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Based on a mean-field theory of a non-rotating turbulent convection (Phys. Rev. E {\bf 66}, 066305, 2002), we perform mean-field simulations (MFS) of sheared convection which takes into account an effect of modification of the turbulent heat flux by the non-uniform large-scale motions. As the result of this effect, there is an excitation of large-scale convective-shear instability, which causes the formation of large-scale semi-organized structures in the form of rolls. The life-times and spatial scales of these structures are much larger compared to the turbulent scales. By means of MFS performed for stress-free and no-slip vertical boundary conditions, we determine the spatial and temporal characteristics of these structures. Our study demonstrates that the modification of the turbulent heat flux by non-uniform flows leads to a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale rolls. During the nonlinear stage of the convective-shear instability, there is a transition from the two-layer vertical structure with two roles in the vertical direction before the system reaches steady-state to the one-layer vertical structure with one role after the system reaches steady-state. This effect is observed for all effective Rayleigh numbers. We find that inside the convective rolls, the spatial distribution of the mean potential temperature includes regions with a positive vertical gradient of the potential temperature caused by the mean heat flux of the convective rolls. This study might be useful for understanding of the origin of large-scale rolls observed in atmospheric convective boundary layers as well as in numerical simulations and laboratory experiments., Comment: 13 pages, 17 figures, revtex4-2, revised. arXiv admin note: text overlap with arXiv:2209.07477

The atmospheric convective boundary layer (CBL) consists of three basic parts: (i) the surface layer unstably stratified and dominated by small-scale turbulence of very complex nature; (ii) the CBL core dominated by the energy-, momentum- and mass-transport of semi-organized structures (large-scale circulations), with a small contribution from small-scale turbulence produced by local structural shears; and (iii) turbulent entrainment layer at the upper boundary, characterized by essentially stable stratification with negative (downward) turbulent flux of potential temperature. The energy- and flux budget (EFB) theory developed previously for atmospheric stably-stratified turbulence and the surface layer in atmospheric convective turbulence is extended to the CBL core using budget equations for turbulent energies and turbulent fluxes of buoyancy and momentum. For the CBL core, we determine global turbulent characteristics (averaged over the entire volume of the semi-organized structure) as well as kinetic and thermal energies of the semi-organized structures as the functions of the aspect ratio of the semi-organized structure, the scale separation parameter between the vertical size of the structures and the integral scale of turbulence and the degree of thermal anisotropy characterized the form of plumes. The obtained theoretical relationships are potentially useful in modeling applications in the atmospheric convective boundary-layer, and analysis of laboratory and field experiments, direct numerical simulations and large-eddy simulations of convective turbulence with large-scale semi-organized structures., Comment: 18 pages, revtex 4-2, revised

Our theoretical and numerical analysis have suggested that for low-mass main sequences stars (of the spectral classes from M5 to G0) rotating much faster than the Sun, the generated large-scale magnetic field is caused by the mean-field $\alpha^2\Omega$ dynamo, whereby the $\alpha^2$ dynamo is modified by a weak differential rotation. Even for a weak differential rotation, the behaviour of the magnetic activity is changed drastically from aperiodic regime to non-linear oscillations and appearance of a chaotic behaviour with increase of the differential rotation. Periods of the magnetic cycles decrease with increase of the differential rotation, and they vary from tens to thousand years. This long-term behaviour of the magnetic cycles may be related to the characteristic time of the evolution of the magnetic helicity density of the small-scale field. The performed analysis is based on the mean-field simulations (MFS) of the $\alpha^2\Omega$ and $\alpha^2$ dynamos and a developed non-linear theory of $\alpha^2$ dynamo. The applied MFS model was calibrated using turbulent parameters typical for the solar convective zone., Comment: 14 pages, final version

Solar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, nonlinear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence) for (i) a forced turbulence, (ii) a shear-produced turbulence and (iii) a convective turbulence. As the result of this effect, a nonlinear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field $\alpha\Omega$, $\alpha^2$ and $\alpha^2\Omega$ dynamo instabilities are always saturated by the strong large-scale magnetic field., Comment: 12 pages, revised paper

We investigate experimentally phenomenon of turbulent thermal diffusion of micron-size solid particles in an inhomogeneous convective turbulence forced by one vertically-oriented oscillating grid in an air flow. This effect causes formation of large-scale inhomogeneities in particle spatial distributions in a temperature-stratified turbulence. We perform detailed comparisons of the experimental results with those obtained in our previous experiments with an inhomogeneous and anisotropic stably stratified turbulence produced by a one oscillating grid in the air flow. Since the buoyancy increases the turbulent kinetic energy for convective turbulence and decreases it for stably stratified turbulence, the measured turbulent velocities for convective turbulence are larger than those for stably stratified turbulence. This tendency is also seen in the measured vertical integral turbulent length scales. Measurements of temperature and particle number density spatial distributions show that particles are accumulated in the vicinity of the minimum of the mean temperature due to phenomenon of turbulent thermal diffusion. This effect is observed in both, convective and stably stratified turbulence, where we find the effective turbulent thermal diffusion coefficient for micron-size particles. The obtained experimental results are in agreement with theoretical predictions., Comment: 13 pages, 11 figures, revtex4-2, revised. arXiv admin note: text overlap with arXiv:2202.13348

