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Topology of interacting coiled vortex rings
- Robert M. Kerr
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- Journal:
- Journal of Fluid Mechanics / Volume 854 / 10 November 2018
- Published online by Cambridge University Press:
- 03 September 2018, R2
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Pairs of nested vortex rings, one with coils, are evolved numerically to compare their topological numbers to those of recent experiments reported in Scheeler et al. (Science, vol. 357, 2017, pp. 487–491). Included are the twist $Tw$, writhe $Wr$ and self-linking ${\mathcal{L}}_{S}$ numbers, plus centreline helicities ${\mathcal{H}}_{c}$. The questions are: can the experimental numbers be validated and do these numbers have roles in the dynamics of the global helicities ${\mathcal{H}}$ and enstrophies $Z$ with respect to cascades? Topological analysis of the experiments $t=0$ analytic centreline vortex trajectories validates only the writhe measurements, not their values of $Tw$ and ${\mathcal{L}}_{S}$, which obey $Tw\lesssim {\mathcal{L}}_{S}=m\gg Wr$ for $m$-coil rings. Not $Tw\ll Wr$. To suggest why the large twists do not contribute to ${\mathcal{H}}$, it is noted that the mapping of the coiled rings onto the mesh is to a first approximation a single pair of Clebsch potentials, whose self-helicity ${\mathcal{H}}_{S}\equiv 0$. Numerical rings with circulations $\unicode[STIX]{x1D6E4}$, including some single rings, show small initial helicities with ${\mathcal{H}}(0)\approx {\mathcal{H}}_{c}\sim (\text{1 to 2})Wr\unicode[STIX]{x1D6E4}^{2}$$\ll {\mathcal{L}}_{S}\unicode[STIX]{x1D6E4}^{2}$. For time and velocity scales that are consistent with the experiments, as the coils evolve, their $Tw$, $Wr$, ${\mathcal{L}}_{S}$ numbers and their helicities are nearly static until reconnection. Nonetheless, $Wr$ and $Tw$ retain important complementary roles in the dynamics of the global helicity ${\mathcal{H}}$ and enstrophy $Z$, with the evolution of the torsion $\unicode[STIX]{x1D70F}(s)$ profile showing the beginnings of a cascade to small scales.
Enstrophy and circulation scaling for Navier–Stokes reconnection
- Robert M. Kerr
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- Journal:
- Journal of Fluid Mechanics / Volume 839 / 25 March 2018
- Published online by Cambridge University Press:
- 25 January 2018, R2
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As reconnection begins and the enstrophy $Z$ grows for two configurations, helical trefoil knots and anti-parallel vortices, two regimes of self-similar collapse are observed. First, during trefoil reconnection a new $\sqrt{\unicode[STIX]{x1D708}}Z$ scaling, where $\unicode[STIX]{x1D708}$ is viscosity, is identified before any $\unicode[STIX]{x1D716}=\unicode[STIX]{x1D708}Z$ dissipation scaling begins. Further rescaling shows linearly decreasing $B_{\unicode[STIX]{x1D708}}(t)=(\sqrt{\unicode[STIX]{x1D708}}Z)^{-1/2}$ at configuration-dependent crossing times $t_{x}$. Gaps in the vortex structures identify the $t_{x}$ as when reconnection ends and collapse onto $\unicode[STIX]{x1D708}$-independent curves can be obtained using $A_{\unicode[STIX]{x1D708}}(t)=(T_{c}(\unicode[STIX]{x1D708})-t_{x})(B_{\unicode[STIX]{x1D708}}(t)-B_{\unicode[STIX]{x1D708}}(t_{x}))$. The critical times $T_{c}(\unicode[STIX]{x1D708})$ are identified empirically by extrapolating the linear $B_{\unicode[STIX]{x1D708}}(t)$ regimes to $B_{\unicode[STIX]{x1D708}}^{{\sim}}(T_{c})=0$, yielding an $A_{\unicode[STIX]{x1D708}}(t)$ collapse that forms early as $\unicode[STIX]{x1D708}$ varies by 256. These solutions are regular or non-singular, as shown by decreasing cubic velocity norms $\Vert u\Vert _{L_{\ell }^{3}}^{}$. For the anti-parallel vortices, first there is an exchange of circulation, from $\unicode[STIX]{x1D6E4}_{y}(y=0)$ to $\unicode[STIX]{x1D6E4}_{z}(z=0)$, mediated by the viscous circulation exchange integral $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6E4}}(t)$, which is followed by a modified $B_{\unicode[STIX]{x1D708}}(t)$ collapse until the reconnection ends at $t_{x}$. Singular Leray scaling and mathematical bounds for higher-order Sobolev norms are used to help explain the origins of the new scaling and why the domain size $\ell$ has to increase to maintain the collapse of $A_{\unicode[STIX]{x1D708}}(t)$ and $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6E4}}$ as $\unicode[STIX]{x1D708}$ decreases.
