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The Role of MHD Turbulence in Magnetic Self-Excitation in The
THE ROLE OF MHD TURBULENCE IN MAGNETIC SELF-EXCITATION: A STUDY OF THE MADISON DYNAMO EXPERIMENT by Mark D. Nornberg A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) at the UNIVERSITY OF WISCONSIN–MADISON 2006 °c Copyright by Mark D. Nornberg 2006 All Rights Reserved i For my parents who supported me throughout college and for my wife who supported me throughout graduate school. The rest of my life I dedicate to my daughter Margaret. ii ACKNOWLEDGMENTS I would like to thank my adviser Cary Forest for his guidance and support in the completion of this dissertation. His high expectations and persistence helped drive the work presented in this thesis. I am indebted to him for the many opportunities he provided me to connect with the world-wide dynamo community. I would also like to thank Roch Kendrick for leading the design, construction, and operation of the experiment. He taught me how to do science using nothing but duct tape, Sharpies, and Scotch-Brite. He also raised my appreciation for the artistry of engineer- ing. My thanks also go to the many undergraduate students who assisted in the construction of the experiment, especially Craig Jacobson who performed graduate-level work. My research partner, Erik Spence, deserves particular thanks for his tireless efforts in modeling the experiment. His persnickety emendations were especially appreciated as we entered the publi- cation stage of the experiment. The conversations during our morning commute to the lab will be sorely missed. I never imagined forging such a strong friendship with a colleague, and I hope our families remain close despite great distance. -
Fluid Mechanics of Liquid Metal Batteries
Fluid Mechanics of Liquid Metal Douglas H. Kelley Batteries Department of Mechanical Engineering, University of Rochester, The design and performance of liquid metal batteries (LMBs), a new technology for grid- Rochester, NY 14627 scale energy storage, depend on fluid mechanics because the battery electrodes and elec- e-mail: [email protected] trolytes are entirely liquid. Here, we review prior and current research on the fluid mechanics of LMBs, pointing out opportunities for future studies. Because the technology Tom Weier in its present form is just a few years old, only a small number of publications have so far Institute of Fluid Dynamics, considered LMBs specifically. We hope to encourage collaboration and conversation by Helmholtz-Zentrum Dresden-Rossendorf, referencing as many of those publications as possible here. Much can also be learned by Bautzner Landstr. 400, linking to extensive prior literature considering phenomena observed or expected in Dresden 01328, Germany LMBs, including thermal convection, magnetoconvection, Marangoni flow, interface e-mail: [email protected] instabilities, the Tayler instability, and electro-vortex flow. We focus on phenomena, materials, length scales, and current densities relevant to the LMB designs currently being commercialized. We try to point out breakthroughs that could lead to design improvements or make new mechanisms important. [DOI: 10.1115/1.4038699] 1 Introduction of their design speed, in order for the grid to function properly. Changes to any one part of the grid affect all parts of the grid. The The story of fluid mechanics research in LMBs begins with implications of this interconnectedness are made more profound one very important application: grid-scale storage. -
Anomalous Viscosity, Resistivity, and Thermal Diffusivity of the Solar
Anomalous Viscosity, Resistivity, and Thermal Diffusivity of the Solar Wind Plasma Mahendra K. Verma Department of Physics, Indian Institute of Technology, Kanpur 208016, India November 12, 2018 Abstract In this paper we have estimated typical anomalous viscosity, re- sistivity, and thermal difffusivity of the solar wind plasma. Since the solar wind is collsionless plasma, we have assumed that the dissipation in the solar wind occurs at proton gyro radius through wave-particle interactions. Using this dissipation length-scale and the dissipation rates calculated using MHD turbulence phenomenology [Verma et al., 1995a], we estimate the viscosity and proton thermal diffusivity. The resistivity and electron’s thermal diffusivity have also been estimated. We find that