It has been previously shown (Phys. Rev. E 66, 066305, 2002) that a non-rotating turbulent convection with nonuniform large-scale flows contributes to the turbulent heat flux. As a result, the turbulent heat flux depends explicitly not only on the gradients of the large-scale temperature, but it also depends on the gradients of the large-scale velocity. This is because the nonuniform large-scale flows produce anisotropic velocity fluctuations which modify the turbulent heat flux. This effect causes an excitation of a convective-wind instability and formation of large-scale semi-organised coherent structures (large-scale convective cells). We perform mean-field numerical simulations of shear-free convection which take into account the modification of the turbulent heat flux by nonuniform large-scale flows. The redistribution of the turbulent heat flux by the nonuniform large-scale motions in turbulent convection plays a crucial role in the formation of the large-scale semi-organised coherent structures. This effect results in a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale convective cells. The convective-wind instability is excited when the scale separation ratio between the height of the convective layer and the integral turbulence scale is large. The level of the mean kinetic energy at saturation increases with the scale separation ratio. Inside the large-scale convective cells, there are local regions with the positive vertical gradient of the potential temperature which implies that these regions are stably stratified., Comment: 13 pages, 14 figures, revtex4-2

Combined action of helical motions of plasma (the $\alpha$ effect) and non-uniform (differential) rotation is a key dynamo mechanism of solar and galactic large-scale magnetic fields. Dynamics of magnetic helicity of small-scale fields is a crucial mechanism in a nonlinear dynamo saturation where turbulent magnetic helicity fluxes allow to avoid catastrophic quenching of the $\alpha$ effect. The convective zone of the Sun and solar-like stars as well as galactic discs are the source for production of turbulent magnetic helicity fluxes. In the framework of the mean-field approach and the spectral $\tau$ approximation, we derive turbulent magnetic helicity fluxes using the Coulomb gauge in a density-stratified turbulence. The turbulent magnetic helicity fluxes include non-gradient and gradient contributions. The non-gradient magnetic helicity flux is proportional to a nonlinear effective velocity (which vanishes in the absence of the density stratification) multiplied by small-scale magnetic helicity, while the gradient contributions describe turbulent magnetic diffusion of the small-scale magnetic helicity. In addition, the turbulent magnetic helicity fluxes contain source terms proportional to the kinetic $\alpha$ effect or its gradients, and also contributions caused by the large-scale shear (solar differential rotation). We have demonstrated that the turbulent magnetic helicity fluxes due to the kinetic $\alpha$ effect and its radial derivative in combination with the nonlinear magnetic diffusion of the small-scale magnetic helicity are dominant in the solar convective zone., Comment: 13 pages, 9 figures, revised

We study experimentally turbulent thermal diffusion of small particles in inhomogeneous and anisotropic stably stratified turbulence produced by one oscillating grid in the air flow. The velocity fields have been measured using a Particle Image Velocimetry (PIV). We have determined various turbulence characteristics: the mean and turbulent velocities, two-point correlation functions of the velocity field and an integral scale of turbulence from the measured velocity fields. The temperature field have been measured with a temperature probe equipped with 12 E thermocouples. Spatial distributions of micron size particles have been determined by a PIV system using the effect of the Mie light scattering by particles in the flow. The experiments have demonstrated that particles are accumulated at the minimum of mean fluid temperature due to phenomenon of turbulent thermal diffusion. Using measured spatial distributions of particles and temperature fields, we have determined the effective turbulent thermal diffusion coefficient of particles in inhomogeneous temperature stratified turbulence. This experimental study has clearly detected phenomenon of turbulent thermal diffusion in inhomogeneous turbulence., Comment: 12 pages, 18 figures, REVTEX4-2, revised

We perform experimental study of turbulent transport of nanoparticles in convective turbulence with the Rayleigh number $\sim 10^8$ in the air flow. We measure temperature field in many locations by a temperature probe equipped with 11 E-thermocouples. Nanoparticles of the size $\sim 70$ nm in diameter are produced by Advanced Electrospray Aerosol Generator. To determine the number density of nanoparticles, we use Condensation Particle Counter. We demonstrate that the joint action of turbulent effects (which are important in the core flow) and molecular effects (which are essential near the boundaries of the chamber) results in an effective accumulation of nanoparticles at the cold wall of the chamber. The turbulent effects are characterised by turbulent diffusion and turbulent thermal diffusion of nanoparticles, while the molecular effects are described by the Brownian diffusion and thermophoresis, as well as the adhesion of nanoparticles at the cold wall of the chamber. In different experiments in convective turbulence in a chamber with the temperature difference $\Delta T$ between the bottom and top walls varying between $\Delta T= 29$ K to $\Delta T= 61$ K, we find that the mean number density of nanoparticles decreases exponentially in time. For instance, the characteristic decay time of the mean number density of nanoparticles varies from 12.8 min for $\Delta T= 61$ K to 24 min for $\Delta T= 29$ K. For better understanding of experimental results, we perform one-dimensional mean-field numerical simulations of the evolution of the mean number density of nanoparticles for conditions pertinent to the laboratory experiments. The obtained numerical results are in a good agreement with the experimental results., Comment: 10 pages, 7 figures, REVTEX4-2, revised

