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Stable three-dimensional vortex families consistent with Jovian observations including the Great Red Spot
- Aidi Zhang, Philip S. Marcus
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- Journal:
- Journal of Fluid Mechanics / Volume 984 / 10 April 2024
- Published online by Cambridge University Press:
- 12 April 2024, A61
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Detailed observations of the velocities of Jovian vortices exist at only one height in the atmosphere, so their vertical structures are poorly understood. This motivates this study that computes stable three-dimensional, long-lived planetary vortices that satisfy the equations of motion. We solve the anelastic equations with a high-resolution pseudo-spectral method using the observed Jovian atmospheric temperatures and zonal flow. We examine several families of vortices and find that constant-vorticity vortices, which have nearly uniform vorticity as a function of height, and horizontal areas that go to zero at their tops and bottoms, converge to stable vortices that look like the Great Red Spot (GRS) and other Jovian anticyclones. In contrast, the constant-area vortices proposed in previous studies, which have nearly uniform areas as a function of height, and vertical vorticities that go to zero at their tops and bottoms, are far from equilibrium, break apart, and converge to constant-vorticity vortices. Our late-time vortices show unexpected properties. Vortices that are initially non-hollow become hollow (i.e. have local minima of vertical vorticity at their centres), which is a feature of the GRS that cannot be explained with two-dimensional simulations. The central axes of the final vortices align with the planetary spin axis even if they align initially with the local direction of gravity. We present scaling laws for how vortex properties change with the Rossby number and other non-dimensional parameters. We prove analytically that the horizontal mid-plane of a stable vortex must lie at a height above the top of the convective zone.
Linear stability analysis of wake vortices by a spectral method using mapped Legendre functions
- Sangjoon Lee, Philip S. Marcus
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- Journal:
- Journal of Fluid Mechanics / Volume 967 / 25 July 2023
- Published online by Cambridge University Press:
- 11 July 2023, A2
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A spectral method using associated Legendre functions with algebraic mapping is developed for a linear stability analysis of wake vortices. These functions serve as Galerkin basis functions, capturing correct analyticity and boundary conditions for vortices in an unbounded domain. The incompressible Euler or Navier–Stokes equations linearised on a swirling flow are transformed into a standard matrix eigenvalue problem of toroidal and poloidal streamfunctions, solving perturbation velocity eigenmodes with their complex growth rate as eigenvalues. This reduces the problem size for computation and distributes collocation points adjustably clustered around the vortex core. Based on this method, strong swirling $q$ vortices with linear perturbation wavenumbers of order unity are examined. Without viscosity, neutrally stable eigenmodes associated with the continuous eigenvalue spectrum having critical-layer singularities are successfully resolved. The inviscid critical-layer eigenmodes numerically tend to appear in pairs, implying their singular degeneracy. With viscosity, the spectra pertaining to physical regularisation of critical layers stretch out toward an area, referring to potential eigenmodes with wavepackets found by Mao & Sherwin (J. Fluid Mech., vol. 681, 2011, pp. 1–23). However, the potential eigenmodes exhibit no spatial similarity to the inviscid critical-layer eigenmodes, doubting that they truly represent the viscous remnants of the inviscid critical-layer eigenmodes. Instead, two distinct continuous curves in the numerical spectra are identified for the first time, named the viscous critical-layer spectrum, where the similarity is noticeable. Moreover, the viscous critical-layer eigenmodes are resolved in conformity with the $Re^{-1/3}$ scaling law. The onset of the two curves is believed to be caused by viscosity breaking the singular degeneracy.
2 - The Centrality of Academic Self-Concept to Motivation and Learning
- from Part I - The Self and Its Impact
- K. Ann Renninger, Swarthmore College, Pennsylvania, Suzanne E. Hidi, University of Toronto
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- Book:
- The Cambridge Handbook of Motivation and Learning
- Published online:
- 15 February 2019
- Print publication:
- 14 February 2019, pp 36-62
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Summary
The construct of self-concept lies at the core of the positive psychology revolution. Historically, as one of the cornerstone constructs in the social sciences, the approach to self-concept has been adapted to focus on how healthy individuals can thrive in life. In this chapter we differentiate between the historical unidimensional perspective of self-concept (centered on self-esteem) and the evolving multifaceted models discriminating between different aspects of self (such as specific academic, social, physical, and emotional components).
