RädlerFest: Alpha Effect and Beyond

Feb 14, 2011, 9:00 AM → Feb 18, 2011, 3:00 PM Europe/Stockholm

Wenner-Gren Center, floor 7, Hörsalen (Wenner Gren Center)

Axel Brandenburg (Nordita)

→Photos by CK Chan
→Photos by Patrik Sanila
→Videos from talks

The alpha effect is a prototype of non-diffusive turbulent transport phenomena that play important roles in understanding the formation of ordered magnetic fields from turbulent and chaotic motions. Examples include the large-scale magnetic field of the Sun, its 11 year cycle, as well as similar phenomena in other stars, accretion disks, and galaxies. Other related effects are the Lambda effect for explaining mean angular momentum transport in rotating bodies, as well as the effects of mean flows and mean magnetic fields on linear momentum transport in stars.

In recent years, this subject has attracted ever growing attention through close comparisons with laboratory and numerical experiments. The purpose of this meeting is to discuss recent progress and to highlight outstanding problems, clarify controversies, and to identify future possibilities for making progress. In this spirit, there will be ample opportunity for formal and informal discussions, in addition to contributed and invited talks.

The meeting will also provide an opportunity to celebrate Karl-Heinz Rädler's 75th birthday (although the actual date was already in May 2010).

The meeting is sponsored jointly by Nordita and the Astrophysical Dynamo ERC Project ..

Logistic issues

Nordita has reserved about 25 apartments for program participants. This is the preferred mode of accommodation, especially for our long-term participants.

How to get here? (this link has a description and several maps). The meeting takes place either in Nordita or in the main AlbaNova building, just next to the Nordita building.

Program (please notify the organizers if there are still mistakes!)

Registration deadline: 1 February 2011 (local people can still sign up until 9 February)

Monday, February 14

9:30 AM → 10:30 AM Session 1

9:30 AM Opening remarks, and phone call to Fritz Krause

Speaker: Axel Brandenburg (Nordita)

10:00 AM Translation of the α effect to the West

Speaker: Prof. Paul Roberts

10:30 AM → 11:00 AM Coffee break

11:00 AM → 12:30 PM Session 2

11:00 AM Understanding the origin of astrophysical magnetic fields

The magnetic field of Earth was the first known example of an astronomical magnetic field. Its form was mapped out by Gilbert (1600) and its origin was attributed to magnetic iron oxide. With the work of Pierre Curie at the end of the 19th century, this explanation became untenable and various atomic effects, e.g. thermoelectricity, were considered. In 1908 Hale showed observationally that a sunspot contains a magnetic field of a few kilogauss. Larmor (1919) suggested that the sunspot is a rapidly rotating cyclonic structure whose circular motion somehow produces the observed magnetic field. This idea motivated Cowling (1934) to explore the inductive effects of a conducting fluid flowing in a magnetic field with axial symmetry, demonstrating his theorem that such a magnetic field cannot be maintained by fluid motions alone. Then in 1945 Walter Elsasser pointed out that none of the known atomic effects are adequate, leaving only the inductive effects of fluid motions as a theoretical possibility for the origin of the magnetic field of Earth. He went on to show that the nonuniform rotation of the core interacts with the dipole field to produce a strong azimuthal (toroidal) magnetic field in the core. The problem, then, was to get around Cowling's dictum that axisymmetric fields cannot be sustained by fluid motions. Note, then, that the 24 hour rotation of Earth implies that the convection in the liquid metal core is cyclonic. It is obvious that a rotating rising volume of fluid raises a bulge in the azimuthal field and rotates that upward bulge into the meridional plane (see the motif on the upper left hand corner of the home page for this meeting), thereby producing a net circulation of magnetic field in the meridional plane. There are many such cyclonic cells at any given time and resistive dissipation merges them all into an overall poloidal circulation of magnetic field in the meridional planes This "alpha effect" amplifies the dipole field, whose continual shearing by the nonuniform rotation regenerates the toroidal field (Parker, 1955), providing an ongoing dynamo. The intermittent contribution of the individual cyclonic cells was first treated in the "short sudden approximation", in which the large cyclonic displacement was introduced as a high speed motion over such a short period of time that resistive diffusion can be neglected. Then the cyclonic moltion is switched off while the resistive diffusion destroys the small-scale field components, leaving only the overall average dipole magnetic field. The nonuniform rotation is considered to be steady in time. The dynamo field equations are naturally formulated in terms of the azimuthal magnetic field and the azimuthal vector potential, representing the poloidal magnetic field. It is immediately obvious from these equations that the basic mode is a migratory dynamo wave, as observed in the magnetic field of the Sun (Parker, 1956). When the propagation of the dynamo wave is blocked by the geometry of the convecting fluid region, the magnetic field may be steady in time, as in Earth. Steenbeck, Krause, and Radler (1966) formulated the physics of the dynamo using the quasilinear approximation, providing a systematic approach to the higher order dynamo effects. The "short sudden" formulation was expanded to all orders (Parker, 1979), providing such things as the flux expulsion dynamo. The essential point is that the basic combination of the nonuniform rotation and the alpha effect, providing a poloidal field (dipole, quadrupole, etc.)or a simple dynamo wave, represents the most efficient field generation and may be presumed to be the origin of the magnetic fields of most astrophysical bodies. It should be noted that an effective turbulent diffusion is an essential part of the generation of the magnetic field in the Sun and other stars, and in the Galaxy. But there is no theory for how this comes about in the strong magnetic fields observed. It should also be appreciated that the intergalactic fields, with scales of a megaparsec or more, cannot be explained by a dynamo effect, nor is the origin of the initial "seed field" known.