The energy- and flux budget (EFB) turbulence closure theory for the atmospheric surface layers in convective and stably stratified turbulence has been developed using budget equations for turbulent energies and fluxes in the Boussinesq approximation. In the lower part of the surface layer in the atmospheric convective boundary layer (CBL), the rate of turbulence production of the turbulent kinetic energy (TKE) caused by the mean-flow surface shear and the shear of self-organised coherent structures is much larger than that caused by the buoyancy, which results in three-dimensional turbulence of very complex nature. In the upper part of the surface layer, the rate of turbulence production of TKE due to the shear is much smaller than that caused by the buoyancy, which causes unusual strongly anisotropic buoyancy-driven turbulence. Considering the applications of the obtained results to the atmospheric convective and stably stratified boundary-layer turbulence, the theoretical relationships potentially useful in modelling applications have been derived. In particular, the developed theory for the surface layers in turbulent convection and stably stratified turbulence allows us to determine the vertical profiles for all turbulent characteristics, including TKE, the intensity of turbulent potential temperature fluctuations, the vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature), the integral turbulence scale, the turbulence anisotropy, the turbulent Prandtl number and the flux Richardson number., Comment: 15 pages, revtex4-2, revised. arXiv admin note: text overlap with arXiv:2104.00500

A turbulent transport of radiation in the solar convective zone is investigated. The mean-field equation for the irradiation intensity is derived. It is shown that due to the turbulent effects, the effective penetration length of radiation can be increased in several times in comparison with the mean penetration length of radiation (defined as an inverse mean absorption coefficient). Using the model of the solar convective zone based on the mixing length theory, where the mean penetration length of radiation is usually much smaller than the turbulent correlation length, it is demonstrated that the ratio of the effective penetration length to the mean penetration length of radiation increases in 2.5 times in the vicinity of the solar surface. The main reason are the compressibility effects that become important in the vicinity of the solar surface where temperature and density fluctuations increase towards the solar surface, enhancing fluctuations of the radiation absorption coefficient and increasing the effective penetration length of radiation., Comment: 10 pages, 7 figures, mn2e class, revised

The energy and flux budget (EFB) closure theory for a passive scalar (non-buoyant and non-inertial particles or gaseous admixtures) is developed for stably stratified turbulence. The physical background of the EFB turbulence closures is based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, as well as the turbulent flux of particles. The EFB turbulence closure is designed for stratified geophysical flows from neutral to very stable stratification and it implies that turbulence is maintained by the velocity shear at any stratification. In a steady-state, expressions for the turbulent flux of passive scalar and the anisotropic non-symmetric turbulent diffusion tensor are derived, and universal flux Richardson number dependencies of the components of this tensor are obtained. The diagonal component in the vertical direction of the turbulent diffusion tensor is suppressed by strong stratification, while the diagonal components in the horizontal directions are not suppressed, and they are dominant in comparison with the other components of turbulent diffusion tensor. This implies that any initially created strongly inhomogeneous particle cloud is evolved into a thin pancake in horizontal plane with very slow increase of its thickness in the vertical direction. The turbulent Schmidt number increases linearly with the gradient Richardson number. Considering the applications of these results to the atmospheric boundary-layer turbulence, the theoretical relationships are derived which allow to determine the turbulent diffusion tensor as a function of the vertical coordinate measured in the units of the local Obukhov length scale. The obtained relations are potentially useful in modelling applications of particle dispersion in the atmospheric boundary-layer turbulence and free atmosphere turbulence., Comment: 18 pages, revtex4-2.cls, revised paper

Compressibility effects in a turbulent transport of temperature field are investigated applying the quasi-linear approach for small P\'eclet numbers and the spectral $\tau$ approach for large P\'eclet numbers. Compressibility of a fluid flow reduces the turbulent diffusivity of the mean temperature field similarly to that for particle number density and magnetic field. However, expressions for the turbulent diffusion coefficient for the mean temperature field in a compressible turbulence are different from those for the mean particle number density and the mean magnetic field. Combined effect of compressibility and inhomogeneity of turbulence causes an increase of the mean temperature in the regions with more intense velocity fluctuations due to a turbulent pumping. Formally, this effect is similar to a phenomenon of compressible turbophoresis found previously [J. Plasma Phys. {\bf 84}, 735840502 (2018)] for non-inertial particles or gaseous admixtures. Gradient of the mean fluid pressure results in an additional turbulent pumping of the mean temperature field. The latter effect is similar to turbulent barodiffusion of particles and gaseous admixtures. Compressibility of a fluid flow also causes a turbulent cooling of the surrounding fluid due to an additional sink term in the equation for the mean temperature field. There is no analog of this effect for particles., Comment: 14 pages, revised, revtex4-2.cls