all our transport quantities are several orders of mag- nitude higher than those calculated earlier using classical transport theories of Braginskii. In this paper we have also estimated the eddy turbulent viscosity. arXiv:chao-dyn/9509002v1 5 Sep 1995 1 1 Introduction The solar wind is a collisionless plasma; the distance travelled by protons between two consecutive Coulomb collisions is approximately 3 AU [Barnes, 1979]. Therefore, the dissipation in the solar wind involves wave-particle interactions rather than particle-particle collisions. For the observational evidence of the wave-particle interactions in the solar wind refer to the review articles by Gurnett [1991], Marsch [1991] and references therein. Due to these reasons for the calculations of transport coefficients in the solar wind, the scales of wave-particle interactions appear more appropriate than those of particle-particle interactions [Braginskii, 1965]. Note that the viscosity in a turbulent fluid is scale dependent. -
Rayleigh-Bernard Convection Without Rotation and Magnetic Field
Nonlinear Convection of Electrically Conducting Fluid in a Rotating Magnetic System H.P. Rani Department of Mathematics, National Institute of Technology, Warangal. India. Y. Rameshwar Department of Mathematics, Osmania University, Hyderabad. India. J. Brestensky and Enrico Filippi Faculty of Mathematics, Physics, Informatics, Comenius University, Slovakia. Session: GD3.1 Core Dynamics Earth's core structure, dynamics and evolution: observations, models, experiments. Online EGU General Assembly May 2-8 2020 1 Abstract • Nonlinear analysis in a rotating Rayleigh-Bernard system of electrical conducting fluid is studied numerically in the presence of externally applied horizontal magnetic field with rigid-rigid boundary conditions. • This research model is also studied for stress free boundary conditions in the absence of Lorentz and Coriolis forces. • This DNS approach is carried near the onset of convection to study the flow behaviour in the limiting case of Prandtl number. • The fluid flow is visualized in terms of streamlines, limiting streamlines and isotherms. The dependence of Nusselt number on the Rayleigh number, Ekman number, Elasser number is examined. 2 Outline • Introduction • Physical model • Governing equations • Methodology • Validation – RBC – 2D – RBC – 3D • Results – RBC – RBC with magnetic field (MC) – Plane layer dynamo (RMC) 3 Introduction • Nonlinear interaction between convection and magnetic fields (Magnetoconvection) may explain certain prominent features on the solar surface. • Yet we are far from a real understanding of the dynamical coupling between convection and magnetic fields in stars and magnetically confined high-temperature plasmas etc. Therefore it is of great importance to understand how energy transport and convection are affected by an imposed magnetic field: i.e., how the Lorentz force affects convection patterns in sunspots and magnetically confined, high-temperature plasmas. -
Toward a Self-Generating Magnetic Dynamo: the Role of Turbulence
PHYSICAL REVIEW E VOLUME 61, NUMBER 5 MAY 2000 Toward a self-generating magnetic dynamo: The role of turbulence Nicholas L. Peffley, A. B. Cawthorne, and Daniel P. Lathrop* Department of Physics, University of Maryland, College Park, Maryland 20742 ͑Received 6 July 1999͒ Turbulent flow of liquid sodium is driven toward the transition to self-generating magnetic fields. The approach toward the transition is monitored with decay measurements of pulsed magnetic fields. These mea- surements show significant fluctuations due to the underlying turbulent fluid flow field. This paper presents experimental characterizations of the fluctuations in the decay rates and induced magnetic fields. These fluc- tuations imply that the transition to self-generation, which should occur at larger magnetic Reynolds number, will exhibit intermittent bursts of magnetic fields. PACS number͑s͒: 47.27.Ϫi, 47.65.ϩa, 05.45.Ϫa, 91.25.Cw I. INTRODUCTION Reynolds number will be quite large for all flows attempting to self-generate ͑where Re ӷ1 yields Reӷ105)—implying The generation of magnetic fields from flowing liquid m turbulent flow. These turbulent flows will cause the transition metals is being pursued by a number of scientific research to self-generation to be intermittent, showing both growth groups in Europe and North America. Nuclear engineering and decay of magnetic fields irregularly in space and time. has facilitated the safe use of liquid sodium, which has con- This intermittency is not something addressed by kinematic tributed to this new generation of experiments. With the dynamo studies. The analysis in this paper focuses on three highest electrical conductivity of any liquid, sodium retains main points: we quantify the approach to self-generation and distorts magnetic fields maximally before they diffuse with increasing Rem , characterize the turbulence of induced away. -