Speaker: Prof. Eugene Parker

12:00 PM The Rädler-effect in supernova-driven turbulence

Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Analytical models based on the uncorrelated-ensemble approach predicted that any created field will be expelled from the disk before a significant amplification can occur. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for vertical stratification and galactic differential rotation, we find an exponential amplification of the mean field on timescales of 100 Myr. We highlight the importance of rotation in the generation of helicity by showing that a similar mechanism based on Cartesian shear does not lead to a sustained amplification of the mean magnetic field.

Speaker: Dr Oliver Gressel

12:30 PM → 2:00 PM Lunch break

2:00 PM → 3:30 PM Session 3

2:00 PM Recent and future liquid metal experiments on cosmic magnetic fields

At the end of 1999, the Riga and Karlsruhe experiments sounded the bell for a period of significant experimental effort to simulate the origin and the action of cosmic magnetic fields. With the main focus on our own activities, we summarize the recent liquid metal experiments on the dynamo effect and related magnetic instabilities, and we delineate our plans for a large scale sodium facility that will comprise a precession experiment and a Taylor-Couette experiment for the combined investigation of the magnetorotational and the Tayler instability.

Speaker: Dr Frank Stefani

2:45 PM Experimental measurement of turbulent magnetic diffusivity

The first direct measurements of effective magnetic diffusivity in turbulent flow of electro-conductive fluids (the so-called beta-effect) under magnetic Reynolds number Rm >> 1 are reported. The measurements are performed in a nonstationary turbulent flow of liquid sodium, generated in a closed toroidal channel. The peak level of the Reynolds number reached ${\rm Re} \approx 3 \cdot 10^6$, which corresponds to the magnetic Reynolds number $Rm \approx 30$. The magnetic diffusivity of the liquid metal was determined by measuring the phase shift between the induced and the applied magnetic fields. The maximal deviation of magnetic diffusivity from its laminar value reaches about 50%.

Speaker: Prof. Peter Frick (Institute of Continuous Media Mechanics)

3:30 PM → 4:00 PM Coffee break

4:00 PM → 5:30 PM Session 4

4:00 PM Helicity generation and α-effect in MHD Taylor-Couette flows

Helical magnetic background fields with adjustable pitch angle are imposed on a conducting fluid in a differentially rotating cylindrical container. The small-scale kinetic and current helicities are calculated for various field geometries, and shown to have the opposite sign as the helicity of the large-scale field. These helicities and also the corresponding $\alpha$-effect scale with the current helicity of the background field. The $\alpha$-tensor is highly anisotropic as the components $\alpha_{\phi\phi}$ and $\alpha_{zz}$ have opposite signs. The amplitudes of the azimuthal $\alpha$-effect computed with the cylindrical 3D MHD code are so small that the operation of an $\alpha\Omega$ dynamo on the basis of the current-driven, kink-type instabilities of toroidal fields is highly questionable. In any case the low value of the $\alpha$-effect would lead to very long growth times of a dynamo in the radiation zone of the Sun and early-type stars of the order of mega-years.

Speaker: Markus Gellert

4:30 PM α effect from buoyancy instability

A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. We calculate the alpha effect due to helical motions caused by a disintegrating magnetic layer in a rotating density-stratified system with angular velocity Omega making an angle theta with the vertical. We also study the dependence of the alpha effect on theta and the strength of the initial magnetic field. We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent EMF due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting alpha effect is inhomogeneous and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" alpha effect. The alpha effect is nonlocal, requiring around 8--16 Fourier modes to reconstruct the actual EMF based on the actual mean field.

Speaker: Piyali Chatterjee

5:00 PM What wavelets can bring to study MHD flows?

We have proposed a wavelet based method, called Coherent Vorticity Extraction (CVE), to extract coherent fluctuations out of fully developed turbulent flows. We will explain its principles and illustrate its use in the context of 3D fluid turbulence. We will then extract coherent vorticity sheets and coherent current sheets from DNS data of 3D forced incompressible MHD turbulence. We will show that it preserves both the vorticity sheets and the current sheets present in the original fields, while retaining only a few percent of the degrees of freedom. Studying the energy flux confirms that the nonlinear dynamics is fully captured by the coherent contributions only.

Speaker: Marie Farge

Tuesday, February 15

9:00 AM → 10:30 AM Session 5

9:00 AM Galactic dynamos need galactic outflows to survive

We discuss mean-field disc dynamos (mainly as applied to galaxies) subject to magnetic helicity conservation constraint. We demonstrate how this constraint enriches the dynamo model with physical contant and facilitates detailed comparison of the theory with observations.

Speaker: Prof. Anvar Shukurov (School of Mathematics and Statistics, Newcastle University, U.K.)