The tilt angle, current helicity and twist of solar magnetic fields can be observed in solar active regions. We carried out estimates of these parameters by two ways. Firstly, we consider the model of turbulent convective cells (super-granules) which have a loop floating structure towards the surface of the Sun. Their helical properties are attained during the rising process in the rotating stratified convective zone. The other estimate is obtained from a simple mean-field dynamo model that accounts magnetic helicity conservation. The both values are shown to be capable to give important contributions to the observable tilt, helicity and twist., Comment: 16 pages, no figures; to appear in Geomagnetism and Aeronomy, in press

A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. A mechanism of formation of the mean tilt is related to the effect of Coriolis force on meso-scale motions of super-granular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the solar differential rotation affects the mean tilt which can explain deviations from the Joy's law for the sunspot bipolar regions at high latitudes. The obtained theoretical results and performed numerical simulations based on the nonlinear mean-field dynamo theory which takes into account conservation of the total magnetic helicity and the budget equation for the evolution of the Wolf number density, are in agreement with observational data of the mean tilt of sunspot bipolar regions over individual solar cycles 15 - 24., Comment: 12 pages, 4 figures, mn2e.cls , revised, final version

We have advanced the energy and flux budget (EFB) turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGW) and the shear-free stably stratified turbulence. This theory is based on the budget equation for the total (kinetic plus potential) energy of IGW, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level, propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate that due to the nonlinear effects more intensive waves produce more strong turbulence, and this, in turns, results in strong damping of IGW. As a result, the penetration length of more intensive waves is shorter than that of less intensive IGW. The anisotropy of the turbulence produced by less intensive IGW is stronger than that caused by more intensive waves. The low amplitude IGW produce turbulence consisting up to 90 \% of turbulent potential energy. This resembles the properties of the observed high altitude tropospheric strongly anisotropic (nearly two-dimensional) turbulence., Comment: 13 pages, 11 figures, REVTEX4-1, revised

Convection over a wavy heated bottom wall in the air flow has been studied in experiments with the Rayleigh number $\sim 10^8$. It is shown that the mean temperature gradient in the flow core inside a large-scale circulation is directed upward, that corresponds to the stably stratified flow. In the experiments with a wavy heated bottom wall, we detect large-scale standing internal gravity waves excited in the regions with the stably stratified flow. The wavelength and the period of these waves are much larger than the turbulent spatial and time scales, respectively. In particular, the frequencies of the observed large-scale waves vary from 0.006 Hz to 0.07 Hz, while the turbulent time in the integral scale is about 0.5 s. The measured spectra of these waves contains several localized maxima, that implies an existence of waveguide resonators for the large-scale standing internal gravity waves. For comparisons, experiments with convection over a smooth plane bottom wall at the same mean temperature difference between bottom and upper walls have been also conducted. In these experiments various locations with a stably stratified flow are also found and the large-scale standing internal gravity waves are observed in these regions., Comment: 12 pages, 17 figures, REVTEX4-1, revised paper

We present a physical mechanism of formation of tilt angles of sunspots due to the process of formation of active regions below the solar photosphere. The contribution of Coriolis force factors on large-scale flows of super-granular convection in turbulent media has been investigated in details. On the basis of earlier works by Kleeorin et al. (2016) and Safiullin et al. (2018) we give physical estimates of orders of magnitude of the effect and estimate the tilt angles near the solar equator, in the "Royal" zone of solar activity. The above model is based on the balance of the small-scale and large scale magnetic helicities and describes in details the sunspot formation process over the last five solar cycles (since 1964). We adopt this model for a wider class of manifestations of solar activity. We present latitudinal dependence of the mean tilt on these five solar cycles and time-latitudinal diagrams over a limited range of latitudes and phases of the solar cycle., Comment: manuscript in Russian, total 17 pages, 4 figures (with Abstract and Figures, Astrophysics[Armenia], accepted for publication in 2019)

The formation of sunspots and starspots is not yet fully understood and is therefore one of the major open problems in solar and stellar physics. Magnetic flux concentrations can be produced by the negative effective magnetic pressure instability (NEMPI). This instability is strongly suppressed by rotation. However, the presence of an outer coronal envelope was previously found to strengthen the flux concentrations and make them more prominent. It also allows for the formation of bipolar regions (BRs). We want to know whether the presence of an outer coronal envelope also changes the excitation conditions and the rotational dependence of NEMPI. We use direct numerical simulations and mean-field simulations. We adopt a simple two-layer model of turbulence that mimics the jump between the convective turbulent and coronal layers below and above the surface of a star, respectively. The computational domain is Cartesian and located at a certain latitude of a rotating sphere. We investigate the effects of rotation on NEMPI by changing the Coriolis number, the latitude, and the box resolution. Rotation has a strong impact on the process of BR formation. Even rather slow rotation is found to suppress their formation. However, increasing the imposed magnetic field strength also makes the structures stronger and alleviates the rotational suppression somewhat. The presence of a coronal layer itself does not significantly alleviate the effects of rotational suppression., Comment: 18 pages, 24 figures, submitted to A&A