UC Santa Cruz 2010 International Summer Institute for Modeling in Astrophysics
UC Santa Cruz 2010 International Summer Institute for Modeling in Astrophysics Title Taming jets in magnetised fluids Permalink https://escholarship.org/uc/item/5ff523wv Authors Kosuga, Yusuke Brummell, Nicholas Publication Date 2010-09-01 eScholarship.org Powered by the California Digital Library University of California Taming Jets in magnetized fluids Y. Kosuga1 and N. H. Brummell2 1)Center for Astrophysics and Space Sciences and Department of physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093 2)Department of Applied Mathematic and Statistics, University of California at Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 Effects of a uniform horizontal magnetic field on jets dynamics in 2D Boussinesq turbulence, i.e. Howard-Krishnamurti problem are studied with a numerical simula- tion. For a fixed fluid and magnetic diffusivity, it is shown that as the imposed field strength becomes larger jets start behaving in a more organized way, i.e. achieve sta- tionary state and are finally quenched. The time evolution of total stress, Reynolds stress, Maxwell stress is examined and all the stresses are shown to vanish when jets are quenched. The quenching of jets is confirmed for different values of magnetic diffusivity, albeit the required field strength increases. It is also shown that the in- clusion of overstable modes reinforces jets where Maxwell stress overcomes Reynolds stress. For a larger imposed field jets are shown to quench. A possible mechanism for the transition to the reinforcement of jets by Maxwell stress is discussed based on the transition in the most unstable mode in the underlying turbulence. -
Turbulent Magnetic Prandtl Number and Magnetic Diffusivity Quenching from Simulations
A&A 411, 321–327 (2003) Astronomy DOI: 10.1051/0004-6361:20031371 & c ESO 2003 Astrophysics Turbulent magnetic Prandtl number and magnetic diffusivity quenching from simulations T. A. Yousef1, A. Brandenburg2,andG.R¨udiger3 1 Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjørn Hejes vei 2B, 7491 Trondheim, Norway 2 NORDITA, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark 3 Astrophysical Institute Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany Received 21 February 2003 / Accepted 25 August 2003 Abstract. Forced turbulence simulations are used to determine the turbulent kinematic viscosity, νt, from the decay rate of a large scale velocity field. Likewise, the turbulent magnetic diffusivity, ηt, is determined from the decay of a large scale magnetic field. In the kinematic regime, when the field is weak, the turbulent magnetic Prandtl number, νt/ηt, is about unity. When the field is nonhelical, ηt is quenched when magnetic and kinetic energies become comparable. For helical fields the quenching is stronger and can be described by a dynamical quenching formula. Key words. magnetohydrodynamics (MHD) – turbulence 1. Introduction however, this instability is suppressed (R¨udiger & Shalybkov 2002). On the other hand, the Reynolds number of the flow is The concept of turbulent diffusion is often invoked when mod- quite large (105 :::106) and the flow therefore most certainly eling large scale flows and magnetic fields in a turbulent turbulent. This led Noguchi et al. (2002) to invoke a turbulent medium. Turbulent magnetic diffusion is similar to turbulent kinematic viscosity, νt, but to retain the microscopic value of η. thermal diffusion which characterizes the turbulent exchange The resulting effective magnetic Prandtl number they used was 2 of patches of warm and cold gas. -
Arxiv:1904.00225V1 [Astro-Ph.SR] 30 Mar 2019 Bilities and Angular Momentum Transport