9:30 AM Dynamo action in thermally unstable interstellar flows

Numerous studies have investigated the role of thermal instability in regulating the phase transition between the cold cloudy and warm diffuse medium of the interstellar medium. Considerable interest has also been devoted in investigating the properties of turbulence in thermally usntable flows, special emphasis on molecular clouds and the possibility of star formation. In this study, we investigate another setting in which this instability may be important, namely its effect on dynamo action in interstellar flows. The setup we consider is a three dimensional periodic cube of gas with an initially weak magnetic field, subject to heating and cooling, the properties of which are such that thermal instability is provoked at certain temperature regime. Dynamo action is established through external forcing on the flow field. By comparing the results with a cooling function with exactly the same net effect but no thermally unstable regime, we find the following. The critical Reynolds number for the onset of the large-scale dynamo was observed to roughly double between the thermally stable versus unstable runs, the conclusion being that the thermal instability makes large-scale dynamo action more difficult. Whereas density and magnetic fields were observed to be almost completely uncorrelated in the thermally stable cases investigated, the action of thermal instability was observed to produce a positive correlation of the form B propto rho^0.2. This correlation is rather weak, and in addition it was observed to break down at the limit of the highest densities.

Speaker: Prof. Maarit Mantere

10:00 AM A Shell Model for Turbulent Magnetic Dynamo

Using the magnetohydrodynamic (MHD) description, we develop a nonlinear dynamo model that couples the evolution of the large scale magnetic field with turbulent dynamics of the plasma at small scale by electromotive force (e.m.f.) in the induction equation at large scale. The nonlinear behavior of the plasma at small scale is described by using a MHD shell model for velocity field and magnetic field fluctuations. The shell model allow to study this problem in a large parameter regime which characterizes the dynamo phenomenon in many natural systems and which is beyond the power of supercomputers at today. Under specific conditions of the plasma turbulent state, the field fluctuations at small scales are able to trigger the dynamo instability. We study this transition considering the stability curve which shows a strong decrease in the critical magnetic Reynolds number for increasing inverse magnetic Prandlt number $\textrm{Pm}^{-1}$ in the range $[10^{-6},1]$ and slows an increase in the range $[1,10^{8}]$. We also obtain hysteretic behavior across the dynamo boundary reveling the subcritical nature of this transition. The system, undergoing this transition, can reach different dynamo regimes, depending on Reynolds numbers of the plasma flow. This shows the critical role that the turbulence plays in the dynamo phenomenon. In particular the model is able to reproduce the dynamical situation in which the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field, reproducing the magnetic reversals as observed in geomagnetic dynamo and in the VKS experiments.

Speaker: Dr Giuseppina Nigro

10:30 AM → 11:00 AM Coffee break

11:00 AM → 12:30 PM Session 6

11:00 AM Coupling of the Earth's core and mantle

The coupling of the Earth's core and mantle is responsible for the largest fluctuations in the length of day. The torques exerted by the core on the mantle are of order 10^18 Nm and are due to viscosity, core-mantle topography, gravity and magnetic field. This talk will focus mainly on gravitational and magnetic coupling, either or both of which might explain the semi-decadal periodicity observed in the length of day record. The magnetic coupling is due to the coupling of torsional waves to the conductivity of the mantle. Whether this is strong enough to account for the semi-decadal signal is one of the topics discussed in this talk.

Speaker: Paul Roberts

12:00 PM α-fluctuations and simple model of geomagnetic inversions

D.Sokoloff, G.Sobko, V.Trukhin, V.Zadkov (Moscow State University, Russia) We suggest a simple dynamo model based onb fluctuations of alpha-coefficient. The model sucsessfully mimic basic properties of inversion of geomagnetic field and magnetostratigraphic time scale.

Speaker: Prof. Dmitry Sokoloff

12:30 PM → 2:00 PM Lunch break

2:00 PM → 3:30 PM Session 7

2:00 PM The negative magnetic pressure effect in stratified turbulence

A reduction of total mean turbulent pressure due to the presence of magnetic fields was previously shown to be a measurable effect in direct numerical simulations. However, in the studied parameter regime the formation of large-scale structures, as anticipated from earlier mean-field simulations, was not found. An analysis of the relevant mean-field parameter dependency and the parameter domain of interest is conducted in order to clarify this apparent discrepancy.

Speaker: Koen Kemel

2:20 PM Magnetic helicity and its effect on the solar dynamo

The roles of magnetic helicity and magnetic helicity fluxes in astrophysical objects are investigated using various models and field configurations. Their roles in dynamo theory are confirmed through magnetohydrodynamic simulations both within the framework of mean-field theory and in direct numerical simulations. The constraint of magnetic helicity conservation in a periodic system at high magnetic Reynolds numbers is analyzed for setups of three magnetic flux rings which can be interlocked. The linking is able to hinder the magnetic field to decay only if the linking implies magnetic helicity. If the magnetic field is not helical the decay shows the same behavior irrespective of the actual linking of the rings which supports the assumption that only the magnetic helicity is the decisive topological quantity in magnetic relaxation. The regime of high magnetic Reynolds numbers is analyzed by using a one-dimensional mean-field model for a helically forced dynamo. A wind with linear profile is imposed such that magnetic helicity can be advected to one of the domain boundaries. It is shown that with vacuum boundary conditions helicity can be shed from of the domain, which alleviates the quenching at high magnetic Reynolds numbers. Additionally the same boundary is closed for a different setup where a diffusive flux is allowed at the midplane of the system. This is shown to also reduce the quenching mechanism and to allow for dynamo action at large magnetic Reynolds numbers. The influence of the gauge on magnetic helicity transport and fluxes is explored in the Weyl gauge, the resistive gauge and the pseudo-Lorenz gauge as well as a newly introduced advecto-resistive gauge. In the first three gauges spatially averaged fluxes are analyzed and compared with the one-dimensional mean-field model. The alleviation of the quenching is independent of the gauge as it was expected since it is a physical effect. In the advecto-resistive gauge magnetic helicity density evolves like a passive scalar in the kinematic regime owing it to the advective nature of the gauge. In the dynamical regime magnetic helicity is advected into length scales of the turbulent eddies.

