27 results
A numerical study of turbulence under temporally evolving axisymmetric contraction and subsequent relaxation
- M. P. Clay, P. K. Yeung
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- Journal:
- Journal of Fluid Mechanics / Volume 805 / 25 October 2016
- Published online by Cambridge University Press:
- 22 September 2016, pp. 460-493
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Direct numerical simulations using up to $4096^{3}$ grid points on a deforming domain have been used to study the response of initially isotropic turbulence to a period of spatially uniform axisymmetric contraction (with one extensional and two equally compressive directions) and subsequent relaxation. A time-dependent strain rate is formulated to closely correspond to the downstream evolution in the wind tunnel experiments of Ayyalasomayajula & Warhaft (J. Fluid Mech., vol. 566, 2006, pp. 273–307), with a smoothly varying 4 : 1 contraction ratio. The application of strain leads to anisotropy in both the large scales and the small scales, in a manner where nonlinear effects not considered in rapid-distortion theory play an important role. Upon termination of strain, the small scales quickly return to isotropy while a residual level of anisotropy appears to persist at the large scales. The simulations are shown to reproduce many key findings from experiments, including distinctive changes in the form of the one-dimensional spectra in the extensional direction that arise at sufficiently high Reynolds number, during both the straining and relaxation periods. Scale-dependent measures of anisotropy are presented in terms of one-dimensional spectra and axisymmetric versions of the energy spectrum. To explain the observed changes in spectral shapes, various terms in the spectral evolution equation representing rapid pressure strain, slow pressure strain, production, nonlinear transfer and viscous dissipation are computed, showing that nonlinear effects take a dominant role when a wide range of scales exists. In particular, the ‘double-peak’ spectral form observed in experiments at high Reynolds number is found to be a consequence of the small scales relaxing towards isotropy much faster than the large scales. A comparison of results obtained from computational domains of varying sizes and grid resolutions show that the numerical findings are robust.
A Lagrangian study of turbulent mixing: forward and backward dispersion of molecular trajectories in isotropic turbulence
- D. Buaria, P. K. Yeung, B. L. Sawford
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- Journal:
- Journal of Fluid Mechanics / Volume 799 / 25 July 2016
- Published online by Cambridge University Press:
- 23 June 2016, pp. 352-382
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Statistics of the trajectories of molecules diffusing via Brownian motion in a turbulent flow are extracted from simulations of stationary isotropic turbulence, using a postprocessing approach applicable in both forward and backward reference frames. Detailed results are obtained for Schmidt numbers ($Sc$) from 0.001 to 1000 at Taylor-scale Reynolds numbers up to 1000. The statistics of displacements of single molecules compare well with the earlier theoretical work of Saffman (J. Fluid Mech. vol. 8, 1960, pp. 273–283) except for the scaling of the integral time scale of the fluid velocity following the molecular trajectories. For molecular pairs we extend Saffman’s theory to include pairs of small but finite initial separation, which is in excellent agreement with numerical results provided that data are collected at sufficiently small times. At intermediate times the separation statistics of molecular pairs exhibit a more robust Richardson scaling behaviour than for the fluid particles. The forward scaling constant is very close to 0.55, whereas the backward constant is approximately 1.53–1.57, with a weak Schmidt number dependence, although no scaling exists if $Sc\ll 1$ at the Reynolds numbers presently accessible. An important innovation in this work is to demonstrate explicitly the practical utility of a Lagrangian description of turbulent mixing, where molecular displacements and separations in the limit of small backward initial separation can be used to calculate the evolution of scalar fluctuations resulting from a known source function in space. Lagrangian calculations of the production and dissipation rates of the scalar fluctuations are shown to agree very well with Eulerian results for the case of passive scalars driven by a uniform mean gradient. Although the Eulerian–Lagrangian comparisons are made only for $Sc\sim O(1)$, the Lagrangian approach is more easily extended to both very low and very high Schmidt numbers. The well-known scalar dissipation anomaly is accordingly also addressed in a Lagrangian context.