Draft version April 2, 2019 Typeset using LATEX twocolumn style in AASTeX62 Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos K. C. Augustson,1 A. S. Brun,1 and J. Toomre2 1AIM, CEA, CNRS, Universit´eParis-Saclay, Universit´eParis Diderot, Sarbonne Paris Cit´e,F-91191 Gif-sur-Yvette Cedex, France 2JILA & Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, Colorado, USA, 80309 ABSTRACT Rotational scaling relationships are examined for the degree of equipartition between magnetic and kinetic energies in stellar convection zones. These scaling relationships are approached from two paradigms, with first a glance at scaling relationship built upon an energy-balance argument and second a look at a force-based scaling. The latter implies a transition between a nearly-constant inertial scaling when in the asymptotic limit of minimal diffusion and magnetostrophy, whereas the former implies a weaker scaling with convective Rossby number. Both scaling relationships are then compared to a suite of 3D convective dynamo simulations with a wide variety of domain geometries, stratifications, and range of convective Rossby numbers. Keywords: Magnetohydrodynamics, Dynamo, Stars: magnetic field, rotation 1. INTRODUCTION an undertaking has been attempted in Emeriau-Viard Magnetic fields influence both the dynamics and evo- & Brun(2017). Alternatively, there exist several mod- lution of stars. Detecting such magnetic fields can be els of convection and its scaling with rotation rate and difficult given that the bulk of their energy resides be- magnetic field, which can provide an estimate of the ki- low the surface. Such magnetic fields are either gen- netic energy in convective regions. -
Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals
Metals 2015, 5, 289-335; doi:10.3390/met5010289 OPEN ACCESS metals ISSN 2075-4701 www.mdpi.com/journal/metals Article Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals Adolfo Ribeiro 1;*, Guillaume Fabre 1;2, Jean-Luc Guermond 3 and Jonathan M. Aurnou 1 1 Department of Earth, Planetary and Space Sciences, University of California, Los Angeles, CA 90095, USA; E-Mail: [email protected] 2 Laboratoire de Physique, École Normale Supérieure, Lyon 69007, France; E-Mail: [email protected] 3 Department of Mathematics, Texas A & M University, College Station, TX 77843, USA; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +1-310-467-6102. Academic Editor: Enrique Louis Received: 25 July 2014 / Accepted: 9 February 2015 / Published: 9 March 2015 Abstract: Planets and stars are often capable of generating their own magnetic fields. This occurs through dynamo processes occurring via turbulent convective stirring of their respective molten metal-rich cores and plasma-based convection zones. Present-day numerical models of planetary and stellar dynamo action are not carried out using fluids properties that mimic the essential properties of liquid metals and plasmas (e.g., using fluids with thermal Prandtl numbers P r < 1 and magnetic Prandtl numbers P m 1). Metal dynamo simulations should become possible, though, within the next decade. In order then to understand the turbulent convection phenomena occurring in geophysical or astrophysical fluids and next-generation numerical models thereof, we present here canonical, end-member examples of thermally-driven convection in liquid gallium, first with no magnetic field or rotation present, then with the inclusion of a background magnetic field and then in a rotating system (without an imposed magnetic field). -
Frequency Power Spectra of Global Quantities in Magnetoconvection
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 March 2021 Article Frequency power spectra of global quantities in magnetoconvection Sandip Das and Krishna Kumar* [1] Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India * Correspondence: [email protected] 1 Abstract: We present the results of direct numerical simulations of power spectral densities for 2 kinetic energy, convective entropy and heat flux for unsteady Rayleigh-Bénard magnetoconvection 3 in the frequency space. For larger values of frequency, the power spectral densities for all the −2 4 global quantities vary with frequency f as f . The scaling exponent is independent of Rayleigh 5 number, Chandrasekhar’s number and thermal Prandtl number. 