X-Ray and Optical Properties of Black Widows and Redbacks
- Mallory S.E. Roberts, Hind Al Noori, Rodrigo A. Torres, Maura A. McLaughlin, Peter A. Gentile, Jason W.T. Hessels, Scott M. Ransom, Paul S. Ray, Matthew Kerr, Rene P. Breton
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- Journal:
- Proceedings of the International Astronomical Union / Volume 13 / Issue S337 / September 2017
- Published online by Cambridge University Press:
- 04 June 2018, pp. 43-46
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- September 2017
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Black widows and redbacks are binary systems consisting of a millisecond pulsar in a close binary with a companion having matter driven off of its surface by the pulsar wind. X-rays due to an intrabinary shock have been observed from many of these systems, as well as orbital variations in the optical emission from the companion due to heating and tidal distortion. We have been systematically studying these systems in radio, optical and X-rays. Here we will present an overview of X-ray and optical studies of these systems, including new XMM-Newton and NuStar data obtained from several of them, along with new optical photometry.
AUGUSTINE'S CANAANITES1
- Josephine Crawley Quinn, Neil McLynn, Robert M. Kerr, Daniel Hadas
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- Journal:
- Papers of the British School at Rome / Volume 82 / October 2014
- Published online by Cambridge University Press:
- 02 October 2014, pp. 175-197
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- October 2014
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There is a widespread idea that the people we call ‘Phoenician’ called themselves ‘Canaanite’. This article argues that the only positive evidence for this hypothesis, a single line in the standard editions of Augustine's unfinished commentary on Paul's letter to the Romans, where he claims that ‘if you ask our local peasants what they are, they answer ‘Canaanite’', is prima facie highly unreliable as historical evidence, and on closer inspection in fact is almost certainly an editorial error: our examination of all the manuscripts — the first to have been carried out — established that what the peasants were really asked in the archetype was not quid sint — ‘what they are’ — but quid sit — ‘what is it’, a phrase that would most obviously refer to their language. While this new reconstruction of the archetype does not necessarily mean that quid sit was what Augustine originally wrote, this passage cannot be used as positive evidence for Canaanite identity in late antique North Africa, or anywhere else.