Speaker: Simon Candelaresi

2:40 PM Effects of magnetic dissipation in a collapse of massive star

Magnetically driven supernovae have been studied well for several years. Although core-collapse simulations without magnetic fields to date cannot reproduce a successful explosion, every numerical simulation with initially strong magnetic field and rotation shows a jet-like explosion along the rotation axis. There a key agent of explosion is toroidal-magnetic pressure amplified by differential rotation around a proto-neutron star surface. Meanwhile, Thompson et al. (2005) showed by their 1-D hydrodynamic simulations that a turbulent resistivity originating from magnetorotational instability (MRI) dissipates magnetic fields, and generated thermal pressure helps the explosion. However, in their study, dynamical roles of magnetic pressure are not treated, since their computation is hydrodynamic and in 1-D. Here, we have done 2-D magnetohydrodynamic simulations of a collapse of massive star with inclusion of a magnetic dissipation. We found that a magnetic dissipation is negative reinforcer for an energetic explosion. Due to magnetic dissipation, the amplification rate of toroidal magnetic fields decreases, which in turn lower the power of the engine. The low-power engine in principle could produce finally same explosion energy as a high-power one, provided sizes of energy reservoirs are same. However, the deeper the collapse proceeds, the harder the matter to be ejected, and thus the low-power engine results in a weak explosion

Speaker: Dr Hidetomo Sawai

3:00 PM Tayler instability in incompressible and compressible domains

The Tayler instability may be a ubiquitous phenomenon in stellar magnetic problems. Previous results on the instability in incompressible domains will be compared to new results on the Tayler instability in compressible media.

Speaker: Dr Rainer Arlt

3:30 PM → 4:00 PM Coffee break

4:00 PM → 5:30 PM Session 8

4:00 PM Test methods for hydro and MHD turbulence

Examples with purely magnetic as well as MHD backgrounds are studied where the quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized method produces the same results as the imposed-field method, where the field-aligned component of the actual electromotive force from the simulation is used. For MHD backgrounds, new mean-field effects are found that depend on cross-correlations between magnetic and velocity fluctuations. In particular, there is a contribution to the mean Lorentz force that is linear in the mean field and hence reverses sign upon a reversal of the mean field. For strong mean fields, α is found to be quenched proportional to the fourth power of the field strength, regardless of the type of background studied. An analogous method for compressible isothermal hydrodynamics is presented which reliably reproduces SOCA results. In particular, the AKA effect and negative turbulent viscosity for the Roberts flow is demonstrated.

Speaker: Dr Matthias Reinhard

5:00 PM Transition from large-scale to small-scale dynamo

The dynamo equations are solved numerically with a helical forcing corresponding to the Roberts flow. In the fully turbulent regime the flow behaves as a Roberts flow on long time scales, plus turbulent fluctuations at short time scales. The dynamo onset is controlled by the long time scales of the flow, in agreement with the former Karlsruhe experimental results. The dynamo mechanism is governed by a generalized $\tilde{\alpha}$-effect which includes both usual $\alpha$-effect and turbulent diffusion, plus all higher order effects. Beyond the onset we find that $\tilde{\alpha}=O(Rm^{-1})$ suggesting the take-over of small-scale dynamo action. This is confirmed by simulations in which dynamo occurs even if the large-scale field is artificially suppressed.

Speaker: Dr Frank Plunian

Wednesday, February 16

9:00 AM → 10:30 AM Session 9

9:00 AM Oscillating α2 dynamos

A simple way to interpret the reversal mechanism of the Earth's magnetic field has been achieved in theoretical models based on the interplay between very few magnetic modes. Motivated by the temporal behavior of elementary multipolar components of the Earth's magnetic field during the last reversal 780ka ago, (Leonhardt & Fabian 2007) the possibility of interacting magnetic modes is examined in a simple mean field model. Field modes that are suitable candidates to be involved in the reversal process are oscillating eigenfunctions of the linear eigenvalue problem for geodynamo models of alpha^2 type. Regarding the spectrum of the dynamo operator time-dependent solutions arise at so called exceptional points where two stationary modes merge and continue at a single oscillating eigenfunction. In the present model this behavior essentially involves dipolar and octupolar modes. The spectrum exhibits further time-dependent modes of higher order that appear at coupling points of different radial field modes. In order to couple odd ("dipolar-like") and even ("quadrupolar-like") modes equatorial symmetry breaking is required. However, instead of oscillating eigenfunctions an equatorial asymmetry results in stationary hemispherical dynamos. This behavior can be explained by the approximate dipole-quadrupole degeneration for the unperturbed problem. More complicated scenarios occur in case of (more realistic) anisotropies of alpha- and beta-effect or through non-linearities caused by the backreaction of the magnetic field (magnetic quenching).