We review:
the definition of self-concept and the reason it is so important;
historical and evolving perspectives of self-concept;
general and domain-specific theoretical models with associated empirical research regarding self-concept, motivation, and performance;
the way different self-concept domains vary as a function of gender and age;
the impact of specific psychological and social traits on self-concept development;
the differentiation between multidimensional perspectives of personality and self-concept;
theoretical models of academic self-concept formation and its relation to achievement;
frame of reference effects in self-concept formation;
a construct-validity approach to self-concept enhancement interventions; and directions for further research.
Stability of three-dimensional Gaussian vortices in an unbounded, rotating, vertically stratified, Boussinesq flow: linear analysis
- Mani Mahdinia, Pedram Hassanzadeh, Philip S. Marcus, Chung-Hsiang Jiang
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- Journal:
- Journal of Fluid Mechanics / Volume 824 / 10 August 2017
- Published online by Cambridge University Press:
- 05 July 2017, pp. 97-134
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The linear stability of three-dimensional vortices in rotating, stratified flows has been studied by analysing the non-hydrostatic inviscid Boussinesq equations. We have focused on a widely used model of geophysical and astrophysical vortices, which assumes an axisymmetric Gaussian structure for pressure anomalies in the horizontal and vertical directions. For a range of Rossby numbers ($-0.5<Ro<0.5$) and Burger numbers ($0.02<Bu<2.3$) relevant to observed long-lived vortices, the growth rate and spatial structure of the most unstable eigenmodes have been numerically calculated and presented as a function of $Ro{-}Bu$. We have found neutrally stable vortices only over a small region of the $Ro{-}Bu$ parameter space: cyclones with $Ro\sim 0.02{-}0.05$ and $Bu\sim 0.85{-}0.95$. However, we have also found that anticyclones in general have slower growth rates compared to cyclones. In particular, the growth rate of the most unstable eigenmode for anticyclones in a large region of the parameter space (e.g. $Ro<0$ and $0.5\lesssim Bu\lesssim 1.3$) is slower than 50 turnaround times of the vortex (which often corresponds to several years for ocean eddies). For cyclones, the region with such slow growth rates is confined to $0<Ro<0.1$ and $0.5\lesssim Bu\lesssim 1.3$. While most calculations have been done for $f/\bar{N}=0.1$ (where $f$ and $\bar{N}$ are the Coriolis and background Brunt–Väisälä frequencies), we have numerically verified and explained analytically, using non-dimensionalized equations, the insensitivity of the results to reducing $f/\bar{N}$ to the more ocean-relevant value of 0.01. The results of our stability analysis of Gaussian vortices both support and contradict the findings of earlier studies with QG or multilayer models or with other families of vortices. The results of this paper provide a stepping stone to study the more complicated problems of the stability of geophysical (e.g. those in the atmospheres of giant planets) and astrophysical vortices (in accretion disks).