B.03 The Canadian neurology graduate survey
- BJ Murray, P Major, A Poppe, C Murphy, M Jenkins, M Nicolle, C Watling, HJ McMillan, M Yeung, D Callen, H Briemberg, DF Tang-Wai, C De Meulemeester, P Brna, M Savard, D Sahlas, A Yeh, G Gubitz, F Moore, K Khan, K Squarey, C Deacon, M Esser, R Vosoughi, S Taylor, S Weiss, E Hollenberg
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- Journal:
- Canadian Journal of Neurological Sciences / Volume 43 / Issue S2 / June 2016
- Published online by Cambridge University Press:
- 17 June 2016, pp. S9-S10
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Background: Planning for neurology training necessitated a reflection on the experience of graduates. We explored practice characteristics, and training experience of recent graduates. Methods: Graduates from 2010-2014 completed a survey. Results: Response rate was 37% of 211. 56% were female. 91% were adult neurologists. 65% practiced in an outpatient setting. 63% worked in academics. 85% completed subspecialty training (median 1 year). 36% work 3 days a week or less. 82% took general call (median 1 night weekly). Role preparation was considered very good or excellent for most; however poor or fair ratings were 17% in advocacy and 8% in leadership. Training feedback was at least “good” for 87%. Burnout a few times a week or more was noted by 5% (6% during residency, particularly PGY1 and 5). 64% felt overly burdened by paperwork. Although most felt training was adequate, it was poor or fair at preparing for practice management (85%) and personal balance (55%). Most conditions were under-observed in training environment. Many noted a need for more independent practice development and community neurology. Conclusions: Although our training was found to be very good, some identified needs included advocacy training, and more training in general neurology in the longitudinal outpatient/community settings.
Abnormalities in left inferior frontal gyral thickness and parahippocampal gyral volume in young people at high genetic risk for bipolar disorder
- G. Roberts, R. Lenroot, A. Frankland, P. K. Yeung, N. Gale, A. Wright, P. Lau, F. Levy, W. Wen, P. B. Mitchell
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- Journal:
- Psychological Medicine / Volume 46 / Issue 10 / July 2016
- Published online by Cambridge University Press:
- 12 April 2016, pp. 2083-2096
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Background
Fronto-limbic structural brain abnormalities have been reported in patients with bipolar disorder (BD), but findings in individuals at increased genetic risk of developing BD have been inconsistent. We conducted a study in adolescents and young adults (12–30 years) comparing measures of fronto-limbic cortical and subcortical brain structure between individuals at increased familial risk of BD (at risk; AR), subjects with BD and controls (CON). We separately examined cortical volume, thickness and surface area as these have distinct neurodevelopmental origins and thus may reflect differential effects of genetic risk.
MethodWe compared fronto-limbic measures of grey and white matter volume, cortical thickness and surface area in 72 unaffected-risk individuals with at least one first-degree relative with bipolar disorder (AR), 38 BD subjects and 72 participants with no family history of mental illness (CON).
ResultsThe AR group had significantly reduced cortical thickness in the left pars orbitalis of the inferior frontal gyrus (IFG) compared with the CON group, and significantly increased left parahippocampal gyral volume compared with those with BD.
ConclusionsThe finding of reduced cortical thickness of the left pars orbitalis in AR subjects is consistent with other evidence supporting the IFG as a key region associated with genetic liability for BD. The greater volume of the left parahippocampal gyrus in those at high risk is in line with some prior reports of regional increases in grey matter volume in at-risk subjects. Assessing multiple complementary morphometric measures may assist in the better understanding of abnormal developmental processes in BD.
Contributors