Speaker: Dr Andre Giesecke

9:30 AM α2 dynamo with oscillations and migrations

We present direct numerical simulations with helical forcing in spherical coordinates which generates a dynamo which shows oscillations and equatorward migration. This DNS can be described by a mean field model with an alpha square dynamo where the alpha has different signs on the two hemispheres.

Speaker: Dhrubaditya Mitra

10:00 AM Oscillatory dynamo models and implications for the solar dynamo

Under which conditions are convection-driven dynamo models oscillatory and do these models provide any implications for the solar dynamo? We perform global direct numerical simulations varying the governing parameters as well as the mechanical boundary conditions and build a sample of oscillatory dynamo models. We identify common characteristics responsible for the oscillatory nature of these dynamos. A mean-field view on some of them reveals the underlying dynamo mechanisms. Somewhat surprisingly, an alpha-omega mechanism does not seem to be a necessary constraint for this class of dynamos. Possible implications for the solar dynamo are also discussed.

Speaker: Dr Martin Schrinner

10:30 AM → 11:00 AM Coffee break

11:00 AM → 12:30 PM Session 10

11:00 AM The onset of strongly localized thermal convection in rotating spherical shells

The onset of instability of a Boussinesq fluid within a rapidly rotating spherical shell is considered, when a thin unstable layer lies adjacent to the inner sphere boundary, radius r_i . This layer, which is of radial extent O(ε^2 r_i ), sits beneath the remaining (stably stratified) fluid. The variable stratification is effected by a combination of differential heating between the inner and outer boundaries and a uniform distribution of heat sinks within the fluid. As in previous small Ekman number E studies, convection takes on the familiar cartridge belt structure which, in view of the differential heating, is localised within a thin layer adjacent to (but outside) the tangent cylinder to the inner sphere (Dormy et al., J. Fluid Mech., vol. 501, 2004, pp. 43–70). We consider the situation when the domain of convection sits entirely within the unstable layer which requires that E ^{1/8} ≪ ε. In this case the axial extent of the convecting column from the equatorial plane is small and of size O(ε r_i ). We investigate the eigensolutions of the ordinary differential equation governing the axial structure both numerically for moderate (but small) values of the stratification parameter ε and analytically for ε ≪ 1. At the lowest order of the expansion in powers of ε, the eigenmodes resemble those for the plane layer convective models of the classical form described by Chandrasekhar (Hydrodynamic and Hydromagnetic Stability, 1961). In particular, the eigenmodes exhibit the features of exchange of stabilities and over- stability although these overstable modes only occur for Prandtl number P less than unity. The onset of convection at large P is steady but for small P it is oscillatory with frequency ±Ω. At the next order, curvature effects remove any plane layer degeneracies. Notably, the exchange of stabilities modes oscillate at low frequency causing the short axial columns to propagate as a wave with a small angular velocity (slow modes), while the magnitudes of both the Rayleigh number and frequency of the two overstable modes (fast modes) split. When P < 1 the slow modes that exist at large azimuthal wavenumbers M make a continuous transition to the preferred fast modes at small M . At all values of P the critical Rayleigh number corresponds to a mode exhibiting prograde propagation, whether it be a fast or slow mode. This feature is shared by the uniform classical convective shell models, as well as Busse’s annulus model (J. Fluid Mech., vol. 44, 1970, pp. 441–460). Those models do not possess any stable stratification and typically are prone to easily excitable Rossby or inertial modes of convection at small P . By way of contrast these structures can not exist in our model for small ε due to the viscous damping in the outer thick stable region.

Speaker: Prof. Andrew Soward

11:30 AM α-effect and large-scale dynamos from convection simulations

The results for the α-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos θ latitude profile for moderate rotation. Turbulent diffusivity, η_t, is proportional to the square of the turbulent vertical velocity in all cases. Whereas ηt decreases approximately inversely proportional to the wavenumber of the field, the α-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak α-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small α-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent α-shear dynamo may also act in the simulations. If both rotation and shear are present, the α-effect is more pronounced. At the same time, the combination of the shear-current and Ω×{ J}-effects is also stronger than in the case of shear alone, but subdominant to the α-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.

Speaker: Dr Petri Käpylä (University of Helsinki)

12:00 PM Dynamo action and magnetic buoyancy in convection with vertical shear

One of the existing hypothesis on sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the convection zone up to the surface. However, several physical constrains are required to be fulfilled for this model to be feasible. In this seminar I will present the results of numerical simulations of thermal convection including a narrow radial shear layer. This model mimics, within the numerical limitations, the conditions in the solar convection zone and the tachocline. The excitation of dynamo action as well as the buoyant properties of the generated magnetic field are explored under different conditions.

Speaker: Dr Gustavo Guerrero

12:30 PM → 2:00 PM Lunch break

2:00 PM → 3:30 PM Session 11

2:00 PM Passive scalar and magnetic field transport in potential flows

It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible fluid showing isotropic turbulence may well be smaller than the molecular diffusivity. This is in full analogy to the old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid (e.g. Krause and Rädler 1980). For both the passive scalar and the magnetic case several analytical results on mean-field diffusivities found within the second-order correlation approximation are presented as well as numerical results obtained by the test-field method, which apply independent of this approximation. Mean-field diffusivities smaller than the molecular diffusivities may occur in compressible turbulence for not too large Peclet or magnetic Reynolds numbers and, in addition, slow variations of the flow patterns. Analogous results has also been found in simple model of anisotropic potential-flow turbulence. The decay of mean fields under the influence of compressible turbulence is strongly influenced by the so-called memory effect (Hubbard and Brandenburg 2009), that is, the relevant diffusivity coefficients depend on the decay rates.