Contributors
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- By John A. Bargh, Lisa Feldman Barrett, Veronica Benet-Martínez, Elliot T. Berkman, Jim Blascovich, Marilynn B. Brewer, Heining Cham, Tanya L. Chartrand, Robert B. Cialdini, William D. Crano, William A. Cunningham, Rick Dale, Jan De Houwer, Alice H. Eagly, J. Mark Eddy, Craig K. Enders, Leandre R. Fabrigar, Susan T. Fiske, Shelly L. Gable, Bertram Gawronski, Kevin J. Grimm, K. Paige Harden, Richard E. Heyman, Oliver P. John, Blair T. Johnson, Charles M. Judd, Deborah A. Kashy, David A. Kenny, Norbert L. Kerr, Nuri Kim, Jon A. Krosnick, Paul J. Lavrakas, Matthew D. Lieberman, Kristen A. Lindquist, Todd D. Little, Yu Liu, Michael F. Lorber, Michael R. Maniaci, Kerry L. Marsh, Gina L. Mazza, Gary H. McClelland, Dominique Muller, Elizabeth Levy Paluck, Karen S. Quigley, Harry T. Reis, Mijke Rhemtulla, Michael J. Richardson, Ronald D. Rogge, Alexander M. Schoemann, Eliot R. Smith, R. Scott Tindale, Eric Turkheimer, Penny S. Visser, Duane T. Wegener, Stephen G. West, Tessa V. West, Keith F. Widaman, Vincent Y. Yzerbyt
- Edited by Harry T. Reis, University of Rochester, New York, Charles M. Judd, University of Colorado Boulder
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- Book:
- Handbook of Research Methods in Social and Personality Psychology
- Published online:
- 05 June 2014
- Print publication:
- 24 February 2014, pp vii-viii
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Vorticity moments in four numerical simulations of the 3D Navier–Stokes equations
- Diego A. Donzis, John D. Gibbon, Anupam Gupta, Robert M. Kerr, Rahul Pandit, Dario Vincenzi
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- Journal:
- Journal of Fluid Mechanics / Volume 732 / 10 October 2013
- Published online by Cambridge University Press:
- 04 September 2013, pp. 316-331
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The issue of intermittency in numerical solutions of the 3D Navier–Stokes equations on a periodic box ${[0, L] }^{3} $ is addressed through four sets of numerical simulations that calculate a new set of variables defined by ${D}_{m} (t)= {({ \varpi }_{0}^{- 1} {\Omega }_{m} )}^{{\alpha }_{m} } $ for $1\leq m\leq \infty $ where ${\alpha }_{m} = 2m/ (4m- 3)$ and ${[{\Omega }_{m} (t)] }^{2m} = {L}^{- 3} \int \nolimits _{\mathscr{V}} {\vert \boldsymbol{\omega} \vert }^{2m} \hspace{0.167em} \mathrm{d} V$ with ${\varpi }_{0} = \nu {L}^{- 2} $. All four simulations unexpectedly show that the ${D}_{m} $ are ordered for $m= 1, \ldots , 9$ such that ${D}_{m+ 1} \lt {D}_{m} $. Moreover, the ${D}_{m} $ squeeze together such that ${D}_{m+ 1} / {D}_{m} \nearrow 1$ as $m$ increases. The values of ${D}_{1} $ lie far above the values of the rest of the ${D}_{m} $, giving rise to a suggestion that a depletion of nonlinearity is occurring which could be the cause of Navier–Stokes regularity. The first simulation is of very anisotropic decaying turbulence; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number respectively; the fourth is of very-high-Reynolds-number forced, stationary, isotropic turbulence at up to resolutions of $409{6}^{3} $.
Bounds for Euler from vorticity moments and line divergence
- Robert M. Kerr
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- Journal:
- Journal of Fluid Mechanics / Volume 729 / 25 August 2013
- Published online by Cambridge University Press:
- 24 July 2013, R2
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The inviscid growth of a range of vorticity moments is compared using Euler calculations of anti-parallel vortices with a new initial condition. The primary goal is to understand the role of nonlinearity in the generation of a new hierarchy of rescaled vorticity moments in Navier–Stokes calculations where the rescaled moments obey ${D}_{m} \geq {D}_{m+ 1} $, the reverse of the usual ${\Omega }_{m+ 1} \geq {\Omega }_{m} $ Hölder ordering of the original moments. Two temporal phases have been identified for the Euler calculations. In the first phase the $1\lt m\lt \infty $ vorticity moments are ordered in a manner consistent with the new Navier–Stokes hierarchy and grow in a manner that skirts the lower edge of possible singular growth with ${ D}_{m}^{2} \rightarrow \sup \vert \boldsymbol{\omega} \vert \sim A_{m}{({T}_{c} - t)}^{- 1} $ where the ${A}_{m} $ are nearly independent of $m$. In the second phase, the new ${D}_{m} $ ordering breaks down as the ${\Omega }_{m} $ converge towards the same super-exponential growth for all $m$. The transition is identified using new inequalities for the upper bounds for the $- \mathrm{d} { D}_{m}^{- 2} / \mathrm{d} t$ that are based solely upon the ratios ${D}_{m+ 1} / {D}_{m} $, and the convergent super-exponential growth is shown by plotting $\log (\mathrm{d} \log {\Omega }_{m} / \mathrm{d} t)$. Three-dimensional graphics show significant divergence of the vortex lines during the second phase, which could be what inhibits the initial power-law growth.