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. Hull, Patricia Huntington, Thomas Hurka, Paul Hurley, Rosalind Hursthouse, Guillermo Hurtado, Ronald E. Hustwit, Sarah Hutton, Jonathan Jenkins Ichikawa, Harry A. Ide, David Ingram, Philip J. Ivanhoe, Alfred L. Ivry, Frank Jackson, Dale Jacquette, Joseph Jedwab, Richard Jeffrey, David Alan Johnson, Edward Johnson, Mark D. Jordan, Richard Joyce, Hwa Yol Jung, Robert Hillary Kane, Tomis Kapitan, Jacquelyn Ann K. Kegley, James A. Keller, Ralph Kennedy, Sergei Khoruzhii, Jaegwon Kim, Yersu Kim, Nathan L. King, Patricia Kitcher, Peter D. Klein, E. D. Klemke, Virginia Klenk, George L. Kline, Christian Klotz, Simo Knuuttila, Joseph J. Kockelmans, Konstantin Kolenda, Sebastian Tomasz Kołodziejczyk, Isaac Kramnick, Richard Kraut, Fred Kroon, Manfred Kuehn, Steven T. Kuhn, Henry E. Kyburg, John Lachs, Jennifer Lackey, Stephen E. Lahey, Andrea Lavazza, Thomas H. Leahey, Joo Heung Lee, Keith Lehrer, Dorothy Leland, Noah M. Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. Mendola, Christopher Menzel, Michael J. Meyer, Christian B. Miller, David W. Miller, Peter Millican, Robert N. Minor, Phillip Mitsis, James A. Montmarquet, Michael S. Moore, Tim Moore, Benjamin Morison, Donald R. Morrison, Stephen J. Morse, Paul K. Moser, Alexander P. D. Mourelatos, Ian Mueller, James Bernard Murphy, Mark C. Murphy, Steven Nadler, Jan Narveson, Alan Nelson, Jerome Neu, Samuel Newlands, Kai Nielsen, Ilkka Niiniluoto, Carlos G. Noreña, Calvin G. Normore, David Fate Norton, Nikolaj Nottelmann, Donald Nute, David S. Oderberg, Steve Odin, Michael O’Rourke, Willard G. Oxtoby, Heinz Paetzold, George S. Pappas, Anthony J. Parel, Lydia Patton, R. P. Peerenboom, Francis Jeffry Pelletier, Adriaan T. Peperzak, Derk Pereboom, Jaroslav Peregrin, Glen Pettigrove, Philip Pettit, Edmund L. Pincoffs, Andrew Pinsent, Robert B. Pippin, Alvin Plantinga, Louis P. Pojman, Richard H. Popkin, John F. Post, Carl J. Posy, William J. Prior, Richard Purtill, Michael Quante, Philip L. Quinn, Philip L. Quinn, Elizabeth S. Radcliffe, Diana Raffman, Gerard Raulet, Stephen L. Read, Andrews Reath, Andrew Reisner, Nicholas Rescher, Henry S. Richardson, Robert C. Richardson, Thomas Ricketts, Wayne D. Riggs, Mark Roberts, Robert C. Roberts, Luke Robinson, Alexander Rosenberg, Gary Rosenkranz, Bernice Glatzer Rosenthal, Adina L. Roskies, William L. Rowe, T. M. Rudavsky, Michael Ruse, Bruce Russell, Lilly-Marlene Russow, Dan Ryder, R. M. Sainsbury, Joseph Salerno, Nathan Salmon, Wesley C. Salmon, Constantine Sandis, David H. Sanford, Marco Santambrogio, David Sapire, Ruth A. Saunders, Geoffrey Sayre-McCord, Charles Sayward, James P. Scanlan, Richard Schacht, Tamar Schapiro, Frederick F. Schmitt, Jerome B. Schneewind, Calvin O. Schrag, Alan D. Schrift, George F. Schumm, Jean-Loup Seban, David N. Sedley, Kenneth Seeskin, Krister Segerberg, Charlene Haddock Seigfried, Dennis M. Senchuk, James F. Sennett, William Lad Sessions, Stewart Shapiro, Tommie Shelby, Donald W. Sherburne, Christopher Shields, Roger A. Shiner, Sydney Shoemaker, Robert K. Shope, Kwong-loi Shun, Wilfried Sieg, A. John Simmons, Robert L. Simon, Marcus G. Singer, Georgette Sinkler, Walter Sinnott-Armstrong, Matti T. Sintonen, Lawrence Sklar, Brian Skyrms, Robert C. Sleigh, Michael Anthony Slote, Hans Sluga, Barry Smith, Michael Smith, Robin Smith, Robert Sokolowski, Robert C. Solomon, Marta Soniewicka, Philip Soper, Ernest Sosa, Nicholas Southwood, Paul Vincent Spade, T. L. S. Sprigge, Eric O. Springsted, George J. Stack, Rebecca Stangl, Jason Stanley, Florian Steinberger, Sören Stenlund, Christopher Stephens, James P. Sterba, Josef Stern, Matthias Steup, M. A. Stewart, Leopold Stubenberg, Edith Dudley Sulla, Frederick Suppe, Jere Paul Surber, David George Sussman, Sigrún Svavarsdóttir, Zeno G. Swijtink, Richard Swinburne, Charles