Speaker: Prof. Karl-Heinz Raedler (Astrophysical Institute Potsdam)

2:30 PM Compressibility effects on turbulent MHD and passive scalar transport

The effects of compressibility (finite Mach number effect) and stratification of turbulent fluid flow on mean-field transport coefficients of magnetic field and passive scalar (number density of particles and temperature field) are studied for small and large magnetic Reynolds numbers (or small and large Peclet and Schmidt numbers) using correspondingly the quasi-linear approach and the spectral tau-approach. For small magnetic Reynolds numbers (or small Peclet numbers) the turbulent diffusion coefficient of both, magnetic and passive scalar fields coincide and decrease with increase of the degree of compressibility of turbulent velocity field (defined as the ratio of the mean square of divergence of velocity fluctuations to the mean square of curl of turbulent velocity field). At some value of the degree of compressibility of turbulent velocity field, the turbulent diffusion coefficient can be negative, but the total diffusion coefficient (molecular + turbulent) is always positive. For large magnetic Reynolds numbers (or large Peclet numbers) the compressibility of fluid flow reduces the turbulent diffusion coefficient, but it is always positive. On the other hand, the compressibility of an inhomogeneous turbulence causes the pumping velocity of the passive scalar in the direction of the gradient of the turbulence intensity, while the density stratification results in a counter gradient pumping velocity. Final effect of the gradient or the counter gradient transport depends on the value of the Mach number. The pumping velocity of the magnetic field is always counter gradient, and for small magnetic Reynolds numbers it is standard (determined by the gradient of the turbulent magnetic diffusion), while for large magnetic Reynolds numbers this velocity can increase with compressibility. The comparison with DNS results are also discussed.

Speaker: Prof. Nathan Kleeorin

3:00 PM Direct statistical simulation of astrophysical flows

Speaker: Prof. Steve Tobias

3:30 PM → 4:00 PM Coffee break

4:00 PM → 5:30 PM Session 12

4:00 PM α effect and helicity fluxes in shearing systems

Magnetic helicity has risen to be a major player in dynamo theory, with the helicity of the small-scale field being linked to the dynamo saturation process for the large-scale field. It is a nearly conserved quantity, which allows its evolution equation to be written in terms of production and flux terms. The flux term can be decomposed in a variety of fashions. One particular contribution that has been expected to play a significant role in dynamos in the presence of mean shear was isolated by Vishniac & Cho. Magnetic helicity fluxes are explicitly gauge dependent however, and the correlations that have come to be called the Vishniac-Cho flux were determined in the Coulomb gauge, which turns out to be fraught with complications in shearing systems. While the fluxes of small-scale helicity are explicitly gauge dependent, their divergences can be gauge independent. We use this property to investigate magnetic helicity fluxes of the small-scale field through direct numerical simulations in a shearing-box system and find that in a numerically usable gauge the divergence of the small-scale helicity flux vanishes, while the divergence of the Vishniac-Cho flux remains finite. We attribute this seeming contradiction to the existence of horizontal fluxes of small-scale magnetic helicity with finite divergences.

Speaker: Alexander Hubbard (Nordita)

4:30 PM Discussion

Thursday, February 17

9:00 AM → 10:30 AM Session 13

9:00 AM Spontaneous discontinuities in magnetic fields with untidy topologies

Speaker: Prof. Eugene Parker

10:00 AM Turbulent cross helicity: Effects and its generation

Non-vanishing pseudo-scalars in turbulence may give rise to an effective suppression of enhanced transports due to turbulence. In the context of dynamo, the turbulent cross helicity (velocity–magnetic-field correlation in fluctuations) as well as the turbulent kinetic and/or current helicty, leads to effective suppression of the turbulent magnetic diffusivity. This is because, in the presence of large-scale vortical motions, the positive (or negative) cross helicity in turbulence should contribute to the turbulent electromotive force parallel (or antiparallel) to the large-scale vorticity. One of the key issues is how and how much the cross helicity can be presented in turbulence. Possible mechanisms that supply turbulence with the cross helicity are investigated by considering the evolution equation of the turbulent cross helicity. Some recent developments in cross-helicity generation mechanism using numerical simulations are also presented.