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- By Francesco Acerbi, Ayca Akgoz, Matthew R. Amans, Ramsey Ashour, Mohammed Ali Aziz-Sultan, H. Hunt Batjer, Donnie Bell, Bernard R. Bendok, Giovanni Broggi, Morgan Broggi, Charles A. Bruno, Steven D. Chang, In Sup Choi, Omar Choudhri, Douglas J. Cook, William P. Dillon, Peter Dirks, Rose Du, Travis M. Dumont, Tarek Y. El Ahmadieh, Najib E. El Tecle, Mohamed Samy Elhammady, Paolo Ferroli, Alana M. Flexman, John C. Flickinger, Kai U. Frerichs, Sasikhan Geibprasert, Adrian W. Gelb, Y. Pierre Gobin, Bradley A. Gross, Seunggu J. Han, Tomoki Hashimoto, Juha Hernesniemi, Roberto C. Heros, Steven W. Hetts, Randall T. Higashida, Joshua A. Hirsch, Nikolai J. Hopf, L. Nelson Hopkins, Maziyar A. Kalani, M. Yashar S. Kalani, Hideyuki Kano, Syed Aftab Karim, Robert M. Koffie, Douglas S. Kondziolka, Timo Krings, Aki Laakso, Giuseppe Lanzino, Michael T. Lawton, Elad I. Levy, L. Dade Lunsford, Adel M. Malek, Michael P. Marks, George A. C. Mendes, Philip M. Meyers, Jacques Morcos, Nitin Mukerji, Christian Musahl, Ludmila Pawlikowska, Matthew B. Potts, Ross Puffer, James D. Rabinov, Jonathan J. Russin, Mina G. Safain, Duke Samson, Marco Schiariti, R. Michael Scott, Jason P. Sheehan, Paul Singh, Edward R. Smith, Scott G. Soltys, Robert F. Spetzler, Gary K. Steinberg, Philip E. Stieg, Hua Su, Karel terBrugge, Kiron Thomas, Tarik Tihan, Babu Welch, Jonathan White, H. Richard Winn, Chun-Po Yen, Jacky T. Yeung, Byron Yip, Samer G. Zammar
- Edited by Robert F. Spetzler, Douglas S. Kondziolka, Randall T. Higashida, University of California, San Francisco, M. Yashar S. Kalani
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- Book:
- Comprehensive Management of Arteriovenous Malformations of the Brain and Spine
- Published online:
- 05 January 2015
- Print publication:
- 08 January 2015, pp x-xiv
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- By Mowaffaq Almikhlafi, Osama Al-muslim, Robert Arntfield, Ian M Ball, Sue Berney, Mohit Bhutani, Clay A Block, Ken Blonde, Rudi Brits, Ron Butler, Lois Champion, Chris Clarke, Linda Denehy, Joseph Dreier, A Ebersohn, Shane W English, Ari Ercole, Darren H Freed, John Fuller, Julio P Zavala Georffino, RT Noel Gibney, Jeff Granton, Donald EG Griesdale, Arun K Gupta, Wael Haddara, Ahmed F Hegazy, Umjeet Singh Jolly, Philip M Jones, Ilya Kagan, Kala Kathirgamanathan, Harneet Kaur, John Kellett, Bhupesh Khadka, Biniam Kidane, Carlos Kidel, Anand Kumar, Alejandro Lazo-Langner, David Leasa, W Robert Leeper, Stephen Y Liang, Tania Ligori, Jaimie Manlucu, Janet Martin, Ian McConachie, Alan McGlennan, Lauralyn McIntyre, Tina Mele, MJ Naisbitt, Raj Nichani, Daniel H Ovakim, Neil Parry, Daniel Castro Pereira, Thomas Piraino, Brian Pollard, Valerie Schulz, Michael D Sharpe, Rohit K Singal, Pierre Singer, Mark Soth, Christian P Subbe, Jaffer Syed, Ravi Taneja, Tom Varughese, Jennifer Vergel Del Dios, Jessie R Welbourne, Christopher W White, Rebecca P Winsett, Titus C Yeung, G Bryan Young, Shelley R Zieroth
- Edited by John Fuller, University of Western Ontario, Jeff Granton, University of Western Ontario, Ian McConachie, University of Western Ontario
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- Book:
- Handbook of ICU Therapy
- Published online:
- 05 February 2015
- Print publication:
- 04 December 2014, pp vii-xii
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Spectrum of passive scalars of high molecular diffusivity in turbulent mixing
- P. K. Yeung, K. R. Sreenivasan
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- Journal:
- Journal of Fluid Mechanics / Volume 716 / 10 February 2013
- Published online by Cambridge University Press:
- 28 January 2013, R14
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We consider the mixing of passive scalars transported in turbulent flow, with a molecular diffusivity that is large compared to the kinematic viscosity of the fluid. This particular case of mixing has not received much attention in experiment or simulation even though the first putative theory, due to Batchelor, Howells & Townsend (J. Fluid Mech., vol. 5, 1959, pp. 134–139), is now more than 50 years old. We study the problem using direct numerical simulation of decaying scalar fields in steadily sustained homogeneous turbulence as the Schmidt number (the ratio of the kinematic viscosity of the fluid to the molecular diffusivity of the scalar) is allowed to vary from $1/ 8$ to $1/ 2048$ for two values of the microscale Reynolds number, ${R}_{\lambda } \approx 140$ and $\approx $240. The simulations show that the passive scalar spectrum assumes a slope of $- 17/ 3$ in a range of scales, as predicted by the theory, when the Schmidt number is small and the Reynolds number is simultaneously large. The observed agreement between theory and simulation in the prefactor in the spectrum is not perfect. We assess the reasons for this discrepancy by a careful examination of the scalar evolution equation in the light of the assumptions of the theory, and conclude that the finite range of scales resolved in simulations is the main reason. Numerical issues specific to the regime of very low Schmidt numbers are also addressed briefly.