C. Taliaferro, Robert B. Talisse, John Tasioulas, Paul Teller, Larry S. Temkin, Mark Textor, H. S. Thayer, Peter Thielke, Alan Thomas, Amie L. Thomasson, Katherine Thomson-Jones, Joshua C. Thurow, Vzalerie Tiberius, Terrence N. Tice, Paul Tidman, Mark C. Timmons, William Tolhurst, James E. Tomberlin, Rosemarie Tong, Lawrence Torcello, Kelly Trogdon, J. D. Trout, Robert E. Tully, Raimo Tuomela, John Turri, Martin M. Tweedale, Thomas Uebel, Jennifer Uleman, James Van Cleve, Harry van der Linden, Peter van Inwagen, Bryan W. Van Norden, René van Woudenberg, Donald Phillip Verene, Samantha Vice, Thomas Vinci, Donald Wayne Viney, Barbara Von Eckardt, Peter B. M. Vranas, Steven J. Wagner, William J. Wainwright, Paul E. Walker, Robert E. Wall, Craig Walton, Douglas Walton, Eric Watkins, Richard A. Watson, Michael V. Wedin, Rudolph H. Weingartner, Paul Weirich, Paul J. Weithman, Carl Wellman, Howard Wettstein, Samuel C. Wheeler, Stephen A. White, Jennifer Whiting, Edward R. Wierenga, Michael Williams, Fred Wilson, W. Kent Wilson, Kenneth P. Winkler, John F. Wippel, Jan Woleński, Allan B. Wolter, Nicholas P. Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- Book:
- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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THE CONVENIENCE OF THE TYPESETTER; NOTATION AND TYPOGRAPHY IN FREGE’S GRUNDGESETZE DER ARITHMETIK
- J. J. GREEN, MARCUS ROSSBERG, PHILIP A. EBERT
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- Journal:
- Bulletin of Symbolic Logic / Volume 21 / Issue 1 / March 2015
- Published online by Cambridge University Press:
- 09 April 2015, pp. 15-30
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- March 2015
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We discuss the typography of the notation used by Gottlob Frege in his Grundgesetze der Arithmetik.
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- By Michael H. Allen, Leora Amira, Victoria Arango, David W. Ayer, Helene Bach, Christopher R. Bailey, Ross J. Baldessarini, Kelsey Ball, Alan L. Berman, Marian E. Betz, Emily A. Biggs, R. Warwick Blood, Kathleen T. Brady, David A. Brent, Jeffrey A. Bridge, Gregory K. Brown, Anat Brunstein Klomek, A. Jacqueline Buchanan, Michelle J. Chandley, Tim Coffey, Jessica Coker, Yeates Conwell, Scott J. Crow, Collin L. Davidson, Yogesh Dwivedi, Stacey Espaillat, Jan Fawcett, Steven J. Garlow, Robert D. Gibbons, Catherine R. Glenn, Deborah Goebert, Erica Goldstein, Tina R. Goldstein, Madelyn S. Gould, Kelly L. Green, Alison M. Greene, Philip D. Harvey, Robert M. A. Hirschfeld, Donna Holland Barnes, Andres M. Kanner, Gary J. Kennedy, Stephen H. Koslow, Benoit Labonté, Alison M. Lake, William B. Lawson, Steve Leifman, Adam Lesser, Timothy W. Lineberry, Amanda L. McMillan, Herbert Y. Meltzer, Michael Craig Miller, Michael J. Miller, James A. Naifeh, Katharine J. Nelson, Charles B. Nemeroff, Alexander Neumeister, Matthew K. Nock, Jennifer H. Olson-Madden, Gregory A. Ordway, Michael W. Otto, Ghanshyam N. Pandey, Giampaolo Perna, Jane Pirkis, Kelly Posner, Anne Rohs, Pedro Ruiz, Molly Ryan, Alan F. Schatzberg, S. Charles Schulz, M. Katherine Shear, Morton M. Silverman, April R. Smith, Marcus Sokolowski, Barbara Stanley, Zachary N. Stowe, Sarah A. Struthers, Leonardo Tondo, Gustavo Turecki, Robert J. Ursano, Kimberly Van Orden, Anne C. Ward, Danuta Wasserman, Jerzy Wasserman, Melinda K. Westlund, Tracy K. Witte, Kseniya Yershova, Alexandra Zagoloff, Sidney Zisook
- Edited by Stephen H. Koslow, University of Miami, Pedro Ruiz, University of Miami, Charles B. Nemeroff, University of Miami
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- Book:
- A Concise Guide to Understanding Suicide
- Published online:
- 05 October 2014
- Print publication:
- 18 September 2014, pp vii-x
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Notes on contributors
