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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

The phenomenon of thermal and compositional (chemical) convection is very common in nature and therefore of great importance from the point of view of understanding of many fundamental aspects of the environment and universe. A number of books have been written on the topic, such as e.g. the seminal work of Chandrasekhar (1961) on Hydrodynamic and Hydromagnetic Stability, a large portion of which is devoted to the convective instability near its onset or the outstanding book of Getling (1998) where systematization of the knowledge on convection has been continued with a thorough description of the weakly nonlinear stages. Most of the works, however, considered weakly stratified, that is the so-called Boussinesq convection. It is the aim of this book to continue the process of systematization. It seems important to put the current knowledge on weakly and strongly stratified convection in order and provide a comprehensive description of the marginal, weakly nonlinear and fully developed stages of convective flow in both cases. To that end the book provides a short compendium of knowledge on the linear and weakly nonlinear limits of the Boussinesq convection, as a useful reference for a reader and than proceeds with a review of the theory on fully developed, weakly stratified convection. The entire third chapter is devoted to a detailed derivation and a study of the three aforementioned stages of stratified (anelastic) convection. The description of stratified convection requires extreme care, since many aspects have to be considered simultaneously for full consistency. Detailed and systematic explanations are therefore provided. This book is meant as a textbook for courses on hydrodynamics and convective flows, for the use of lecturers and students, however, it may also be of use for the entire scientific community as a practical reference., Comment: Textbook

The fully developed turbulent Boussinesq convection is known to form large-scale rolls, often termed the 'large-scale circulation' (LSC). It is an interesting question how such a large-scale flow is created, in particular in systems when the energy input occurs at small scales, when inverse cascade is required in order to transfer energy into the large-scale modes. Here, the small-scale driving is introduced through stochastic, randomly distributed heat source (say radiational). The mean flow equations are derived by means of simplified renormalization group technique, which can be termed 'weakly nonlinear renormalization procedure' based on consideration of only the leading order terms at each step of the recursion procedure, as full renormalization in the studied anisotropic case turns out unattainable. The effective, anisotropic viscosity is obtained and it is shown, that the inverse energy cascade occurs via an effective 'motive force' which takes the form of transient negative, vertical diffusion.

Anelastic convection at high Rayleigh number in a plane parallel layer with no slip boundaries is considered. Energy and entropy balance equations are derived, and they are used to develop scaling laws for the heat transport and the Reynolds number. The appearance of an entropy structure consisting of a well-mixed uniform interior, bounded by thin layers with entropy jumps across them, makes it possible to derive explicit forms for these scaling laws. These are given in terms of the Rayleigh number, the Prandtl number, and the bottom to top temperature ratio, which measures how stratified the layer is. The top and bottom boundary layers are examined and they are found to be very different, unlike in the Boussinesq case. Elucidating the structure of these boundary layers plays a crucial part in determining the scaling laws. Physical arguments governing these boundary layers are presented, concentrating on the case in which the boundary layers are thin even when the stratification is large, the incompressible boundary layer case. Different scaling laws are found, depending on whether the viscous dissipation is primarily in the boundary layers or in the bulk. The cases of both high and low Prandtl number are considered. Numerical simulations of no-slip anelastic convection up to a Rayleigh number of $10^7$ have been performed and our theoretical predictions are compared with the numerical results.

The relaxation of a helical magnetic field ${\bf B}({\bf x}, t)$ in a high-conductivity plasma contained in the annulus between two perfectly conducting coaxial cylinders is considered. The plasma is of low density and its pressure is negligible compared with the magnetic pressure; the flow of the plasma is driven by the Lorentz force and and energy is dissipated primarily by the viscosity of the medium. The axial and toroidal fluxes of magnetic field are conserved in the perfect-conductivity limit, as is the mass per unit axial length. The magnetic field relaxes during a rapid initial stage to a force-free state, and then decays slowly, due to the effect of weak resistivity $\eta$, while constrained to remain approximately force-free. Interest centres on whether the relaxed field may attain a Taylor state; but under the assumed conditions with axial and toroidal flux conserved inside every cylindrical Lagrangian surface, this is not possible. The effect of an additional $\alpha$-effect associated with instabilities and turbulence in the plasma is therefore investigated in exploratory manner. An assumed pseudo-scalar form of $\alpha$ proportional to $q\,\eta\, ({\bf j}\cdot {\bf B})$ is adopted, where $ {\bf j}=\nabla\times {\bf B}$ and $q$ is an $\mathcal{O}(1)$ dimensionless parameter. It is shown that, when $q$ is less that a critical value $q_c$, the evolution remains smooth and similar to that for $q=0$; but that if $q>q_c$, negative-diffusivity effects act on the axial component of $\bf B$, generating high-frequency rapidly damped oscillations and an associated transitory appearance of reversed axial field. However, the scalar quantity $\gamma={\bf j}\cdot {\bf B}/B^2$ remains highly non-uniform, so that again the field shows no sign of relaxing to a Taylor state for which $\gamma$ would have to be constant., Comment: 17 pages, 7 figures

Rotne-Prager-Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation is that it includes all long-range terms (i.e. decaying as R^-3 or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne-Prager-Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne-Prager-Yamakawa approximation can be generalized for other geometries and boundary conditions., Comment: to be published in J. Fluid. Mech

It has been recently suggested that the magneto-rotational instability (MRI) is a limiting case of the magneto-elliptic instability (MEI). This limit is obtained for horizontal modes in the presence of rotation and an external vertical magnetic field, when the aspect ratio of the elliptic streamlines tends to infinite. In this paper we unveil the link between these previously unconnected mechanisms, explaining both the MEI and the MRI as different manifestations of the same Magneto-Elliptic-Rotational Instability (MERI). The growth rates are found and the influence of the magnetic and rotational effects is explained, in particular the effect of the magnetic field on the range of negative Rossby numbers at which the horizontal instability is excited. Furthermore, we show how the horizontal rotational MEI in the rotating shear flow limit links to the MRI by the use of the local shearing box model, typically used in the study of accretion discs. In such limit the growth rates of the two instability types coincide for any power-type background angular velocity radial profile with negative exponent corresponding to the value of the Rossby number of the rotating shear flow. The MRI requirement for instability is that the background angular velocity profile is a decreasing function of the distance from the centre of the disk which corresponds to the horizontal rotational MEI requirement of negative Rossby numbers. Finally a physical interpretation of the horizontal instability, based on a balance between the strain, the Lorentz force and the Coriolis force is given., Comment: 15 pages, 3 figures. Accepted for publication in the Journal of Fluid Mechanics