Dissipation, enstrophy and pressure statistics in turbulence simulations at high Reynolds numbers
- P. K. Yeung, D. A. Donzis, K. R. Sreenivasan
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- Journal:
- Journal of Fluid Mechanics / Volume 700 / 10 June 2012
- Published online by Cambridge University Press:
- 08 February 2012, pp. 5-15
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We use data from well-resolved direct numerical simulations at Taylor-scale Reynolds numbers from 140 to 1000 to study the statistics of energy dissipation rate and enstrophy density (i.e. the square of local vorticity). Despite substantial variability in each of these variables, their extreme events not only scale in a similar manner but also progressively tend to occur spatially together as the Reynolds number increases. Though they possess non-Gaussian tails of enormous amplitudes, ratios of some characteristic properties can be closely linked to those of isotropic Gaussian random fields. We present results also on statistics of the pressure Laplacian and conditional mean pressure given both dissipation and enstrophy. At low Reynolds number intense negative pressure fluctuations are preferentially associated with rotation-dominated regions but at high Reynolds number both high dissipation and high enstrophy have similar effects.
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. Phan, Isabel Apawo Phiri, William S. F. Pickering, Derrick G. Pitard, William Elvis Plata, Zlatko Plese, John Plummer, James Newton Poling, Ronald Popivchak, Andrew Porter, Ute Possekel, James M. Powell, Enos Das Pradhan, Devadasan Premnath, Jaime Adrían Prieto Valladares, Anne Primavesi, Randall Prior, María Alicia Puente Lutteroth, Eduardo Guzmão Quadros, Albert Rabil, Laurent William Ramambason, Apolonio M. Ranche, Vololona Randriamanantena Andriamitandrina, Lawrence R. Rast, Paul L. Redditt, Adele Reinhartz, Rolf Rendtorff, Pål Repstad, James N. Rhodes, John K. Riches, Joerg Rieger, Sharon H. Ringe, Sandra Rios, Tyler Roberts, David M. Robinson, James M. Robinson, Joanne Maguire Robinson, Richard A. H. Robinson, Roy R. Robson, Jack B. Rogers, Maria Roginska, Sidney Rooy, Rev. Garnett Roper, Maria José Fontelas Rosado-Nunes, Andrew C. Ross, Stefan Rossbach, François Rossier, John D. Roth, John K. Roth, Phillip Rothwell, Richard E. Rubenstein, Rosemary Radford Ruether, Markku Ruotsila, John E. Rybolt, Risto Saarinen, John Saillant, Juan Sanchez, Wagner Lopes Sanchez, Hugo N. Santos, Gerhard Sauter, Gloria L. Schaab, Sandra M. Schneiders, Quentin J. Schultze, Fernando F. Segovia, Turid Karlsen Seim, Carsten Selch Jensen, Alan P. F. Sell, Frank C. Senn, Kent Davis Sensenig, Damían Setton, Bal Krishna Sharma, Carolyn J. Sharp, Thomas Sheehan, N. Gerald Shenk, Christian Sheppard, Charles Sherlock, Tabona Shoko, Walter B. Shurden, Marguerite Shuster, B. Mark Sietsema, Batara Sihombing, Neil Silberman, Clodomiro Siller, Samuel Silva-Gotay, Heikki Silvet, John K. Simmons, Hagith Sivan, James C. Skedros, Abraham Smith, Ashley A. Smith, Ted A. Smith, Daud Soesilo, Pia Søltoft, Choan-Seng (C. S.) Song, Kathryn Spink, Bryan Spinks, Eric O. Springsted, Nicolas Standaert, Brian Stanley, Glen H. Stassen, Karel Steenbrink, Stephen J. Stein, Andrea Sterk, Gregory E. Sterling, Columba Stewart, Jacques Stewart, Robert B. Stewart, Cynthia Stokes Brown, Ken Stone, Anne Stott, Elizabeth Stuart, Monya Stubbs, Marjorie Hewitt Suchocki, David Kwang-sun Suh, Scott W. Sunquist, Keith Suter, Douglas Sweeney, Charles H. Talbert, Shawqi N. Talia, Elsa Tamez, Joseph B. Tamney, Jonathan Y. Tan, Yak-Hwee Tan, Kathryn Tanner, Feiya Tao, Elizabeth S. Tapia, Aquiline Tarimo, Claire Taylor, Mark Lewis Taylor, Bishop Abba Samuel Wolde Tekestebirhan, Eugene TeSelle, M. Thomas Thangaraj, David R. Thomas, Andrew Thornley, Scott Thumma, Marcelo Timotheo da Costa, George E. “Tink” Tinker, Ola Tjørhom, Karen Jo Torjesen, Iain R. Torrance, Fernando Torres-Londoño, Archbishop Demetrios [Trakatellis], Marit Trelstad, Christine Trevett, Phyllis Trible, Johannes Tromp, Paul Turner, Robert G. Tuttle, Archbishop Desmond Tutu, Peter Tyler, Anders Tyrberg, Justin Ukpong, Javier Ulloa, Camillus Umoh, Kristi Upson-Saia, Martina Urban, Monica Uribe, Elochukwu Eugene Uzukwu, Richard Vaggione, Gabriel Vahanian, Paul Valliere, T. J. Van Bavel, Steven Vanderputten, Peter Van der Veer, Huub Van de Sandt, Louis Van Tongeren, Luke A. Veronis, Noel Villalba, Ramón Vinke, Tim Vivian, David Voas, Elena Volkova, Katharina von Kellenbach, Elina Vuola, Timothy Wadkins, Elaine M. Wainwright, Randi Jones Walker, Dewey D. Wallace, Jerry Walls, Michael J. Walsh, Philip Walters, Janet Walton, Jonathan L. Walton, Wang Xiaochao, Patricia A. Ward, David Harrington Watt, Herold D. Weiss, Laurence L. Welborn, Sharon D. Welch, Timothy Wengert, Traci C. West, Merold Westphal, David Wetherell, Barbara Wheeler, Carolinne White, Jean-Paul Wiest, Frans Wijsen, Terry L. Wilder, Felix Wilfred, Rebecca Wilkin, Daniel H. Williams, D. Newell Williams, Michael A. Williams, Vincent L. Wimbush, Gabriele Winkler, Anders Winroth, Lauri Emílio Wirth, James A. Wiseman, Ebba Witt-Brattström, Teofil Wojciechowski, John Wolffe, Kenman L. Wong, Wong Wai Ching, Linda Woodhead, Wendy M. Wright, Rose Wu, Keith E. Yandell, Gale A. 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