Speaker: Dr Nobumitsu Yokoi (Institute of Industrial Science, University of Tokyo)

10:30 AM → 11:00 AM Coffee break

11:00 AM → 12:30 PM Session 14

11:00 AM Tyger phenomenon for the Galerkin-truncated Burgers and Euler equations

It is shown that the solutions of inviscid hydrodynamical equations with suppression of all spatial Fourier modes having wavenumbers in excess of a threshold $\kg$ exhibit unexpected features. The study is carried out for both the one-dimensional Burgers equation and the two-dimensional incompressible Euler equation. At large $\kg$, for smooth initial conditions, the first symptom of truncation, a localized short-wavelength oscillation which we call a "tyger", is caused by a resonant interaction between fluid particle motion and truncation waves generated by small-scale features (shocks, layers with strong vorticity gradients, etc). These tygers appear when complex-space singularities come within one Galerkin wavelength $\lambdag = 2\pi/\kg$ from the real domain and typically arise far away from preexisting small-scale structures at locations whose velocities match that of such structures. Tygers are weak and strongly localized at first - in the Burgers case at the time of appearance of the first shock their amplitudes and widths are proportional to $\kg ^{-2/3}$ and $\kg ^{-1/3}$ respectively - but grow and eventually invade the whole flow. They are thus the first manifestations of the thermalization predicted by T.D. Lee in 1952. The sudden dissipative anomaly-the presence of a finite dissipation in the limit of vanishing viscosity after a finite time $\ts$-, which is well known for the Burgers equation and sometimes conjectured for the 3D Euler equation, has as counterpart in the truncated case the ability of tygers to store a finite amount of energy in the limit $\kg\to\infty$. This leads to Reynolds stresses acting on scales larger than the Galerkin wavelength and thus prevents the flow from converging to the inviscid-limit solution. There are indications that it may be possible to purge the tygers and thereby to recover the correct inviscid-limit behaviour. (Based on a paper by Samriddhi Sankar Ray, Uriel Frisch, Sergei Nazarenko and Takeshi Matsumoto, available at http://arxiv.org/abs/1011.1826)

Speaker: Prof. Uriel Frisch

12:00 PM Local anisotropy in MHD turbulence

Goldreich & Sridhar (1995) proposed that MHD turbulence is anisotropic. Energy cascades faster in directions that are perpendicular to the background guide field. On one hand, the (global) anisotropic spectrum is verified by numerical simulations when there are strong guide fields. On the other hand, local anisotropy is expected even the MHD turbulence is globally isotropic. We extent the works by Cho & Vishniac (2000) to study the cylindrically-integrated energy and helicity spectra, with and without guide fields. We will present preliminary result from this study.

Speaker: Dr Chi-kwan Chan

12:30 PM → 2:00 PM Lunch break

2:00 PM → 3:30 PM Session 15

2:00 PM Proxies of mean magnetic field and α-effect from solar vector magnetic fields

My scientific interests comprise solar and stellar dynamos, their observational manifestations and simple models enabling to reproduce observational data. Thorough analysis of recently available data of systematic ground-based and space-born observational instruments enable us with higher order moments of magnetic field such as helicities. Simple models based of WKB asymptotics within the short wave limit are capable to reproduce some key observable features.

Speaker: Dr Kirill Kuzanyan (IZMIRAN, Russia)

2:30 PM Dynamo-driven plasmoid ejections above a spherical surface

Magnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical forcing to produce a large-scale dynamo-generated magnetic field, which rises even without magnetic buoyancy. A two layer system is used as computational domain where the upper part represents the solar atmosphere. Here, the evolution of the magnetic field is solved with the stress--and--relax method. Below this region a magnetic field is produced by a helical forcing function in the momentum equation, which leads to dynamo action. We find twisted magnetic fields emerging frequently to the outer layer, forming arch-like structures. In addition, recurrent plasmoid ejections can be found by looking at space--time diagrams of the magnetic field. Recent simulations in spherical coordinates show similar results.

Speaker: Mr Jörn Warnecke (Nordita)

2:50 PM Multiscale α2 dynamo model

Speaker: Dr Rodion Stephanov

3:10 PM α2 dynamo with SPH

We are able to reproduce analitical resultrs from Meinel (1990) of Alfa^2 dynamo in Gadget, an SPH code.

Speaker: Mr Federico STASYSZYN

3:30 PM → 4:00 PM Coffee break

4:00 PM → 5:00 PM Session 16

4:00 PM Advection dominated dynamo in solar-type stars: cycle periods and parity selection problem

Most probably the sunspot cycle period is ruled by a meridional flow located near the base of the convection zone (Hathaway et al. 2003). On the other hand, if the eddy diffusivity is low enough, dramatic modification of the standard α2Ω-dynamo by the meridional flow are expected. In this paper we shall discuss the dependence of periods, dynamo numbers and the sign of the current helicity as a function of the magnetic Reynolds number for a double cell meridional circulation and for a positive α-effect at the base of the convection zone. The dynamo action occurs at lower latitudes and its location is at the interface between equatorward and poleward motions near the base of the convection zone. In spite of the complexity of the flow pattern, our simulations show that the resulting dynamo action reproduces several observed features of the solar cycle.

Speaker: Prof. Alfio Bonanno

4:30 PM Photometric time series analysis and Doppler imaging of late type stars

We present surface (Doppler) imaging temperature maps of the FK Comae-type star HD 199178 (V1794 Cyg). The maps have been calculated from high resolution spectra and simultaneous Johnson V-photometry obtained between 1994 and 1997. All maps reveal a high latitude spot, which is 1200-1600 K cooler than the mean surface temperature. The observed slightly flat bottomed absorption lines can be explained by antisolar surface differential rotation. The presence of differential rotation is supported by the variations in the photometric rotation period.