Contributors
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- By Giovanni Abbruzzese, Brooke Adair, Ana Aragon, Alfredo Berardelli, Belinda Bilney, David J. Brooks, Emma Campagna, Louise A. Corben, Mary Danoudis, Martin B. Delatycki, Georg Dirnberger, H. Kerr Graham, Ralph Hampson, Robert Iansek, Marjan Janahshahi, Lynette Joubert, Jill Kings, Sue Lord, Andres M. Lozano, Victor McConvey, Rachael McDonald, Jennifer L. McGinley, Kulthida Methawasin, Sarah Milne, Meg E. Morris, John Olver, Nicola Pavese, Alan Pearce, E. Diane Playford, Barry Rawicki, Nicole Rinehart, Lynn Rochester, Chloe Stanley-Cary, Antonio Suppa, Louis C. S. Tan, Siok Bee Tan, Deborah Theodoros, Pam Thomason, Travis S. Tierney, Daniele Volpe, Allison F. Williams, David R. Williams, Gavin Williams
- Edited by Robert Iansek, Monash University, Victoria, Meg E. Morris, La Trobe University, Victoria
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- Book:
- Rehabilitation in Movement Disorders
- Published online:
- 05 June 2013
- Print publication:
- 23 May 2013, pp viii-x
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2 - Structure and Dynamics of Vorticity in Turbulence
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- By Jörg Schumacher, Ilmenau University of Technology, Robert M. Kerr, University of Warwick, Kiyosi Horiuti, Tokyo Institute of Technology
- Edited by Peter A. Davidson, University of Cambridge, Yukio Kaneda, Katepalli R. Sreenivasan, New York University
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- Book:
- Ten Chapters in Turbulence
- Published online:
- 05 February 2013
- Print publication:
- 06 December 2012, pp 43-86
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Summary
Introduction
Ancient depictions of fluids, going back to the Minoans, envisaged waves and moving streams. They missed what we would call vortices and turbulence. The first artist to depict the rotational properties of fluids, vortical motion and turbulent flows was da Vinci (1506 to 1510). He would recognize the term vortical motion as it comes from the Latin vortere or vertere: to turn, meaning that vorticity is where a gas or liquid is rapidly turning or spiraling. Mathematically, one represents this effect as twists in the velocity derivative, that is the curl or the anti-symmetric component of the velocity gradient tensor. If the velocity field is u, then for the vorticity is ω = ∇ × u.
The aspect of turbulence which this chapter will focus upon is the structure, dynamics and evolution of vorticity in idealized turbulence – either the products of homogeneous, isotropic, statistically stationary states in forced, periodic simulations, or flows using idealized initial conditions designed to let us understand those states. The isotropic state is often viewed as a tangle of vorticity (at least when the amplitudes are large), an example of which is given in Fig. 2.1. This visualization shows isosurfaces of the magnitude of the vorticity, and similar techniques have been discussed before (see e.g. Pullin and Saffman, 1998; Ishihara et al., 2009; Tsinober, 2009). The goal of this chapter is to relate these graphics to basic relations between the vorticity and strain, to how this subject has evolved to using vorticity as a measure of regularity, then focus on the structure and dynamics of vorticity in turbulence, in experiments and numerical investigations, before considering theoretical explanations. Our discussions will focus upon three-dimensional turbulence.