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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X-Ray Mapping and Analysis of the Interfacial Region of Kiln Cast Composites
- T Lucey, P Huggett, R Wuhrer, K Moran, W Yeung
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- Microscopy and Microanalysis / Volume 16 / Issue S2 / July 2010
- Published online by Cambridge University Press:
- 01 August 2010, pp. 1674-1675
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- July 2010
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Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 – August 5, 2010.
Methods for enumerating Escherichia coli in subtropical waters
- W. H. S. Cheung, D. K. K. Ha, K. Y. Yeung, R. P. S. Hung
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- Epidemiology & Infection / Volume 106 / Issue 2 / April 1991
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- 15 May 2009, pp. 345-354
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The standard membrane filtration method of the UK has been modified in order to improve its specificity for enumerating Escherichia coli in the subtropical waters of Hong Kong. This involves incorporating into the membrane lauryl sulphate (mLS) method either an in situ urease test (the mLS-UA method), or an in situ β-glucuronidase test (the mLS-GUD method). The false-positive errors of the mLS-UA and mLS-GUD methods are low, ranging from 3–5%. A comparison between the membrane filtration (mLS-UA) method and the multiple tube technique in testing E. coli in subtropical beach-waters has demonstrated that the former can give much more precise counts, and is the method of choice for such a purpose. The mLS-GUD method, for which automated counting of E. coli colonies is possible, is a good alternative to mLS-UA in routine enumeration of this bacterial indicator in environmental waters.
Lagrangian conditional statistics, acceleration and local relative motion in numerically simulated isotropic turbulence
- P. K. YEUNG, S. B. POPE, E. A. KURTH, A. G. LAMORGESE
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- Journal of Fluid Mechanics / Volume 582 / 10 July 2007
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- 14 June 2007, pp. 399-422
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Lagrangian statistics of fluid-particle velocity and acceleration conditioned on fluctuations of dissipation, enstrophy and pseudo-dissipation representing different characteristics of local relative motion are extracted from a direct numerical simulation database of stationary (forced) homogeneous isotropic turbulence. The grid resolution in the simulations is up to 20483, and the Taylor-scale Reynolds number ranges from about 40 to 650, where characteristics of small-scale intermittency in the Eulerian flow field are well developed. A key joint statistic of the conditioning variables is the dissipation-enstrophy cross-correlation, which is asymmetric, but becomes less so at high Reynolds number. Conditional velocity autocorrelations are consistent with rapid changes in the velocity of fluid particles moving in regions of large velocity gradients. Examination of statistics conditioned upon enstrophy, especially in a local coordinate frame moving with the vorticity vector, and of the centripetal acceleration suggests the presence of vortex-trapping effects which persist for several Kolmogorov time scales. Further results on acceleration statistics and joint velocity-acceleration autocorrelations are also presented to help characterize in detail the properties of a joint stochastic process of velocity, acceleration and the pseudo-dissipation. Together with recent work on Eulerian conditional acceleration and Reynolds-number dependence of basic Lagrangian quantities, the present results are directly useful for the development of a new stochastic model formulated to account for intermittency and Reynolds-number effects as described in detail in a companion paper.