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- By James Eli Adams, Joseph Bristow, Oliver S. Buckton, Barbara Caine, Richard Cave, David Clifford, Harry Cocks, Matt Cook, Joseph Donohue, Richard Dorment, Sos Eltis, Helen Freshwater, Josephine M. Guy, Ellis Hanson, Merlin Holland, Russell Jackson, Jarlath Killeen, Leon Litvack, Ruth Livesey, Jerusha McCormack, Michèle Mendelssohn, Susan Owens, Kerry Powell, Steven Price, Peter Raby, Mark Ravenhill, John Paul Riquelme, Anthony Roche, Sean Ryder, Jan-Melissa Schramm, Ian Small, Philip E. Smith, Margaret D. Stetz, John Stokes, Mark W. Turner, Lynn Voskuil, Marcus Waithe
- Edited by Kerry Powell, Miami University, Peter Raby, Homerton College, Cambridge
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- Book:
- Oscar Wilde in Context
- Published online:
- 18 December 2013
- Print publication:
- 12 December 2013, pp xvi-xxii
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- By Diogo Almeida, Sergio Balari, Douglas Bemis, Antonio Benítez-Burraco, Derek Bickerton, Michal Biran, Cedric Boeckx, Ina Bornkessel-Schlesewsky, Jonathan Brennan, Perrine Brusini, Elodie Cauvet, Anne Christophe, Albert Costa, Dror Dotan, Naama Friedmann, Kleanthes K. Grohmann, Mireia Hernández, Gregory Hickok, William J. Idsardi, Lyle Jenkins, Simon Kirby, Ellen F. Lau, Jeffrey Lidz, Víctor M. Longa, Guillermo Lorenzo, Gary F. Marcus, Clara D. Martin, Brian McElree, James McGilvray, Jürgen M. Meisel, Séverine Millotte, Philip J. Monahan, Kazuo Okanoya, Lisa Pearl, Massimo Piattelli-Palmarini, Liina Pylkkänen, Cristina D. Rabaglia, Hugh Rabagliati, Matthias Schlesewsky, Núria Sebastián-Galles, Jon Sprouse, Ianthi Maria Tsimpli, Matthew Wagers, Ken Wexler, Klaus Zuberbühler
- Edited by Cedric Boeckx, Kleanthes K. Grohmann, University of Cyprus
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- Book:
- The Cambridge Handbook of Biolinguistics
- Published online:
- 05 May 2013
- Print publication:
- 14 February 2013, pp xiii-xiv
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The universal aspect ratio of vortices in rotating stratified flows: theory and simulation
- Pedram Hassanzadeh, Philip S. Marcus, Patrice Le Gal
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- Journal:
- Journal of Fluid Mechanics / Volume 706 / 10 September 2012
- Published online by Cambridge University Press:
- 25 May 2012, pp. 46-57
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We derive a relationship for the vortex aspect ratio (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt–Väisälä frequencies within the vortex and in the background fluid outside the vortex , the Coriolis parameter and the Rossby number of the vortex: . This relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and the background density gradient need not be uniform. Our relation for has many consequences for equilibrium vortices in rotating stratified flows. For example, cyclones must have ; weak anticyclones (with ) must have ; and strong anticyclones must have . We verify our relation for with numerical simulations of the three-dimensional Boussinesq equations for a wide variety of vortices, including: vortices that are initially in (dissipationless) equilibrium and then evolve due to an imposed weak viscous dissipation or density radiation; anticyclones created by the geostrophic adjustment of a patch of locally mixed density; cyclones created by fluid suction from a small localized region; vortices created from the remnants of the violent breakups of columnar vortices; and weakly non-axisymmetric vortices. The values of the aspect ratios of our numerically computed vortices validate our relationship for , and generally they differ significantly from the values obtained from the much-cited conjecture that in quasi-geostrophic vortices.