Chandra observations of black widow pulsars
- P. Gentile, M. McLaughlin, M. Roberts, F. Camilo, J. Hessels, M. Kerr, S. Ransom, P. Ray, I. Stairs
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- Journal:
- Proceedings of the International Astronomical Union / Volume 8 / Issue S291 / August 2012
- Published online by Cambridge University Press:
- 20 March 2013, pp. 389-391
- Print publication:
- August 2012
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We describe the first X-ray observations of binary millisecond pulsars PSR J0023+0923, J1810+1744, J2215+5135, and J2256−1024. All are Fermi gamma-ray sources and three are ‘black-widow’ pulsars, with companions of mass < 0.1 M⊙. Data were taken using the Chandra X-Ray Observatory and covered a full binary orbit for each pulsar. PSRs J2215+5135 and J2256−1024, show significant orbital variability and X-ray flux minima coinciding with eclipses seen at radio wavelengths. This is consistent with intrabinary shock emission characteristic of black-widow pulsars. The other two pulsars, PSRs J0023+0923 and J1810+1744, do not demonstrate significant variability, but are fainter than the other two sources. Spectral fits yield power-law indices that range from 1.4 to 2.3 and blackbody temperatures in the hundreds of eV. The spectrum for PSR J2215+5135 shows a significant hard X-ray component (41% of counts are above 2 keV), which is additional evidence for the presence of intrabinary shock emission.
Contributors
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. Flowers, Carole Fontaine, David Ford, Mary Ford, Stephanie A. Ford, Jim Forest, William Franke, Robert M. Franklin, Ruth Franzén, Edward H. Friedman, Samuel Frouisou, Lorelei F. Fuchs, Jojo M. Fung, Inger Furseth, Richard R. Gaillardetz, Brandon Gallaher, China Galland, Mark Galli, Ismael García, Tharscisse Gatwa, Jean-Marie Gaudeul, Luis María Gavilanes del Castillo, Pavel L. Gavrilyuk, Volney P. Gay, Metropolitan Athanasios Geevargis, Kondothra M. George, Mary Gerhart, Simon Gikandi, Maurice Gilbert, Michael J. Gillgannon, Verónica Giménez Beliveau, Terryl Givens, Beth Glazier-McDonald, Philip Gleason, Menghun Goh, Brian Golding, Bishop Hilario M. Gomez, Michelle A. Gonzalez, Donald K. Gorrell, Roy Gottfried, Tamara Grdzelidze, Joel B. Green, Niels Henrik Gregersen, Cristina Grenholm, Herbert Griffiths, Eric W. Gritsch, Erich S. Gruen, Christoffer H. Grundmann, Paul H. Gundani, Jon P. Gunnemann, Petre Guran, Vidar L. Haanes, Jeremiah M. Hackett, Getatchew Haile, Douglas John Hall, Nicholas Hammond, Daphne Hampson, Jehu J. Hanciles, Barry Hankins, Jennifer Haraguchi, Stanley S. Harakas, Anthony John Harding, Conrad L. Harkins, J. William Harmless, Marjory Harper, Amir Harrak, Joel F. Harrington, Mark W. Harris, Susan Ashbrook Harvey, Van A. Harvey, R. Chris Hassel, Jione Havea, Daniel Hawk, Diana L. Hayes, Leslie Hayes, Priscilla Hayner, S. Mark Heim, Simo Heininen, Richard P. Heitzenrater, Eila Helander, David Hempton, Scott H. Hendrix, Jan-Olav Henriksen, Gina Hens-Piazza, Carter Heyward, Nicholas J. Higham, David Hilliard, Norman A. Hjelm, Peter C. Hodgson, Arthur Holder, M. Jan Holton, Dwight N. Hopkins, Ronnie Po-chia Hsia, Po-Ho Huang, James