A conditionally cubic-Gaussian stochastic Lagrangian model for acceleration in isotropic turbulence
- A. G. LAMORGESE, S. B. POPE, P. K. YEUNG, B. L. SAWFORD
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- Journal of Fluid Mechanics / Volume 582 / 10 July 2007
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- 14 June 2007, pp. 423-448
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The modelling of fluid-particle acceleration in homogeneous isotropic turbulence in terms of stochastic models for the Lagrangian velocity, acceleration and a dissipation rate variable is considered. The basis for the Reynolds model (A. M. Reynolds, Phys. Rev. Lett. vol. 91, 2003, 084503) is reviewed and examined by reference to direct numerical simulations (DNS) of isotropic turbulence at Taylor-scale Reynolds number (Rλ) up to about 650. In particular, we show DNS data that support stochastic modelling of the logarithm of pseudo-dissipation as an Ornstein–Uhlenbeck process and reveal non-Gaussianity of the acceleration conditioned on fluctuations of the pseudo-dissipation rate. The DNS data are used to construct a new stochastic model that is exactly consistent with Gaussian velocity and conditionally cubic-Gaussian acceleration statistics. This model captures the effects of small-scale intermittency on acceleration and the conditional dependence of acceleration on pseudo-dissipation (which differs from that predicted by the refined Kolmogorov hypotheses). Non-Gaussianity of the conditionally standardized acceleration probability density function (PDF) is accounted for in terms of model nonlinearity. The large-time behaviour of the new model is that of a velocity-dissipation model that can be matched with DNS data for conditional second-order Lagrangian velocity structure functions. As a result, the diffusion coefficient for the new model incorporates two-time information and its Reynolds-number dependence as observed in DNS. The resulting model predictions for conditional and unconditional velocity autocorrelations and time scales are shown to be in very good agreement with DNS.
Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients
- P. K. Yeung
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- Journal of Fluid Mechanics / Volume 321 / 25 August 1996
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- 26 April 2006, pp. 235-278
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The spectral mechanisms of the differential diffusion of pairs of passive scalars with different molecular diffusivities are studied in stationary isotropic turbulence, using direct numerical simulation data at Taylor-scale Reynolds number up to 160 on 1283 and 2563 grids. Of greatest interest are the roles of nonlinear triadic interactions between different scale ranges of the velocity and scalar fields in the evolution of spectral coherency between the scalars, and the effects of mean scalar gradients.
Analysis of single-scalar spectral transfer (extending the results of a previous study) indicates a robust local forward cascade behaviour at high wavenumbers, which is strengthened by both high diffusivity and mean gradients. This cascade is driven primarily by moderately non-local interactions in which two small-scale scalar modes are coupled via a lower-wavenumber velocity mode near the peak of the energy dissipation spectrum. This forward cascade is coherent, tending to increase the coherency between different scalars at high wavenumbers but to decrease it at lower wavenumbers. However, at early times coherency evolution at high wavenumbers is dominated by de-correlating effects due to a different type of non-local triad consisting of two scalar modes with a moderate scale separation and a relatively high-wavenumber velocity mode. Consequently, although the small-scale motions play little role in spectral transfer, they are responsible for the rapid de-correlation observed at early times. At later times both types of competing triadic interactions become important over a wider wavenumber range, with increased relative strength of the coherent cascade, so that the coherency becomes slow-changing. When uniform mean scalar gradients are present, a stationary state develops in the coherency spectrum as a result of a balance between a coherent mean gradient contribution (felt within about 1 eddy-turnover time) and the net contribution from scale interactions. The latter is made less de-correlating because of a strengthened coherent forward cascade, which is in turn caused by uniform mean gradients acting as a primarily low-wavenumber source of scalar fluctuations with the same spectral content as the velocity field.