The universal aspect ratio of vortices in rotating stratified flows: experiments and observations
- Oriane Aubert, Michael Le Bars, Patrice Le Gal, Philip S. Marcus
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- Journal:
- Journal of Fluid Mechanics / Volume 706 / 10 September 2012
- Published online by Cambridge University Press:
- 25 May 2012, pp. 34-45
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We validate a new law for the aspect ratio of vortices in a rotating, stratified flow, where and are the vertical half-height and horizontal length scale of the vortices. The aspect ratio depends not only on the Coriolis parameter and buoyancy (or Brunt–Väisälä) frequency of the background flow, but also on the buoyancy frequency within the vortex and on the Rossby number of the vortex, such that . This law for is obeyed precisely by the exact equilibrium solution of the inviscid Boussinesq equations that we show to be a useful model of our laboratory vortices. The law is valid for both cyclones and anticyclones. Our anticyclones are generated by injecting fluid into a rotating tank filled with linearly stratified salt water. In one set of experiments, the vortices viscously decay while obeying our law for , which decreases over time. In a second set of experiments, the vortices are sustained by a slow continuous injection. They evolve more slowly and have larger while still obeying our law for . The law for is not only validated by our experiments, but is also shown to be consistent with observations of the aspect ratios of Atlantic meddies and Jupiter’s Great Red Spot and Oval BA. The relationship for is derived and examined numerically in a companion paper by Hassanzadeh, Marcus & Le Gal (J. Fluid Mech., vol. 706, 2012, pp. 46–57).
Contributors
- Edited by Fiona Ritchie, McGill University, Montréal, Peter Sabor, McGill University, Montréal
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- Book:
- Shakespeare in the Eighteenth Century
- Published online:
- 05 August 2012
- Print publication:
- 19 April 2012, pp ix-xi
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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. 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Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
- Published online:
- 05 August 2012
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- 20 September 2010, pp xi-xliv
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- By Susan E. Abbey, James J. Amos, Philip A. Bialer, James A. Bourgeois, Joanne A. Byars, Jaspreet Chahal, Kathy Coffman, Mary Ann Cohen, Catherine Crone, Carlos Fernandez-Robles, Jess G. Fiedorowicz, Mary J. Fitz-Gerald, Gregory Fricchione, Donna Greenberg, Thomas W. Heinrich, Debra R. Kahn, Raheel A. Khan, Robin C. Kopelman, Jeanne M. Lackamp, Joseph A. Locala, Michael Marcangelo, Laura Marsh, Anthony C. Miller, Romina Mizrahi, Megan Moore Brennan, Maryland Pao, John Querques, Davin Quinn, Vani Rao, Robert G. Robinson, Oludamilola Salami, Sanjeev Sockalingam, Sergio E. Starkstein, Scott Stuart, Adrienne Tan, Janeta Tansey, Scott Temple, Alex Thompson, Susan Turkel, Michelle Weckmann, Marcus Wellen, Thomas Wise
- Edited by James J. Amos, University of Iowa, Robert G. Robinson, University of Iowa
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- Psychosomatic Medicine
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- 04 August 2010
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- 27 May 2010, pp xi-xiv
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- By Phillip L. Ackerman, Neil Anderson, Jens B. Asendorpf, R. Michael Bagby, Michael Harris Bond, Gregory J. Boyle, Andrea L. Briggs, Giles St J. Burch, Turhan Canli, David Canter, Gianvittorio Caprara, Charles S. Carver, Douglas F. Cellar, Gordon Claridge, Susan Cloninger, Elisabeth D. Conradt, Philip J. Corr, Sharon Dawe, Ian J. Deary, Boele De Raad, Edward L. Deci, Colin G. DeYoung, M. Brent Donnellan, Juris G. Draguns, Marko Elovainio, Aurelio José Figueredo, David C. Funder, Paul Gladden, Rapson Gomez, Samuel D. Gosling, Jeremy R. Gray, Robert D. Hare, B. Austin Harley, Edward Helmes, Robert Hogan, Lauri A. Jensen-Campbell, Daniel Nelson Jones, Mika Kivimäki, Jennifer M. Knack, James T. Lamiell, Natalie J. Loxton, Geoff MacDonald, Gerald Matthews, Robert R. McCrae, Mario Mikulincer, Stephanie N. Mullins-Sweatt, Marcus R. Munafò, Vickie Nam, Craig S. Newmann, Rainer Reisenzein, Madeline Rex-Lear, Richard W. Robins, Michael D. Robinson, Mary K. Rothbart, Richard M. Ryan, Gerard Saucier, Michael F. Scheier, Constantine Sedikides, Phillip R. Shaver, Brad E. Sheese, Yuichi Shoda, Ronald E. Smith, Alice F. Stuhlmacher, Rhonda Swickert, Avril Thorne, David D. Vachon, Geneva Vásquez, Michele Vecchione, Seth A. Wagerman, Fiona Warren, Hannelore Weber, Thomas A. Widiger, Pedro Sofio Abril Wolf, Donna Youngs, Moshe Zeidner