6 Keywords: Magnetoconvection, Turbulent flow, Power spectral densities (PSD) 7 1. Introduction 8 The temporal fluctuations of spatially averaged (or, global) quantities are of interest 9 in several fields of research including turbulent flows [1–4], nanofluids [5], biological 10 fluids [6,7], geophysics [8,9], phase transitions [10,11]. The probability density function 11 (PDF) of the temporal fluctuations of thermal flux in turbulent Rayleigh-Bénard con- 12 vection (RBC) was found to have normal distribution with slight asymmetries at the 13 tails. The direct numerical simulations (DNS) of the Nusselt number Nu, which is a 14 measure of thermal flux, also showed the similar behaviour in presence of the Lorentz 15 force [12]. The power spectral density (PSD) of the thermal flux in the frequency ( f ) −2 16 space [3,12,13] was found to vary as f . In this work, we present the results obtained 17 by DNS of temporal signals of global quantities: spatially averaged kinetic energy per Citation: Das, S.; Kumar, K. -
Turbulent Viscosity and Magnetic Prandtl Number from Simulations of Isotropically Forced Turbulence P
Astronomy & Astrophysics manuscript no. paper c ESO 2020 February 18, 2020 Turbulent viscosity and magnetic Prandtl number from simulations of isotropically forced turbulence P. J. Kapyl¨ a¨1;2, M. Rheinhardt2, A. Brandenburg3;4;5;6, and M. J. Kapyl¨ a¨7;2 1 Georg-August-Universitat¨ Gottingen,¨ Institut fur¨ Astrophysik, Friedrich-Hund-Platz 1, D-37077 Gottingen,¨ Germany e-mail: [email protected] 2 ReSoLVE Centre of Excellence, Department of Computer Science, Aalto University, PO Box 15400, FI-00076 Aalto, Finland 3 Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden 4 Department of Astronomy, Stockholm University, SE-10691 Stockholm, Sweden 5 JILA and Department of Astrophysical and Planetary Sciences, Box 440, University of Colorado, Boulder, CO 80303, USA 6 Laboratory for Atmospheric and Space Physics, 3665 Discovery Drive, Boulder, CO 80303, USA 7 Max-Planck-Institut fur¨ Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Gottingen,¨ Germany Revision: 1.225 ABSTRACT Context. Turbulent diffusion of large-scale flows and magnetic fields plays a major role in many astrophysical systems, such as stellar convection zones and accretion discs. Aims. Our goal is to compute turbulent viscosity and magnetic diffusivity which are relevant for diffusing large-scale flows and mag- netic fields, respectively. We also aim to compute their ratio, which is the turbulent magnetic Prandtl number, Pmt, for isotropically forced homogeneous turbulence. Methods. We used simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity was computed either from the resulting Reynolds stress or from the decay rate of the large- scale flow. -
Thermal Convection Experiments in Liquid Metal Flows with and Without
Thermal convection experiments in liquid metal flows with and without magnetic field Dissertation zur Erlangung des akademischen Grades Doktoringenieur (Dr.-Ing.) vorgelegt der Fakultät für Maschinenbau der Technischen Universität Ilmenau von Herrn M.Sc. Till Zürner geboren am 1. Oktober 1990 in Dresden, Deutschland 1. Gutachter: Univ.-Prof. Dr. rer. nat. habil. Jörg Schumacher 2. Gutachter: Dr. rer. nat. Sven Eckert 3. Gutachter: Prof. Dr. Alban Pothérat Tag der Einreichung: 2. Juli 2019 Tag der wissenschaftlichen Aussprache: 12. November 2019 urn:nbn:de:gbv:ilm1-2019000433 Abstract The interaction of electrically conducting fluid flows with magnetic fields appears in numerous natural phenomena and technical applications. Since the relevant fluids – such as liquid metals and plasmas – are generally very hot, the flows are often accompanied or even driven by thermal convection. The study of this so-called magnetoconvection is thus of interest for a number of physical systems. Two aspects are investigated in this thesis. The first concerns the case when an imposed magnetic field does not alter the fluid flow. The second case explores the changes of the flow structure and global transport properties in the presence of strong magnetic fields. The first point is relevant for inductive measurement techniques, which are required to probe the flow without disturbing it. Here, the size of the fluid volume affected by a localised magnetic field is of major importance. This topic is investigated theoretically by deriving an algorithm to calculate the penetration depth of the magnetic field into the medium. This allows the prediction of a magnetic field strength, above which a flow is significantly disturbed.