Lagrangian statistics from direct numerical simulations of isotropic turbulence
- P. K. Yeung, S. B. Pope
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- Journal of Fluid Mechanics / Volume 207 / October 1989
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- 26 April 2006, pp. 531-586
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A comprehensive study is reported of the Lagrangian statistics of velocity, acceleration, dissipation and related quantities, in isotropic turbulence. High-resolution direct numerical simulations are performed on 643 and 1283 grids, resulting in Taylor-scale Reynolds numbers Rλ in the range 38-93. The low-wavenumber modes of the velocity field are forced so that the turbulence is statistically stationary. Using an accurate numerical scheme, of order 4000 fluid particles are tracked through the computed flow field, and hence time series of Lagrangian velocity and velocity gradients are obtained.
The results reported include: velocity and acceleration autocorrelations and spectra; probability density functions (p.d.f.'s) and moments of Lagrangian velocity increments; and p.d.f.'s, correlation functions and spectra of dissipation and other velocity-gradient invariants. It is found that the acceleration variance (normalized by the Kolmogorov scales) increases as R½λ - a much stronger dependence than predicted by the refined Kolmogorov hypotheses. At small time lags, the Lagrangian velocity increments are distinctly non-Gaussian with, for example, flatness factors in excess of 10. The enstrophy (vorticity squared) is found to be more intermittent than dissipation, having a standard-deviation-to-mean ratio of about 1.5 (compared to 1.0 for dissipation). The acceleration vector rotates on a timescale about twice the Kolmogorov scale, while the timescales of acceleration magnitude, dissipation and enstrophy appear to scale with the Lagrangian velocity timescale.
Dynamics of direct large-small scale couplings in coherently forced turbulence: concurrent physical- and Fourier-space views
- P. K. Yeung, James G. Brasseur, Qunzhen Wang
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- Journal of Fluid Mechanics / Volume 283 / 25 January 1995
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- 26 April 2006, pp. 43-95
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As discussed in a recent paper by Brasseur & Wei (1994), scale interactions in fully developed turbulence are of two basic types in the Fourier-spectral view. The cascade of energy from large to small scales is embedded within ‘local-to-non-local’ triadic interactions separated in scale by a decade or less. ‘Distant’ triadic interactions between widely disparate scales transfer negligible energy between the largest and smallest scales, but directly modify the structure of the smallest scales in relationship to the structure of the energy-dominated large scales. Whereas cascading interactions tend to isotropize the small scales as energy moves through spectral shells from low to high wavenumbers, distant interactions redistribute energy within spectral shells in a manner that leads to anisotropic redistributions of small-scale energy and phase in response to anisotropic structure in the large scales. To study the role of long-range interactions in small-scale dynamics, Yeung & Brasseur (1991) carried out a numerical experiment in which the marginally distant triads were purposely stimulated through a coherent narrow-band anisotropic forcing at the large scales readily interpretable in both the Fourier- and physical-space views. It was found that, after one eddy turnover time, the smallest scales rapidly became anisotropic as a direct consequence of the marginally distant triadic group in a manner consistent with the distant triadic equations. Because these asymptotic equations apply in the infinite Reynolds number limit, Yeung & Brasseur argued that the observed long-range effects should be applicable also at high Reynolds numbers.
We continue the analysis of forced simulations in this study, focusing (i) on the detailed three-dimensional restructuring of the small scales as predicted by the asymptotic triadic equations, and (ii) on the relationship between Fourier- and physical-space evolution during forcing. We show that the three-dimensional restructuring of small-scale energy and vorticity in Fourier space from large-scale forcing is predicted in some detail by the distant triadic equations. We find that during forcing the distant interactions alter small-scale structure in two ways: energy is redistributed anisotropically within high-wavenumber spectral shells, and phase correlations are established at the small scales by the distant interactions. In the numerical experiments, the long-range interactions create two pairs of localized volumes of concentrated energy in three-dimensional Fourier space at high wavenumbers in which the Fourier modes are phase coupled. Each pair of locally phase-correlated volumes of Fourier modes separately corresponds to aligned vortex tubes in physical space in two orthogonal directions. We show that the dynamics of distant interactions in creating small-scale anisotropy may be described in physical space by differential advection and distortion of small-scale vorticity by the coherent large-scale energy-containing eddies, producing anisotropic alignment of small-scale vortex tubes.