- Edited by Philip J. Corr, University of East Anglia, Gerald Matthews, University of Cincinnati
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- The Cambridge Handbook of Personality Psychology
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- 05 June 2012
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- 16 July 2009, pp xv-xvii
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White-matter hyperintensities in first-episode psychosis
- Marcus V. Zanetti, Maristela S. Schaufelberger, Cláudio C. de Castro, Paulo R. Menezes, Márcia Scazufca, Philip K. McGuire, Robin M. Murray, Geraldo F. Busatto
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- The British Journal of Psychiatry / Volume 193 / Issue 1 / July 2008
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- 02 January 2018, pp. 25-30
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- July 2008
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Background
White-matter hyperintensities have been associated with both schizophrenia and mood disorders, particularly bipolar disorder, but results are inconsistent across studies
AimsTo examine whether white-matter hyperintensities are a vulnerability marker for psychosis or are specifically associated with bipolar disorder
MethodT2-weighted magnetic resonance imaging data were acquired in 129 individuals with first-episode psychosis (either affective or non-affective psychoses) and 102 controls who were randomly selected from the same geographical areas. Visual white-matter hyperintensity ratings were used for group and subgroup comparisons
ResultsThere were no statistically significant between-group differences in white-matter hyperintensity frequency or severity scores. No significant correlations were found between white-matter hyperintensity scores and duration of illness, duration of untreated psychosis, or severity of psychotic, manic or depressive symptoms
ConclusionsWhite-matter hyperintensities are not associated with vulnerability to psychosis in general, or specifically with affective psychoses. Further, first-episode psychosis investigations using more quantitative methods are warranted to confirm these findings
Structural brain abnormalities in individuals with an at-risk mental state who later develop psychosis
- Stefan J. Borgwardt, Philip K. McGuire, Jacqueline Aston, Gregor Berger, Paola Dazzan, Ute Gschwandtner, Marlon Pflüger, Marcus D'Souza, Ernst-Wilhelm Radue, Anita Riecher-Rössler
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- Journal:
- The British Journal of Psychiatry / Volume 191 / Issue S51 / December 2007
- Published online by Cambridge University Press:
- 02 January 2018, pp. s69-s75
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- December 2007
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Background
Neuroanatomical abnormalities are a well-established feature of schizophrenia. However, the timing of their emergence and the extent to which they are related to vulnerability to the disorder as opposed to psychotic illness itself is unclear
AimsTo assess regional grey matter volume in the at-risk individuals who subsequently developed psychosis
MethodMagnetic resonance imaging data from at-risk individuals who developed psychosis (n = 12) within the following 25 months were compared with data from healthy volunteers (n=22) and people with first-episode psychosis (n=25)
ResultsCompared with healthy volunteers, individuals who subsequently developed psychosis had smaller grey matter volume in the posterior cingulate gyrus, precuneus, and paracentral lobule bilaterally and in the left superior parietal lobule, and greater grey matter volume in a left parietal/posterior temporal region. Compared with first-episode patients, they had relatively greater grey matter volume in the temporal gyrus bilaterally and smaller grey matter volume in the right lentiform nucleus
ConclusionsSome of the structural brain abnormalities in individuals with an at-risk mental state may be related to an increased vulnerability to psychosis, while others are associated with the development of a psychotic illness
Vortex dynamics in a shearing zonal flow
- Philip S. Marcus
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- Journal:
- Journal of Fluid Mechanics / Volume 215 / June 1990
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- 26 April 2006, pp. 393-430