A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on a combined effect of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral tau approach which is valid for large Reynolds and Peclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation., Comment: 13 pages, 5 figures, jpp.cls, revised. arXiv admin note: text overlap with arXiv:astro-ph/0602544

We discuss a mean-field theory of generation of large-scale vorticity in a rotating density stratified developed turbulence with inhomogeneous kinetic helicity. We show that the large-scale nonuniform flow is produced due to ether a combined action of a density stratified rotating turbulence and uniform kinetic helicity or a combined effect of a rotating incompressible turbulence and inhomogeneous kinetic helicity. These effects result in the formation of a large-scale shear, and in turn its interaction with the small-scale turbulence causes an excitation of the large-scale instability (known as a vorticity dynamo) due to a combined effect of the large-scale shear and Reynolds stress-induced generation of the mean vorticity. The latter is due to the effect of large-scale shear on the Reynolds stress. A fast rotation suppresses this large-scale instability., Comment: 13 pages, revised, jpp.cls

We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $\tau$-approach. We find that compressibility decreases the $\alpha$ effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large P\'eclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases it for small Rm. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large P\'eclet numbers. It can be interpreted as compressible turbophoresis of noninertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity., Comment: 26 pages, 1 figure, final paper accepted for publication to JPP, jpp.cls

We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the alpha effect, where the equation for the dynamic nonlinearity is derived from the conservation law for the magnetic helicity. The budget equation for the evolution of the Wolf number is based on a formation mechanism of sunspots related to the negative effective magnetic pressure instability. This instability redistributes the magnetic flux produced by the mean-field dynamo. To predict solar activity on the time scale of one month we use a method based on a combination of the numerical solution of the nonlinear mean-field dynamo equations and the artificial neural network. A comparison of the results of the prediction of the solar activity with the observed Wolf numbers demonstrates a good agreement between the forecast and observations., Comment: 15 pages, 6 figures, jpp.cls, final version

It is known that unconfined dust explosions consist of a relatively weak primary (turbulent) deflagrations followed by a devastating secondary explosion. The secondary explosion may propagate with a speed of up to 1000 m/s producing overpressures of over 8-10 atm. Since detonation is the only established theory that allows a rapid burning producing a high pressure that can be sustained in open areas, the generally accepted view was that the mechanism explaining the high rate of combustion in dust explosions is deflagration to detonation transition. In the present work we propose a theoretical substantiation of the alternative propagation mechanism explaining origin of the secondary explosion producing the high speeds of combustion and high overpressures in unconfined dust explosions. We show that clustering of dust particles in a turbulent flow gives rise to a significant increase of the thermal radiation absorption length ahead of the advancing flame front. This effect ensures that clusters of dust particles are exposed to and heated by the radiation from hot combustion products of large gaseous explosions sufficiently long time to become multi-point ignition kernels in a large volume ahead of the advancing flame front. The ignition times of fuel-air mixture by the radiatively heated clusters of particles is considerably reduced compared to the ignition time by the isolated particle. The radiation-induced multi-point ignitions of a large volume of fuel-air ahead of the primary flame efficiently increase the total flame area, giving rise to the secondary explosion, which results in high rates of combustion and overpressures required to account for the observed level of overpressures and damages in unconfined dust explosions, such as e.g. the 2005 Buncefield explosion and several vapor cloud explosions of severity similar to that of the Buncefield incident., Comment: 21 pages, 7 Figures, revised

We develop a theory of three-dimensional slow Rossby waves in rotating spherical density stratified convection. The Rossby waves with frequencies which are much smaller than the rotating frequency, are excited by a non-axisymmetric instability from the equilibrium based on the developed convection. These waves interact with the inertial waves and the density stratified convection. The density stratification is taken into account using the anelastic approximation for very low-Mach-number flows. We study long-term planetary Rossby waves with periods which are larger than two years. We suggest that these waves are related to the Southern Oscillation and El Ni\~{n}o. The El Ni\~{n}o is an irregularly periodical variation in winds and sea surface temperatures over the tropical Pacific Ocean, while the Southern Oscillation is an oscillation in surface air pressure between the tropical eastern and the western Pacific Ocean. The strength of the Southern Oscillation is characterised by the Southern Oscillation Index (SOI). The developed theory is applied for the interpretation of the observed periods of the SOI. This study demonstrates a good agreement between the theoretical predictions and the observations., Comment: 7 pages, 4 figures, REVTEX4-1, revised

The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (\emph{chiral magnetic effect}). We present a self-consistent treatment of the \emph{chiral MHD equations}, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfv\'{e}n wave for incompressible flows, increases the frequencies of the Alfv\'{e}n wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark--gluon plasma., Comment: 23 pages, 4 figures