Hudnut-Beumler, Jennifer S. Hughes, Leonard M. Hummel, Mary E. Hunt, Laennec Hurbon, Mark Hutchinson, Susan E. Hylen, Mary Beth Ingham, H. Larry Ingle, Dale T. Irvin, Jon Isaak, Paul John Isaak, Ada María Isasi-Díaz, Hans Raun Iversen, Margaret C. Jacob, Arthur James, Maria Jansdotter-Samuelsson, David Jasper, Werner G. Jeanrond, Renée Jeffery, David Lyle Jeffrey, Theodore W. Jennings, David H. Jensen, Robin Margaret Jensen, David Jobling, Dale A. Johnson, Elizabeth A. Johnson, Maxwell E. Johnson, Sarah Johnson, Mark D. Johnston, F. Stanley Jones, James William Jones, John R. Jones, Alissa Jones Nelson, Inge Jonsson, Jan Joosten, Elizabeth Judd, Mulambya Peggy Kabonde, Robert Kaggwa, Sylvester Kahakwa, Isaac Kalimi, Ogbu U. Kalu, Eunice Kamaara, Wayne C. Kannaday, Musimbi Kanyoro, Veli-Matti Kärkkäinen, Frank Kaufmann, Léon Nguapitshi Kayongo, Richard Kearney, Alice A. Keefe, Ralph Keen, Catherine Keller, Anthony J. Kelly, Karen Kennelly, Kathi Lynn Kern, Fergus Kerr, Edward Kessler, George Kilcourse, Heup Young Kim, Kim Sung-Hae, Kim Yong-Bock, Kim Yung Suk, Richard King, Thomas M. King, Robert M. Kingdon, Ross Kinsler, Hans G. Kippenberg, Cheryl A. Kirk-Duggan, Clifton Kirkpatrick, Leonid Kishkovsky, Nadieszda Kizenko, Jeffrey Klaiber, Hans-Josef Klauck, Sidney Knight, Samuel Kobia, Robert Kolb, Karla Ann Koll, Heikki Kotila, Donald Kraybill, Philip D. W. Krey, Yves Krumenacker, Jeffrey Kah-Jin Kuan, Simanga R. Kumalo, Peter Kuzmic, Simon Shui-Man Kwan, Kwok Pui-lan, André LaCocque, Stephen E. Lahey, John Tsz Pang Lai, Emiel Lamberts, Armando Lampe, Craig Lampe, Beverly J. Lanzetta, Eve LaPlante, Lizette Larson-Miller, Ariel Bybee Laughton, Leonard Lawlor, Bentley Layton, Robin A. Leaver, Karen Lebacqz, Archie Chi Chung Lee, Marilyn J. Legge, Hervé LeGrand, D. L. LeMahieu, Raymond Lemieux, Bill J. Leonard, Ellen M. Leonard, Outi Leppä, Jean Lesaulnier, Nantawan Boonprasat Lewis, Henrietta Leyser, Alexei Lidov, Bernard Lightman, Paul Chang-Ha Lim, Carter Lindberg, Mark R. Lindsay, James R. Linville, James C. Livingston, Ann Loades, David Loades, Jean-Claude Loba-Mkole, Lo Lung Kwong, Wati Longchar, Eleazar López, David W. Lotz, Andrew Louth, Robin W. Lovin, William Luis, Frank D. Macchia, Diarmaid N. J. MacCulloch, Kirk R. MacGregor, Marjory A. MacLean, Donald MacLeod, Tomas S. Maddela, Inge Mager, Laurenti Magesa, David G. Maillu, Fortunato Mallimaci, Philip Mamalakis, Kä Mana, Ukachukwu Chris Manus, Herbert Robinson Marbury, Reuel Norman Marigza, Jacqueline Mariña, Antti Marjanen, Luiz C. L. Marques, Madipoane Masenya (ngwan'a Mphahlele), Caleb J. D. Maskell, Steve Mason, Thomas Massaro, Fernando Matamoros Ponce, András Máté-Tóth, Odair Pedroso Mateus, Dinis Matsolo, Fumitaka Matsuoka, John D'Arcy May, Yelena Mazour-Matusevich, Theodore Mbazumutima, John S. McClure, Christian McConnell, Lee Martin McDonald, Gary B. McGee, Thomas McGowan, Alister E. McGrath, Richard J. McGregor, John A. McGuckin, Maud Burnett McInerney, Elsie Anne McKee, Mary B. McKinley, James F. McMillan, Ernan McMullin, Kathleen E. McVey, M. Douglas Meeks, Monica Jyotsna Melanchthon, Ilie Melniciuc-Puica, Everett Mendoza, Raymond A. Mentzer, William W. Menzies, Ina Merdjanova, Franziska