Speaker: Dr Thomas Hackmann

Friday, February 18

9:00 AM → 10:30 AM Session 17

9:00 AM Vorticity production from potentially forced flows

In the absence of rotation and shear, and under the assumption of constant temperature or specific entropy, purely potential forcing by localized expansion waves is known to produce irrotational flows that have no vorticity. Here we study the production of vorticity under idealized conditions when there is rotation, shear, or baroclinicity, to address the problem of vorticity generation in the interstellar medium in a systematic fashion. We use three-dimensional periodic box numerical simulations to investigate the various effects in isolation. We find that for slow rotation, vorticity production in an isothermal gas is small in the sense that the ratio of the root-mean-square values of vorticity and velocity is small compared with the wavenumber of the energy carrying motions. For Coriolis numbers above a certain level, vorticity production saturates at a value where the aforementioned ratio becomes comparable with the wavenumber of the energy carrying motions. Shear also raises the vorticity production, but no saturation is found. When the assumption of isothermality is dropped, there is significant vorticity production by the baroclinic term once the turbulence becomes supersonic. In galaxies, shear and rotation are estimated to be insufficient to produce significant amounts of vorticity, leaving therefore only the baroclinic term as the most favorable candidate. We also demonstrate vorticity production visually as a result of colliding shock fronts.

Speaker: Fabio Del Sordo (NORDITA)

9:20 AM Galactic dynamos from torsion modes of Lorentz violation

GR MHd dynamo equation of marklund and clarkson (MNRAS-2005) is used to show that the extra galactic source magnetic contrast is well within the limit stablished by Reinhardt of 1.7. Actually the result obtained is 2.0 minus expansion terms in friedmann universe.

Speaker: Dr luiz garcia (dept pf theoretical physics)

9:40 AM Nonlocal turbulent transport

The turbulent diffusivity tensor is determined for linear shear flow turbulence using numerical simulations. For moderately strong shear, the diagonal components are found to increase quadratically with Peclet and Reynolds numbers below about 10 and then become constant. The diffusivity tensor is found to have components proportional to the symmetric and antisymmetric parts of the velocity gradient matrix, as well as products of these. All components decrease with the wave number of the mean field in a Lorentzian fashion. The components of the diffusivity tensor are found not to depend significantly on the presence of helicity in the turbulence. The signs of the leading terms in the expression for the diffusion tensor are found to be in good agreement with estimates based on a simple closure assumption.

Speaker: Axel Brandenburg (Nordita)

10:00 AM A study of magnetic helicity in forced and decaying 3D-MHD turbulence

Large-scale magnetic structure formation in the universe is one of the problems in modern astrophysics, which lacks a clear solution. A possible explanation for the formation of such structures could be offered from a property of 3D- magnetohydrodynamic (MHD) turbulence, namely inverse cascade of magnetic helicity. Magnetic helicity is defined as the volume integral of the dot product of the magnetic field and the magnetic vector potential. Inverse cascade means the transfer of that quantity spectrally from small scales to large scales, with a constant flux. We report some of the important results form the spectral and structural study of this property using high resolution Direct Numerical Simulations (DNS) in two setups namely, forced 3D-MHD turbulence and decaying 3D-MHD turbulence. These results include self-similar behavior in various quantities of the turbulent flow in their spectra; which were hitherto unknown. A new relation involving magnetic helicity, magnetic energy, kinetic helicity and kinetic energy; has been obtained from the dimensional analysis of the eddy damped quasi normal Markovian (EDQNM) approximation equation for magnetic helicity. This relation is satisfied by the obtained power laws of these quantities in both the forced and decaying turbulence cases . Further, this relation can also be written in a form to represent the alpha effect. We also propose a new mechanism involving both forced and decaying turbulences to explain large-scale magnetic structures. Statistical analysis of structures in the the turbulent fields in both the cases will also be presented. Reference: A Study of Magnetic Helicity in Forced and Decaying 3D-MHD Turbulence, Ph.d thesis, Shiva Kumar. Malapaka (http://edoc.mpg.de/display.epl?mode=doc&id=464051&col=33&grp=1311)

Speaker: Dr Shiva Kumar Malapaka

10:30 AM → 11:00 AM Coffee break

11:00 AM → 12:30 PM Session 18

11:00 AM Future of mean-field dynamo theory

Different mean-field approaches, ranges of validity of the approaches, approximations, different models of the background turbulence are described. Role of budget equations in the mean-field theory is considered. Open questions in the mean-field dynamo theory are discussed. Different problems, e.g., large-scale shear dynamos, dynamos in turbulence with cosmic rays, dynamo in turbulent convection, etc. are discussed.

Speaker: Prof. Igor Rogachevskii (Ben-Gurion University of the Negev)

12:00 PM K.-H. Rädler for popular sciences

To understand Dynamo Theory is really not so easy for "people on the street". Results of this theory concerning for example solar or Earth magnetic field processes are nevertheless fascinating for many of them. Karl-Heinz Rädler´s work has prepared a lot for a better understanding of the fundamentals of Dynamo Theory in the scientific community, which is the background to present the essential insights even in the field of popular sciences, which is as well a real important and necessary task for scientists to do. In this context I will appreciate the special merits of Karl-Heinz Rädler in my talk.

Speaker: Mr Ulrich v. Kusserow

12:30 PM → 2:00 PM Lunch break

2:00 PM → 3:00 PM Session 19

2:00 PM Conference summary

Speaker: Prof. Anvar Shukurov (School of Mathematics and Statistics, Newcastle University, U.K.)