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously (Phys. Rev. E {\bf 90}, 053001, 2014) is generalized for large yet finite Reynolds numbers, and the dependence of turbulent diffusion coefficient versus two parameters, the Reynolds number and Damk\"ohler number (which characterizes a ratio of turbulent and reaction time scales) is obtained. Three-dimensional direct numerical simulations (DNS) of a finite thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in a good agreement with the developed theory., Comment: 8 pages, 6 figures, REVTEX4-1, revised

It is known that unconfined dust explosions typically starts off with a relatively weak primary flame followed by a severe secondary explosion. We show that clustering of dust particles in a temperature stratified turbulent flow ahead of the primary flame may give rise to a significant increase in the radiation penetration length. These particle clusters, even far ahead of the flame, are sufficiently exposed and heated by the radiation from the flame to become ignition kernels capable to ignite a large volume of fuel-air mixtures. This efficiently increases the total flame surface area and the effective combustion speed, defined as the rate of reactant consumption of a given volume. We show that this mechanism explains the high rate of combustion and overpressures required to account for the observed level of damage in unconfined dust explosions, e.g., at the 2005 Buncefield vapor-cloud explosion. The effect of the strong increase of radiation transparency due to turbulent clustering of particles goes beyond the state-of-the-art of the application to dust explosions and has many implications in atmospheric physics and astrophysics., Comment: 5 pages, REVTEX4-1, revised

Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a non-diffusive turbulent flux of particles in the direction of the turbulent heat flux. This non-diffusive turbulent flux of particles is proportional to the product of the mean particle number density and the effective velocity of inertial particles. The theory of this effect has been previously developed only for small temperature gradients and small Stokes numbers (Phys. Rev. Lett. {\bf 76}, 224, 1996). In this study a generalized theory of turbulent thermal diffusion for arbitrary temperature gradients and Stokes numbers has been developed. The laboratory experiments in the oscillating grid turbulence and in the multi-fan produced turbulence have been performed to validate the theory of turbulent thermal diffusion in strongly stratified turbulent flows. It has been shown that the ratio of the effective velocity of inertial particles to the characteristic vertical turbulent velocity for large Reynolds numbers is less than 1. The effective velocity of inertial particles as well as the effective coefficient of turbulent thermal diffusion increase with Stokes numbers reaching the maximum at small Stokes numbers and decreases for larger Stokes numbers. The effective coefficient of turbulent thermal diffusion also decreases with the mean temperature gradient. It has been demonstrated that the developed theory is in a good agreement with the results of the laboratory experiments., Comment: 10 pages, 6 figures, REVTEX4-1

We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution of Wolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behavior of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 years ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 % correlation over all intervals of observation (about 270 years). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependencies are in good agreement with observations., Comment: 9 pages, 13 figures, final revised paper for MNRAS

(abridged) Context: The mechanisms that cause the formation of sunspots are still unclear. Aims: We study the self-organisation of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods: We perform simulations of magnetoconvection in Cartesian domains that are $8.5$-$24$ Mm deep and $34$-$96$ Mm wide. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow. Results: We find that super-equipartition magnetic flux concentrations are formed near the surface with domain depths of $12.5$ and $24$ Mm. The size of the concentrations increases as the box size increases and the largest structures ($20$ Mm horizontally) are obtained in the 24 Mm deep models. The field strength in the concentrations is in the range of $3$-$5$ kG. The concentrations grow approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in the majority of the domain, which is unfavourable for the negative effective magnetic pressure instability (NEMPI). Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions: The linear growth of large-scale flux concentrations implies that their dominant formation process is tangling of the large-scale field rather than an instability. One plausible mechanism explaining both the linear growth and the concentrate on of the flux in the regions of converging flow pattern is flux expulsion. Possible reasons for the absence of NEMPI are that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign and that there may not be sufficient scale separation., Comment: 13 pages, 13 figures, submitted to Astronomy & Astrophysics, associated animations can be found at http://research.ics.aalto.fi/cmdaa/group-Movies.shtml

We investigated experimentally stably stratified turbulent flows in a lid driven cavity with a non-zero vertical mean temperature gradient in order to identify the parameters governing the mean and turbulent flows and to understand their effects on the momentum and heat transfer. We found that the mean velocity patterns (e.g., the form and the sizes of the large-scale circulations) depend strongly on the degree of the temperature stratification. In the case of strong stable stratification, the strong turbulence region is located in the vicinity of the main large-scale circulation. We detected the large-scale nonlinear oscillations in the case of strong stable stratification which can be interpreted as nonlinear internal gravity waves. The ratio of the main energy-containing frequencies of these waves in velocity and temperature fields in the nonlinear stage is about 2. The amplitude of the waves increases in the region of weak turbulence (near the bottom wall of the cavity), whereby the vertical mean temperature gradient increases., Comment: 11 pages, 14 figures, REVTEX4-1

