15th European Turbulence Conference 2015
August 25-28th, 2015, Delft, The Netherlands

Invited speakers:

Prof. Marc Brachet. Ecole Normale Superieure, Paris, France

Prof. Peter G. Frick, Institute of Continuous Media Mechanics, Perm, Russia

Prof. Bettina Frohnapfel,  Karlsruher Institut fur Technology, Germany

Prof. Andrea Mazzino, Dipartimento di Fisica, University of Genova, Italy

Prof. Bernhard Mehlig. Department of Physics, University of Gothenburg, Sweden

Prof. Lex Smits, Mechanical and Aerospace Engineering, Princeton University, USA

Prof. Chao Sun Physics of Fluids, University of Twente, The Netherlands

Prof. Steve Tobias, Applied Mathematics, University of Leeds, United Kingdom

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15:00   Magnetohydrodynamics 2
Chair: Yasuhito Narita
15 mins
Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field
Basile Gallet, Charles R. Doering
Abstract: We investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: for very strong applied magnetic field, is the flow mostly two-dimensional, with remaining weak three-dimensional fluctuations, or does it become exactly 2D, with no dependence along the vertical? We restrict attention to low-magnetic-Reynolds number (Rm) flow. Because liquid metals have low magnetic Prandtl number, such low-$Rm$ flows can have a kinetic Reynolds number as large as one million and therefore be strongly turbulent. We first focus on the quasi-static approximation, i.e. the asymptotic limit of vanishing magnetic Reynolds number Rm << 1: we prove that the flow becomes exactly 2D asymptotically in time, regardless of the initial condition and provided the interaction parameter N is larger than a threshold value. We call this property absolute two-dimensionalization: the attractor of the system is necessarily a (possibly turbulent) 2D flow. We then consider the full-magnetohydrodynamic equations and we prove that, for low enough Rm and large enough N, the flow becomes exactly two-dimensional in the long-time limit provided the initial vertically-dependent perturbations are infinitesimal. We call this phenomenon linear two-dimensionalization: the (possibly turbulent) 2D flow is an attractor of the dynamics, but it is not necessarily the only attractor of the system. Some 3D attractors may also exist and be attained for strong enough initial 3D perturbations. These results shed some light on the existence of a dissipative anomaly for magnetohydrodynamic flows subject to a strong external magnetic field.
15 mins
Nonhelical inverse transfer of a decaying turbulent magnetic field
Axel Brandenburg, Tina Kahniashvili, Alexander Tevzadze
Abstract: In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of a universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two-dimensionality and the shallower k^2 subinertial range spectrum of kinetic energy forcing the magnetic field with a k^4 subinertial range to attain larger-scale coherence. The inertial range shows a clear k^{-2} spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling.
15 mins
Prandtl number dependence of kinetic-to-magnetic dissipation ratio
Axel Brandenburg
Abstract: Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the ratio of kinetic-to-magnetic energy dissipation always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of the energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfven kinks.
15 mins
Density-variance effects in turbulent magnetic reconnection
Nobumitsu Yokoi
Abstract: Density variance effects in the turbulent magnetic reconnection are investigated in the framework of the magnetohydrodynamics (MHD). In the presence of the density variance, which is expected to be large in the vicinity of shock where a large density gradient is located, several turbulent correlations arising from the density fluctuations affect the mean field evolutions. A contribution to the turbulent electromotive force (EMF) arises from the obliqueness of the mean magnetic field and the density gradient. In the slow mode MHD shock configuration, this effect is expected to enhance the turbulence level in the vicinity of shock front.
15 mins
Wenjun Liu, Dmitry Krasnov, Andre Thess
Abstract: Direct numerical simulations of natural convection in liquid metal within rectangular box heated uniformly from below with uniform strong vertical magnetic field are conducted. The main aim is to explore the possibilities and mechanisms of convection instabilities in such flows. The effects of parameter range on the flow structure, i.e. variations in Hartmann number, Rayleigh number and aspect ratio, are analyzed. It is shown that the magnetic field can completely change the structure and orientation of convection rolls by leading a new flow structure lined magnetic field. And if the magnetic field is strong enough, convection in the system can be fully suppressed.
15 mins
The 2D/3D dynamics of wall-bounded low-Rm magnetohydrodynamic (MHD) turbulence
Nathaniel Baker, Alban Potherat, Laurent Davoust, Francois Debray
Abstract: With this experimental study, we give evidence that the dynamics of low-Rm MHD turbulence depends on the diffusion length l_z, which corresponds to the distance over which the Lorentz force is able to diffuse momentum before it is balanced by inertia.
15 mins
Rodion Stepanov, Irina Mizeva, Peter Frick
Abstract: Magnetohydrodynamic (MHD) turbulence is an important part of astrophysical processes, which gives rise to global cosmic magnetic fields. Over the last few decades, the peculiarities of MHD turbulence have attracted the interest of researchers in astrophysics and fluid dynamics, significant attention has been paid to the role of magnetic helicity in fully developed MHD turbulence. Magnetic helicity, together with the energy and cross-helicity, is one of the three integrals of motion in ideal MHD. We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD turbulence, we study the high Reynolds number magnetohydrodynamic turbulence with well separated scales of energy input, magnetic helicity input and magnetic helicity sink. We obtain three inertial ranges with different scaling properties. In a short range of scales larger than the forcing scale of magnetic helicity, a bottleneck-like effect appears, which results in a local reduction of the spectral slope. The slope changes in a domain with a high level of relative magnetic helicity, which determines that part of the magnetic energy related to the helical modes at a given scale. In the infrared part of the spectra we observe simultaneous inverse cascade of energy and magnetic helicity. Our results indicate that a large-scale dynamo can be affected by the magnetic helicity generated at small scales. The kinetic helicity, in particular, is not involved in the process at all.
15 mins
Reynolds number dependence of the dimensionless dissipation rate in stationary magnetohydrodynamic turbulence
Mairi E. McKay, Moritz F. Linkmann, Arjun Berera, W. David McComb
Abstract: Results on the Reynolds number dependence of the dimensionless total dissipation rate C_ε are presented, obtained from medium to high resolution direct numerical simulations (DNSs) of mechanically forced stationary homogeneous magnetohydrodynamic (MHD) turbulence in the absence of a mean magnetic field, showing that C_ε -> const with increasing Reynolds number. Furthermore, a model equation for the Reynolds number dependence of the dimensionless dissipation rate is derived from the real-space energy balance equation by asymptotic expansion in terms of Reynolds number of the second- and third-order correlation functions of the Elsässer fields z± = u ± b. At large Reynolds numbers we find that a model of the form C_ε = C_ε,∞ + C/R describes the data well, while at lower Reynolds numbers the model needs to be extended to second order in 1/R in order to obtain a good fit to the data, where R is a generalised Reynolds number with respect to the Elsässer field z-.