the context of magnetic reconnection are investigated with special emphasis on the mutual interaction between flow (large-scale inhomogeneous structure) and turbulence. In order to evaluate the effective transport due to turbulence, in addition to the {\it intensity} information of turbulence represented by the turbulent energy, the {\it structure} information represented by pseudoscalar statistical quantities (helicities) is important. On the basis of the evolution equation, mechanisms that provide turbulence with cross helicity are presented. Magnetic-flux freezing in highly turbulent media is considered with special emphasis on the spatial distribution of the turbulent cross helicity. The cross-helicity effects in the context of magnetic reconnection are also investigated. It is shown that the large-scale flow and magnetic-field configurations favorable for the cross-helicity generation is compatible with the fast reconnection. In this sense, turbulence and large-scale structures promote magnetic reconnection mediated by the turbulent cross helicity., Comment: 15 pages, 10 figures

It has been recognized that the turbulent cross helicity (correlation between the velocity and magnetic-field fluctuations) can play an important role in several magnetohydrodynamic (MHD) plasma phenomena such as the global magnetic-field generation, turbulence suppression, etc. Despite its relevance to the cross-helicity evolution, little attention has been paid to the dissipation rate of the turbulent cross helicity, $\epsilon_W$. In this paper, we consider the model expression for the dissipation rate of the turbulent cross helicity. In addition to the algebraic model, an evolution equation of $\epsilon_W$ is proposed on the basis of the statistical analytical theory of inhomogeneous turbulence. A turbulence model with the modeling of $\epsilon_W$ is applied to the solar-wind turbulence. Numerical results on the large-scale evolution of the cross helicity is compared with the satellite observations. It is shown that, as far as the solar-wind application is concerned, the simplest possible algebraic model for $\epsilon_W$ is sufficient for elucidating the large-scale spatial evolution of the solar-wind turbulence. Dependence of the cross-helicity evolution on the large-scale velocity structures such as velocity shear and flow expansion is also discussed., Comment: 37 pages, 4 figures

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.