We perform direct numerical simulations of the equations of magnetohydrodynamics with external random forcing and in the presence of gravity. The domain is divided into two parts: a lower layer where the forcing is helical and an upper layer where the helicity of the forcing is zero with a smooth transition in between. At early times, a large-scale helical dynamo develops in the bottom layer. At later times the dynamo saturates, but the vertical magnetic field continues to develop and rises to form dynamic bipolar structures at the top, which later disappear and reappear. Some of the structures look similar to $\delta$ spots observed in the Sun. This is the first example of magnetic flux concentrations, owing to strong density stratification, from self-consistent dynamo simulations that generate bipolar, super-equipartition strength, magnetic structures whose energy density can exceeds the turbulent kinetic energy by even a factor of ten., Comment: Published in Monthly Notices of Royal Astronomical Society

Condensation of water vapor on active cloud condensation nuclei produces micron-size water droplets. To form rain, they must grow rapidly into at least 50-100 $\mu$m droplets. Observations show that this process takes only 15-20 minutes. The unexplained physical mechanism of such fast growth, is crucial for understanding and modeling of rain, and known as "condensation-coalescence bottleneck in rain formation". We show that the recently discovered phenomenon of the tangling clustering instability of small droplets in temperature-stratified turbulence (Phys. Fluids 25, 085104, 2013) results in the formation of droplet clusters with drastically increased droplet number densities. The mechanism of the tangling clustering instability is much more effective than the previously considered by us the inertial clustering instability caused by the centrifugal effect of turbulent vortices. This is the reason of strong enhancement of the collision-coalescence rate inside the clusters. The mean-field theory of the droplet growth developed in this study can be useful for explanation of the observed fast growth of cloud droplets in warm clouds from the initial 1 micron size droplets to 40-50 micron size droplets within 15-20 minutes., Comment: 12 pages (two-column-format), 4 figures, revtex4-1, revised

Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding the growth rate of this large-scale instability, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached. This results in magnetic spots that are reminiscent of sunspots. Here we want to find out under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. We use a combination of MFS, DNS, and implicit large-eddy simulations to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. We confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using turbulence simulations, we find that magnetic flux concentrations occur for different values of the Mach number between 0.1 and 0.7. DNS and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated., Comment: 16 pages, 22 figures, Astron. Astrophys., in press

Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers for which the density scale height is constant throughout. We now study the validity of earlier conclusions about the size and growth rate of magnetic structures in the case of polytropic layers, which scale height decreases sharply towards the surface. To allow for a continuous transition from isothermal to polytropic layers, we employ a generalization of the exponential function known as the q-exponential. Now, the top of the polytropic layer shifts with the polytropic index such that the scale height at some reference height is always the same. We use both mean-field and direct numerical simulations of forced stratified turbulence to determine the resulting flux concentrations. Magnetic structures begin to form at a depth where magnetic field strength is about 3-4% the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic one the growth rates decreases for structures deeper down. For vertical fields, magnetic structures of super-equipartition strengths are formed because such fields survive downward advection, unlike NEMPI under horizontal magnetic fields. The horizontal cross-section of such structures is approximately circular. Results based on isothermal models can be applied locally to polytropic layers. For vertical fields, magnetic flux concentrations of super-equipartition strengths form, which supports suggestions that sunspot formation might be a shallow phenomenon., Comment: 12 pages, 17 figures, acepted A&A

In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable to spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, called the negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios where most of the magnetic field resides in the bulk of the convection zone, and not at the bottom. Recent work using the mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1.}{Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity from direct numerical simulations (DNS) and compare with earlier work.}{To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the $\tau$ approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the 3D hydromagnetic equations in a Cartesian domain.}{We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below about 0.06. In that case, kinetic and magnetic helicities are found to be weak. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated.}{Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the upper-most layers of the Sun, where the convective turnover time is less than 2 hours.}, Comment: 13 pages, 13 figures submitted to A&A

We investigate to what extent the current helicity distribution observed in solar active regions is compatible with solar dynamo models. We use an advanced 2D mean-field dynamo model with dynamo action largely concentrated near the bottom of the convective zone, and dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtain butterfly diagrams for both the small-scale current helicity and the large-scale magnetic helicity, and compare them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by $-A \cdot B$ evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here $B$ and $A$ are respectively the dynamo generated mean magnetic field and its vector potential., Comment: Proceedings IAU Symposium no. 294 (2012)

We present preliminary results from high resolution magneto-convection simulations where we find the formation of flux concentrations from an initially uniform magnetic field. We compute the effective magnetic pressure but find that the concentrations appear also in places where it is positive. The structures appear in roughly ten convective turnover times and live close to a turbulent diffusion time. The time scales are compatible with the negative effective magnetic pressure instability (NEMPI), although structure formation is not restricted to regions where the effective magnetic pressure is negative., Comment: 6 pages, 6 figures, to appear in IAUS 294 proceedings

Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers. Thus, the contribution of density stratification is less important than that of turbulent velocity. The alpha effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence) we find that the contribution of density stratification might be even less important than suggested by the analytic theory., Comment: 10 pages, 9 figures, revised version, Astrophys. J., in press

