Turbulent flows are known to produce enhanced effective magnetic and passive scalar diffusivities, which can fairly accurately be determined with numerical methods. It is now known that, if the flow is also helical, the effective magnetic diffusivity is reduced relative to the nonhelical value. Neither the usual second-order correlation approximation nor the various τ approaches have been able to capture this. Here we show that the helicity effect on the turbulent passive scalar diffusivity works in the opposite sense and leads to an enhancement. We have also demonstrated that the correlation time of the turbulent velocity field increases with the kinetic helicity. This is a key point in the theoretical interpretation of the obtained numerical results. Simulations in which helicity is being produced self-consistently by stratified rotating turbulence resulted in a turbulent passive scalar diffusivity that was found to be decreasing with increasing rotation rate.

In the standard model of particle physics, the chiral anomaly can occur in relativistic plasmas and plays a role in the early Universe, protoneutron stars, heavy-ion collisions, and quantum materials. It gives rise to a magnetic instability if the number densities of left- and right-handed electrically charged fermions are unequal. Using direct numerical simulations, we show this can result just from spatial fluctuations of the chemical potential, causing a chiral dynamo instability, magnetically driven turbulence, and ultimately a large-scale magnetic field through the magnetic 𝛼 effect.

At high energies, the dynamics of a plasma with charged fermions can be described in terms of chiral magnetohydrodynamics. Using direct numerical simulations, we demonstrate that chiral magnetic waves (CMWs) can produce a chiral asymmetry μ5=μL-μR from a spatially fluctuating (inhomogeneous) chemical potential μ=μL+μR, where μL and μR are the chemical potentials of left- and right-handed electrically charged fermions, respectively. If the frequency of the CMW is less than or comparable to the characteristic growth rate of the chiral dynamo instability, the magnetic field can be amplified on small spatial scales. The growth rate of this small-scale chiral dynamo instability is determined by the spatial maximum value of μ5 fluctuations. Therefore, the magnetic field amplification occurs during periods when μ5 reaches temporal maxima during the CMW. If the small-scale chiral dynamo instability leads to a magnetic field strength that exceeds a critical value, which depends on the resistivity and the initial value of μ, magnetically dominated turbulence is produced. Turbulence gives rise to a large-scale dynamo instability, which we find to be caused by the magnetic alpha effect. Our results have consequences for the dynamics of certain high-energy plasmas, such as the early Universe.

The dissipation rates of the basic second-order moments are the key parameters playing a vital role in turbulence modelling and controlling turbulence energetics and spectra and turbulent fluxes of momentum and heat. In this paper, we use the results of direct numerical simulations (DNSs) to evaluate dissipation rates of the basic second-order moments and revise the energy and flux budget (EFB) turbulence closure theory for stably stratified turbulence. We delve into the theoretical implications of this approach and substantiate our closure hypotheses through DNS data. We also show why the concept of down-gradient turbulent transport becomes incomplete when applied to the vertical turbulent flux of potential temperature under stable stratification. We reveal essential feedback between the turbulent kinetic energy (TKE), the vertical turbulent flux of buoyancy, and the turbulent potential energy (TPE), which is responsible for maintaining shear-produced stably stratified turbulence for any Richardson number.

The atmospheric convective boundary layer (CBL) consists of three basic parts: (1) the surface layer unstably stratified and dominated by small-scale turbulence of very complex nature; (2) 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 (3) 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 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.

Small-scale dynamos play important roles in modern astrophysics, especially on galactic and extragalactic scales. Owing to dynamo action, purely hydrodynamic Kolmogorov turbulence hardly exists and is often replaced by hydromagnetic turbulence. Understanding the size of dissipative magnetic structures is important in estimating the time-scale of galactic scintillation and other observational and theoretical aspects of interstellar and intergalactic small-scale dynamos. Here we show that, during the kinematic phase of the small-scale dynamo, the cutoff wavenumber of the magnetic energy spectra scales as expected for large magnetic Prandtl numbers, but continues in the same way also for moderately small values – contrary to what is expected. For a critical magnetic Prandtl number of about 0.3, the dissipative and resistive cutoffs are found to occur at the same wavenumber. In the non-linearly saturated regime, the critical magnetic Prandtl number becomes unity. The cutoff scale now has a shallower scaling with magnetic Prandtl number below a value of about three, and a steeper one otherwise compared to the kinematic regime.

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.

In this chapter, we discuss a mean field solar dynamo model with algebraic and dynamic nonlinearities, various mechanisms of sunspot formation, and prediction of solar activity. The algebraic nonlinearity describes the quenching of the alpha effect, turbulent magnetic diffusion, and the effective pumping velocity due to feedback from the growing large-scale magnetic field on the fluid motion. The dynamic nonlinearity is due to the evolution of the magnetic helicity of the small-scale magnetic field during the nonlinear stage of the dynamo; it is derived from conservation of the total (large-scale plus small-scale) magnetic helicity for very small microscopic magnetic diffusivity.We discuss observations of magnetic helicity in the Sun and their connection with the nonlinear mean field dynamo. We derive a budget equation for sunspot numbers taking into account sunspot formation mechanism due to the negative effective magnetic pressure instability. To predict solar activity, we use dynamo simulations as input to an artificial neural network that learns sunspot dynamics from available observations. Finally, we analyze the contribution of magnetic helicity transport to the formation of tilt in sunspot bipolar regions and compare the results with available observational data over the last 10 solar cycles (15-24).

We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high-energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential μ5 with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of μ5 are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuations grow by many orders of magnitude due to the small-scale chiral dynamo instability. Once the nonlinear backreaction of the generated magnetic field on fluctuations of μ5 sets in, the ratio of these scales decreases and the dynamo saturates. When magnetic fluctuations grow sufficiently to drive turbulence via the Lorentz force before reaching maximum field strength, an additional mean-field dynamo phase is identified. The mean magnetic field grows on a scale that is larger than the integral scale of turbulence after the amplification of the fluctuating component saturates. The growth rate of the mean magnetic field is caused by a magnetic α effect that is proportional to the current helicity. With the onset of turbulence, the power spectrum of μ5 develops a universal k−1 scaling independently of its initial shape, while the magnetic energy spectrum approaches a k−3 scaling.

The energy- and flux-budget (EFB) theory developed previously for atmospheric stably stratified turbulence is extended to the surface layer in atmospheric convective turbulence. This theory is based on 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, the rate of turbulence production of the turbulent kinetic energy (TKE) caused by the surface shear 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 boundary-layer turbulence, the theoretical relationships potentially useful in modeling applications have been derived. The developed EFB theory allows us to obtain a smooth transition between a stably stratified turbulence to a convective turbulence. The EFB theory for the surface layer in a convective turbulence provides an analytical expression for the entire surface layer including the transition range between the lower and upper parts of the surface layer, and it 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.