Mean-field transport in stratified and/or rotating turbulence

We investigate the mean electromotive force in the kinematic framework, that is, ignoring the back-reaction of the magnetic field on the fluid velocity, under the assumption of axisymmetric turbulence determined by the presence of either rotation, density stratification, or both. We use an analogous approach for the mean passive scalar flux. As an alternative to convection, we consider forced turbulence in an isothermal layer. When using standard ansatzes, the mean magnetic transport is then determined by nine, and the mean passive scalar transport by four coefficients. We give results for all these transport coefficients. We use the test-field method and the test-scalar method, where transport coefficients are determined by solving sets of equations with properly chosen mean magnetic fields or mean scalars. These methods are adapted to mean fields which may depend on all three space coordinates. We find the anisotropy of turbulent diffusion to be moderate in spite of rapid rotation or strong density stratification. Contributions to the mean electromotive force determined by the symmetric part of the gradient tensor of the mean magnetic field, which were ignored in several earlier investigations, turn out to be important. In stratified rotating turbulence, the $\alpha$ effect is strongly anisotropic, suppressed along the rotation axis on large length scales, but strongly enhanced at intermediate length scales. Also the \OO\times\meanJJ effect is enhanced at intermediate length scales. The turbulent passive scalar diffusivity is typically almost twice as large as the turbulent magnetic diffusivity. Both magnetic and passive scalar diffusion are slightly enhanced along the rotation axis, but decreased if there is gravity.Comment: 12 pages, 8 figures, A&A, publishe

The mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow

The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean--field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-like dynamo. In view of this application the second--order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the $\alpha$--effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.Comment: 16 pages, 2 figures, in PRE pres

Simulations of the anisotropic kinetic and magnetic alpha effects

The validity of a closure called the minimal tau approximation (MTA), is tested in the context of dynamo theory, wherein triple correlations are assumed to provide relaxation of the turbulent electromotive force. Under MTA, the alpha effect in mean field dynamo theory becomes proportional to a relaxation time scale multiplied by the difference between kinetic and current helicities. It is shown that the value of the relaxation time is positive and, in units of the turnover time at the forcing wavenumber, it is of the order of unity. It is quenched by the magnetic field -- roughly independently of the magnetic Reynolds number. However, this independence becomes uncertain at large magnetic Reynolds number. Kinetic and current helicities are shown to be dominated by large scale properties of the flow.Comment: 6 pages, 6 figures, accepted by Astron. Nach

Mean-field effects in the Galloway-Proctor flow

The coefficients defining the mean electromotive force in a Galloway-Proctor flow are determined. This flow shows a two-dimensional pattern and is helical. The pattern wobbles in its plane. Apart from one exception a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes and Tobias (2006, Phys. Rev. Lett., 96, 034503). An analytic theory of the alpha effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an alpha effect but no gamma effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for alpha and show that gamma is in general nonzero. Both alpha and gamma show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the wobbling motion. Some results for the magnetic diffusivity eta_t and a related quantity are given, too. Finally a result for alpha in the case of a randomly varying flow without the aforementioned circular motion is presented. This flow may be a more appropriate model for studying the alpha effect and related effects in flows that are statistical isotropic in a plane.Comment: 12 pages, 14 figures, submitted to MNRA

On the measurement of weak repulsive and frictional colloidal forces by reflection interference contrast microscopy

terference contrast (RIC) microscopy in combination with real-time image processing. The temporal fluctuations of the absolute sphere-to-substrate distance are determined from changes of interference fringe pattern (Newtonian rings). Both the shape about its minimum and the absolute minimum equilibrium distance of the interaction potential can be obtained by analyzing the distribution of distances in terms of a Boltzmann distribution. The timeautocorrelation function of distances yields the hydrodynamic friction. The method has been applied to the interaction of latex spheres with glass substrates in salt solutions of different ionic strength. The results correspond to classical electrostatic double layer theory that leads to a characteristic dependence of the mean separation distance and the mean square displacement on the radius of the spheres. The hydrodynamic friction close to a wall exhibits the predicted inverse proportionality to the sphere-wall distance. It is demonstrated that the method can be applied to study the interaction between biologically relevant objects such as giant vesicles with bilayer covered substrates

Imaging optical thicknesses and separation distances of phospholipid vesicles at solid surfaces

We present the application of reflection interference contrast microscopy (RICM) (1) to map the optical density of supported bilayers and vesicles and (2) to image the contact profile of phospholipid vesicles at surfaces. The resolution in the surface profile is 0.2 $\mu$m laterally and 1 nm out of plane. The optical thickness of the membrane can be determined with 0.2 nm accuracy. We outline the theoretical basis of RICM and derive the interference intensities of adhering vesicles from first principles. An analytical expression for the decaying contrast of the intrference fringes is given. The contact contour of vesicles is determined for various substrates. We further demonstrate that deposition of a magnesium fluoride layer on the glass substrate enhances the contrast and allows the optical density of adsorbed membranes to be imaged. By contrast variation of the buffer solution, the layer thicknesses and the indices of refraction can be measured. The novel method was applied to image lipid domains of different chain lengths in a substrate supported monolayer

Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the P\`eclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to non-local and non-instantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.Comment: 13 pages, 10 figures, published on PR

On the effects of turbulence on a screw dynamo

In an experiment in the Institute of Continuous Media Mechanics in Perm (Russia) an non--stationary screw dynamo is intended to be realized with a helical flow of liquid sodium in a torus. The flow is necessarily turbulent, that is, may be considered as a mean flow and a superimposed turbulence. In this paper the induction processes of the turbulence are investigated within the framework of mean--field electrodynamics. They imply of course a part which leads to an enhanced dissipation of the mean magnetic field. As a consequence of the helical mean flow there are also helical structures in the turbulence. They lead to some kind of $\alpha$--effect, which might basically support the screw dynamo. The peculiarity of this $\alpha$--effect explains measurements made at a smaller version of the device envisaged for the dynamo experiment. The helical structures of the turbulence lead also to other effects, which in combination with a rotational shear are potentially capable of dynamo action. A part of them can basically support the screw dynamo. Under the conditions of the experiment all induction effects of the turbulence prove to be rather weak in comparison to that of the main flow. Numerical solutions of the mean--field induction equation show that all the induction effects of the turbulence together let the screw dynamo threshold slightly, at most by one per cent, rise. The numerical results give also some insights into the action of the individual induction effects of the turbulence.Comment: 15 pages, 7 figures, in GAFD prin

Velocity-Dependent Forces in Atomic Force Microscopy Imaging of Lipid Films

We have imaged adsorbed fluid lipid bilayers by atomic force microscopy. The patches were formed by rupture of phospholipid vesicles onto magnesium fluoride. We show that the membrane patches are fluid but can be stably imaged at scan rates higher than 6 p d s . At lower scan rates the tip penetrates through the layer. The penetrating tip does not destroy the fluid patches, and the previous image can be restored after increasing the scanning velocity. The dynamic forces that possibly explain the effect are discussed