Scaling arguments indicate a disparity in timescale between distant triadic interactions and energy-cascading local-to-non-local interactions which increases with scale separation. Consequently, the small scales respond to forcing initially through the distant interactions. However, as energy cascades from the large-scale to the small-scale Fourier modes, the stimulated distant interactions become embedded within a sea of local-to-non-local energy cascading interactions which reduce (but do not eliminate) small-scale anisotropy at later times. We find that whereas the small-scale structure is still anisotropic at these later times, the second-order velocity moment tensor is insensitive to this anisotropy. Third-order moments, on the other hand, do detect the anisotropy. We conclude that whereas a single statistical measure of anisotropy can be used to indicate the presence of anisotropy, a null result in that measure does not necessarily imply that the signal is isotropic. The results indicate that non-equilibrium non-stationary turbulence is particularly sensitive to long-range interactions and deviations from local isotropy.
Scalar dissipation rate and dissipative anomaly in isotropic turbulence
- D. A. DONZIS, K. R. SREENIVASAN, P. K. YEUNG
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- Journal of Fluid Mechanics / Volume 532 / 10 June 2005
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- 27 May 2005, pp. 199-216
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We examine available data from experiment and recent numerical simulations to explore the supposition that the scalar dissipation rate in turbulence becomes independent of the fluid viscosity when the viscosity is small and of scalar diffusivity when the diffusivity is small. The data are interpreted in the context of semi-empirical spectral theory of Obukhov and Corrsin when the Schmidt number, $\hbox{\it Sc}$, is below unity, and of Batchelor's theory when $\hbox{\it Sc}$ is above unity. Practical limits in terms of the Taylor-microscale Reynolds number, $R_\lambda$, as well as $\hbox{\it Sc}$, are deduced for scalar dissipation to become sensibly independent of molecular properties. In particular, we show that such an asymptotic state is reached if $R_\lambda \hbox{\it Sc}^{1/2}\,{\gg}\,1$ for $\hbox{\it Sc} \,{<}\, 1$, and if $\ln(\hbox{\it Sc})/R_\lambda\,{\ll}\,1$ for $\hbox{\it Sc} \,{>}\,1$.
Very fine structures in scalar mixing
- J. SCHUMACHER, K. R. SREENIVASAN, P. K. YEUNG
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- Journal of Fluid Mechanics / Volume 531 / 25 May 2005
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- 18 May 2005, pp. 113-122
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We explore very fine scales of scalar dissipation in turbulent mixing, below Kolmogorov and around Batchelor scales, by performing direct numerical simulations at much finer grid resolution than was usually adopted in the past. We consider the resolution in terms of a local fluctuating Batchelor scale and study the effects on the tails of the probability density function and multifractal properties of the scalar dissipation. The origin and importance of these very fine-scale fluctuations are discussed. One conclusion is that they are unlikely to be related to the most intense dissipation events.
Relative dispersion in isotropic turbulence. Part 1. Direct numerical simulations and Reynolds-number dependence
- P. K. YEUNG, MICHAEL S. BORGAS
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- Journal of Fluid Mechanics / Volume 503 / 25 March 2004
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- 01 March 2004, pp. 93-124
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The relative dispersion of fluid particle pairs in isotropic turbulence is studied using direct numerical simulation, in greater detail and covering a wider Reynolds number range than previously reported. A primary motivation is to provide an important resource for stochastic modelling incorporating information on Reynolds-number dependence. Detailed results are obtained for particle-pair initial separations from less than one Kolmogorov length scale to larger than one integral length scale, and for Taylor-scale Reynolds numbers from about 38 to 230. Attention is given to several sources of uncertainty, including sample size requirements, value of the one-particle Lagrangian Kolmogorov constant, and the temporal variability of space-averaged quantities in statistically stationary turbulence.
Relative dispersion is analysed in terms of the evolution of the magnitude and angular orientation of the two-particle separation vector. Early-time statistics are consistent with the Eulerian spatial structure of the flow, whereas the large-time behaviour is consistent with particle pairs far apart moving independently. However, at intermediate times of order several Kolmogorov time scales, and especially for small initial separation and higher Reynolds numbers, both the separation distance and its rate of change (called the separation speed) are highly intermittent, with flatness factors much higher than those of Eulerian velocity differences in space. This strong intermittency is a consequence of relative dispersion being affected by a wide range of length scales in the turbulent flow as some particle pairs drift relatively far apart. Numerical evidence shows that substantial dispersion occurs in the plane orthogonal to the initial separation vector, which implies that the orientation of this vector has, especially for small initial separation, only limited importance.
Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study
- Prakash Vedula, P. K. Yeung, R. O. Fox
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- Journal of Fluid Mechanics / Volume 503 / 25 March 2004
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- 01 March 2004, p. 377
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Journal of Fluid Mechanics, vol. 433 (2001), pp. 29–60