Metzger, Constant J. Mews, Marvin Meyer, Carol Meyers, Vasile Mihoc, Gunner Bjerg Mikkelsen, Maria Inêz de Castro Millen, Clyde Lee Miller, Bonnie J. Miller-McLemore, Alexander Mirkovic, Paul Misner, Nozomu Miyahira, R. W. L. Moberly, Gerald Moede, Aloo Osotsi Mojola, Sunanda Mongia, Rebeca Montemayor, James Moore, Roger E. Moore, Craig E. Morrison O.Carm, Jeffry H. Morrison, Keith Morrison, Wilson J. Moses, Tefetso Henry Mothibe, Mokgethi Motlhabi, Fulata Moyo, Henry Mugabe, Jesse Ndwiga Kanyua Mugambi, Peggy Mulambya-Kabonde, Robert Bruce Mullin, Pamela Mullins Reaves, Saskia Murk Jansen, Heleen L. Murre-Van den Berg, Augustine Musopole, Isaac M. T. Mwase, Philomena Mwaura, Cecilia Nahnfeldt, Anne Nasimiyu Wasike, Carmiña Navia Velasco, Thulani Ndlazi, Alexander Negrov, James B. Nelson, David G. Newcombe, Carol Newsom, Helen J. Nicholson, George W. E. Nickelsburg, Tatyana Nikolskaya, Damayanthi M. A. Niles, Bertil Nilsson, Nyambura Njoroge, Fidelis Nkomazana, Mary Beth Norton, Christian Nottmeier, Sonene Nyawo, Anthère Nzabatsinda, Edward T. Oakes, Gerald O'Collins, Daniel O'Connell, David W. Odell-Scott, Mercy Amba Oduyoye, Kathleen O'Grady, Oyeronke Olajubu, Thomas O'Loughlin, Dennis T. Olson, J. Steven O'Malley, Cephas N. Omenyo, Muriel Orevillo-Montenegro, César Augusto Ornellas Ramos, Agbonkhianmeghe E. Orobator, Kenan B. Osborne, Carolyn Osiek, Javier Otaola Montagne, Douglas F. Ottati, Anna May Say Pa, Irina Paert, Jerry G. Pankhurst, Aristotle Papanikolaou, Samuele F. Pardini, Stefano Parenti, Peter Paris, Sung Bae Park, Cristián G. Parker, Raquel Pastor, Joseph Pathrapankal, Daniel Patte, W. Brown Patterson, Clive Pearson, Keith F. Pecklers, Nancy Cardoso Pereira, David Horace Perkins, Pheme Perkins, Edward N. Peters, Rebecca Todd Peters, Bishop Yeznik Petrossian, Raymond Pfister, Peter C. 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- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Velocity, scalar and transfer spectra in numerical turbulence
- Robert M. Kerr
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- Journal of Fluid Mechanics / Volume 211 / February 1990
- Published online by Cambridge University Press:
- 26 April 2006, pp. 309-332
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Velocity and passive-scalar spectra for turbulent fields generated by a forced three-dimensional simulation with 1283 grid points and Taylor-microscale Reynolds numbers up to 83 are shown to have convective and diffusive spectral regimes. One-and three-dimensional spectra are compared with experiment and theory. If normalized by the Kolmogorov dissipation scales and scalar dissipation, velocity spectra and scalar spectra for given Prandtl numbers collapse to single curves in the dissipation regime with exponential tails. If multiplied by k⅗ the velocity spectra show an anomalously high Kolmogorov constant that is consistent with low Reynolds number experiments. When normalized by the Batchelor scales, the scalar spectra show a universal dissipation regime that is independent of Prandtl numbers from 0.1 to 1.0. The time development of velocity spectra is illustrated by energy-transfer spectra in which distinct pulses propagate to high wavenumbers.