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When vortices are embedded in a shearing zonal flow their interactions are changed qualitatively. If the zonal flow's shear and the vortex's strength are of the same order and opposite sign, the vortex is pulled into a thin spiral, fragments, and is destroyed in a turn-around time. If the signs are the same, the vortex redistributes its vorticity so that its maximum value is at the centre, and its shape is determined by the ratio of its vorticity to the shear of the surrounding zonal flow. The dynamics depends crucially on the exchange between the self-energy of the vortices and the interaction energy of the zonal flow with the vortices. A numerical example that shows all of these effects is the breakup of a vortex layer: either a single large vortex is formed or successively smaller and more numerous thin filaments of vorticity are created. Two stable vortices are shown to merge if their initial separation in the cross-zonal direction is smaller than a critical distance which is approximately equal the vortices’ radii. The motions of large vortices are constrained by conservation laws, but when the zonal flow is filled with small-scale filaments of vorticity, the large vortices exchange energy with the filaments so that they are no longer constrained by these laws, and their dynamics become richer. Energy is shown to flow from the large vortices to the filaments, and this observation is used to predict the strength of boundary layers and the critical separation distance for vortex merging.
Simulation of flow between concentric rotating spheres. Part 1. Steady states
- Philip S. Marcus, Laurette S. Tuckerman
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- Journal:
- Journal of Fluid Mechanics / Volume 185 / December 1987
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- 21 April 2006, pp. 1-30
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Axisymmetric spherical Couette flow between two concentric differentially rotating spheres is computed numerically as an initial-value problem. The time-independent spherical Couette flows with zero, one and two Taylor vortices computed in our simulations are found to be reflection-symmetric about the equator despite the fact that our pseudospectral numerical method did not impose these properties. Our solutions are examined for self-consistency, compared with other numerical calculations, and tested against laboratory experiments. At present, the most precise laboratory measurements are those that measure Taylor-vortex size as a function of Reynolds number, and our agreement with these results is within a few per cent. We analyse our flows by plotting their meridional circulations, azimuthal angular velocities, and energy spectra. At Reynolds numbers just less than the critical value for the onset of Taylor vortices, we find that pinches develop in the flow in which the meridional velocity redistributes the angular momentum. Taylor vortices are easily differentiated from pinches because the fluid in a Taylor vortex is isolated from the rest of the fluid by a streamline that extends from the inner to the outer sphere, whereas the fluid in a pinch mixes with the rest of the flow.
Simulation of flow between concentric rotating spheres. Part 2. Transitions
- Philip S. Marcus, Laurette S. Tuckerman
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- Journal of Fluid Mechanics / Volume 185 / December 1987
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- 21 April 2006, pp. 31-65
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We examine the transitions among the steady-state axisymmetric spherical Couette flows with zero, one, and two vortices per hemisphere. The steady flows are reflection symmetric with respect to the equator, but some of the transitions that we find break this symmetry. This is the first study to reproduce numerically the transitions to the one-vortex flow from the zero- and two-vortex flows. In our study, we use a numerical initial-value code to: (i) compute the bifurcation diagrams of the steady (stable and unstable) states, (ii) solve for the most unstable or least stable linear eigenmode and eigenvalue of a steady state, (iii) calculate the velocity field as a function of time during both the linear and nonlinear stages of the transitions, and (iv) determine the energy transfer mechanism into and out of the antireflection-symmetric components of the flow during the transitions.
Our study provides the explanation of the laboratory observation that some transitions occur only when the inner sphere of the Couette-flow apparatus is accelerated or decelerated quickly, whereas other transitions occur only when the acceleration is slow.