The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of non-uniform magnetic structures, can be excited over the scale of many turbulent eddies or convection cells. This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions and perhaps sunspots. We want to understand the effects of rotation on this instability in both two and three dimensions. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to be in agreement with those of direct numerical simulations. We find that the instability is suppressed already for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. The prograde rotation of the magnetic pattern near the equator is argued to be a possible explanation for the faster rotation speed of magnetic tracers found on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern., Comment: 8 pages, 13 figures, submitted to A&A

We study experimentally temperature fluctuations in stably stratified forced turbulence in air flow. In the experiments with an imposed vertical temperature gradient, the turbulence is produced by two oscillating grids located nearby the side walls of the chamber. Particle Image Velocimetry is used to determine the turbulent and mean velocity fields, and a specially designed temperature probe with sensitive thermocouples is employed to measure the temperature field. We found that the ratio $\big[(\ell_x \nabla_x \bar{T})^2 + (\ell_y \nabla_y \bar{T})^2 + (\ell_z \nabla_z \bar{T})^2\big] / <\theta^2 >$ is nearly constant, is independent of the frequency of the grid oscillations and has the same magnitude for both, stably and unstably stratified turbulent flows, where $\ell_i$ are the integral scales of turbulence along $x, y, z$ directions, $\bar{T}$ and $\theta$ are the mean and turbulent fluctuations components of the fluid temperature. We demonstrated that for large frequencies of the grid oscillations, the temperature field can be considered as a passive scalar, while for smaller frequencies the temperature field behaves as an active field. The theoretical predictions based on the budget equations for turbulent kinetic energy, turbulent potential energy ($\propto <\theta^2 >)$ and turbulent heat flux, are in a good agreement with the experimental results. Detailed comparison with experimental results obtained previously in unstably stratified forced turbulence is performed., Comment: 12 pages, 18 figures, REVTEX4-1, revised version. arXiv admin note: substantial text overlap with arXiv:0912.2588

In this study we discuss two key issues related to a small-scale dynamo instability at low magnetic Prandtl numbers and large magnetic Reynolds numbers, namely: (i) the scaling for the growth rate of small-scale dynamo instability in the vicinity of the dynamo threshold; (ii) the existence of the Golitsyn spectrum of magnetic fluctuations in small-scale dynamos. There are two different asymptotics for the small-scale dynamo growth rate: in the vicinity of the threshold of the excitation of the small-scale dynamo instability, $\lambda \propto \ln({\rm Rm}/ {\rm Rm}^{\rm cr})$, and when the magnetic Reynolds number is much larger than the threshold of the excitation of the small-scale dynamo instability, $\lambda \propto {\rm Rm}^{1/2}$, where ${\rm Rm}^{\rm cr}$ is the small-scale dynamo instability threshold in the magnetic Reynolds number ${\rm Rm}$. We demonstrated that the existence of the Golitsyn spectrum of magnetic fluctuations requires a finite correlation time of the random velocity field. On the other hand, the influence of the Golitsyn spectrum on the small-scale dynamo instability is minor. This is the reason why it is so difficult to observe this spectrum in direct numerical simulations for the small-scale dynamo with low magnetic Prandtl numbers., Comment: 14 pages, 1 figure, revised version

In this paper we advance physical background of the energy- and flux-budget turbulence closure based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time-scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth rotation. In accordance to modern experimental evidence, the closure implies maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: "strong turbulence" at Ri << 1 typical of boundary-layer flows and characterised by the practically constant turbulent Prandtl number; and "weak turbulence" at Ri > 1 typical of the free atmosphere or deep ocean, where the turbulent Prandtl number asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy-viscosity and eddy-conductivity, and general non-gradient model based on prognostic equations for all basic parameters of turbulence including turbulent fluxes., Comment: 50 pages, 12 figures, revised (corrected misprints)

We demonstrate that the current helicity observed in solar active regions traces the magnetic helicity of the large-scale dynamo generated field. We use an advanced 2D mean-field dynamo model with dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtained butterfly diagrams both for the small-scale current helicity and also for the large-scale magnetic helicity, and compared them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by $-{\bf A \cdot B}$ evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here ${\bf B}$ and ${\bf A}$ are respectively the dynamo generated mean magnetic field and its vector potential. A theoretical interpretation of these results is given., Comment: 11 pages, 5 figures, revised version

As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter beta_* characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter beta_*. The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI., Comment: 6 pages, 6 figures, 1 table; Astron. Nachr. (published)

Using different analytical methods (the quasi-linear approach, the path-integral technique and tau-relaxation approximation) we develop a comprehensive mean-field theory for a pumping effect of the mean magnetic field in homogeneous non-rotating helical turbulence with imposed large-scale shear. The effective pumping velocity is proportional to the product of alpha effect and large-scale vorticity associated with the shear, and causes a separation of the toroidal and poloidal components of the mean magnetic field along the direction of the mean vorticity. We also perform direct numerical simulations of sheared turbulence in different ranges of hydrodynamic and magnetic Reynolds numbers and use a kinematic test-field method to determine the effective pumping velocity. The results of the numerical simulations are in agreement with the theoretical predictions., Comment: 12 pages, 9 figures, REVTEX4-1, revised version