Rayleigh number scaling in numerical convection
- Robert M. Kerr
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- Journal of Fluid Mechanics / Volume 310 / 10 March 1996
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- 26 April 2006, pp. 139-179
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Using direct simulations of the incompressible Navier-Stokes equations with rigid upper and lower boundaries at fixed temperature and periodic sidewalls, scaling with respect to Rayleigh number is determined. At large aspect ratio (6:6:1) on meshes up to 288 × 288 × 96, a single scaling regime consistent with the properties of ‘hard’ convective turbulence is found for Pr = 0.7 between Ra = 5 × 104 and Ra = 2 × 107. The properties of this regime include Nu ∼ RaβT with βT = 0.28 ≈ 2/7, exponential temperature distributions in the centre of the cell, and velocity and temperature scales consistent with experimental measurements. Two velocity boundary-layer thicknesses are identified, one outside the thermal boundary layer that scales as Ra−1/7 and the other within it that scales as Ra−3/7. Large-scale shears are not observed; instead, strong local boundary-layer shears are observed in regions between incoming plumes and an outgoing network of buoyant sheets. At the highest Rayleigh number, there is a decade where the energy spectra are close to k−5/3 and temperature variance spectra are noticeably less steep. It is argued that taken together this is good evidence for ‘hard’ turbulence, even if individually each of these properties might have alternative explanations.
Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence
- Robert M. Kerr
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- Journal:
- Journal of Fluid Mechanics / Volume 153 / April 1985
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- 20 April 2006, pp. 31-58
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In a three-dimensional simulation higher-order derivative correlations, including skewness and flatness (or kurtosis) factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. Up to 1283 grid points are used with periodic boundary conditions in all three directions to achieve Rλ to 82.9. The equations are forced to maintain steady-state turbulence and collect statistics. The scalar-derivative flatness is found to increase much faster with Reynolds number than the velocity-derivative flatness, and the velocity- and mixed-derivative skewnesses do not increase with Reynolds number. Separate exponents are found for the various fourth-order velocity-derivative correlations, with the vorticity-flatness exponent the largest. This does not support a major assumption of the lognormal and β models, but is consistent with some aspects of structural models of the small scales. Three-dimensional graphics show strong alignment between the vorticity, rate-of-strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short $-\frac{5}{3}$ spectral regime is observed.
Comparison of direct numerical simulations with predictions of two-point closures for isotropic turbulence convecting a passive scalar
- Jackson R. Herring, Robert M. Kerr
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- Journal:
- Journal of Fluid Mechanics / Volume 118 / May 1982
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- 20 April 2006, pp. 205-219
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Results of direct numerical simulations (DNS) for the decay of an initially Gaussian field of turbulence convecting a passive scalar are compared with equivalent results for the direct-interaction approximation (DIA) and the test-field model (TFM). The Taylor microscale Reynolds number Rλ and the equivalent Péclet number Pλ of the comparison ranged from 20–8 and 10–4, respectively. The Prandtl number Pr equals 0·5. Our results show a satisfactory agreement of both theories and numerical simulations, with the DIA giving better overall agreement, especially at small scales. This improved small-scale agreement - which appears to hold up to Rλ ≃ 30 - is related to the relatively long coherence times of the small scales, and to the fact that the TFM, containing as it does a built-in compliance to the fluctuation dissipation theorem, cannot properly cope with this fact. We also give a comparison of results for the velocity skewness with the experiments of Tavoularis, Bennett & Corrsin (1978).
Prandtl number dependence of Nusselt number in direct numerical simulations
- ROBERT M. KERR, JACKSON R. HERRING
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- Journal of Fluid Mechanics / Volume 419 / 25 September 2000
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- 20 October 2000, pp. 325-344
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The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr number is determined for 104 < Ra < 107 and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are calculated. For Nu there are good comparisons with experimental data and scaling laws for all the cases, including Ra2/7 laws at Pr = 0.7 and Pr = 7 and at low Pr, a Ra1/4 regime. Calculations at Pr = 0.3 predict a new Nu ∼ Ra2/7 regime at slightly higher Ra than the Pr = 0.07 calculations reported here and the mercury Pr = 0.025 experiments.