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Imagery re-scripting for PTSD: session content and its relation to symptom improvement
- Gary Brown, Caroline Salter, Eleanor Parker, Hannah Murray, Kathy Looney, Sharif El Leithy, Evelina Medin, Barbora Novakova, Jonathan Wheatley
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- Journal:
- Behavioural and Cognitive Psychotherapy / Volume 51 / Issue 1 / January 2023
- Published online by Cambridge University Press:
- 19 October 2022, pp. 1-10
- Print publication:
- January 2023
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Imagery rescripting (ImRs) is a therapy technique that, unlike traditional re-living techniques, focuses less on exposure and verbal challenging of cognitions and instead encourages patients to directly transform the intrusive imagery to change the depicted course of events in a more desired direction. However, a comprehensive account of how and in what circumstances ImRs brings about therapeutic change is required if treatment is to be optimised, and this is yet to be developed. The present study reports on the development of a coding scheme of ImRs psychotherapy elements identified in the literature as potential ImRs mechanisms. The codes were assessed in relation to short-term outcomes of 27 individuals undergoing ImRs for post-traumatic stress disorder. The timing of the change in the image, degree of activation of the new image and associated cognitive, emotional and physiological processes, self-guided rescripting, rescript believability, narrative coherence and cognitive and emotional shift were identified as being related to symptom change and so are potentially important factors for the re-scripting process.
A history of high-power laser research and development in the United Kingdom
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- Colin N. Danson, Malcolm White, John R. M. Barr, Thomas Bett, Peter Blyth, David Bowley, Ceri Brenner, Robert J. Collins, Neal Croxford, A. E. Bucker Dangor, Laurence Devereux, Peter E. Dyer, Anthony Dymoke-Bradshaw, Christopher B. Edwards, Paul Ewart, Allister I. Ferguson, John M. Girkin, Denis R. Hall, David C. Hanna, Wayne Harris, David I. Hillier, Christopher J. Hooker, Simon M. Hooker, Nicholas Hopps, Janet Hull, David Hunt, Dino A. Jaroszynski, Mark Kempenaars, Helmut Kessler, Sir Peter L. Knight, Steve Knight, Adrian Knowles, Ciaran L. S. Lewis, Ken S. Lipton, Abby Littlechild, John Littlechild, Peter Maggs, Graeme P. A. Malcolm, OBE, Stuart P. D. Mangles, William Martin, Paul McKenna, Richard O. Moore, Clive Morrison, Zulfikar Najmudin, David Neely, Geoff H. C. New, Michael J. Norman, Ted Paine, Anthony W. Parker, Rory R. Penman, Geoff J. Pert, Chris Pietraszewski, Andrew Randewich, Nadeem H. Rizvi, Nigel Seddon, MBE, Zheng-Ming Sheng, David Slater, Roland A. Smith, Christopher Spindloe, Roy Taylor, Gary Thomas, John W. G. Tisch, Justin S. Wark, Colin Webb, S. Mark Wiggins, Dave Willford, Trevor Winstone
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- Journal:
- High Power Laser Science and Engineering / Volume 9 / 2021
- Published online by Cambridge University Press:
- 27 April 2021, e18
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The first demonstration of laser action in ruby was made in 1960 by T. H. Maiman of Hughes Research Laboratories, USA. Many laboratories worldwide began the search for lasers using different materials, operating at different wavelengths. In the UK, academia, industry and the central laboratories took up the challenge from the earliest days to develop these systems for a broad range of applications. This historical review looks at the contribution the UK has made to the advancement of the technology, the development of systems and components and their exploitation over the last 60 years.
Eighteen years of paediatric extracorporeal membrane oxygenation and ventricular assist devices: insight regarding late outcomes
- Shawn M. Shah, David W. Kays, Sharon R. Ghazarian, Tom R. Karl, Plato Alexander, Nathaniel Sznycer-Taub, Jason Parker, Molly Oldeen, Melvin C. Almodovar, Gary Stapleton, James A. Quintessenza, Alfred Asante-Korang, Vyas Kartha, Jade Hanson, Ernest Amankwah, Joeli Roth, Jeffrey P. Jacobs
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- Journal:
- Cardiology in the Young / Volume 28 / Issue 11 / November 2018
- Published online by Cambridge University Press:
- 17 September 2018, pp. 1316-1322
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Background
We reviewed all patients who were supported with extracorporeal membrane oxygenation and/or ventricular assist device at our institution in order to describe diagnostic characteristics and assess mortality.
MethodsA retrospective cohort study was performed including all patients supported with extracorporeal membrane oxygenation and/or ventricular assist device from our first case (8 October, 1998) through 25 July, 2016. The primary outcome of interest was mortality, which was modelled by the Kaplan–Meier method.
ResultsA total of 223 patients underwent 241 extracorporeal membrane oxygenation runs. Median support time was 4.0 days, ranging from 0.04 to 55.8 days, with a mean of 6.4±7.0 days. Mean (±SD) age at initiation was 727.4 days (±146.9 days). Indications for extracorporeal membrane oxygenation were stratified by primary indication: cardiac extracorporeal membrane oxygenation (n=175; 72.6%) or respiratory extracorporeal membrane oxygenation (n=66; 27.4%). The most frequent diagnosis for cardiac extracorporeal membrane oxygenation patients was hypoplastic left heart syndrome or hypoplastic left heart syndrome-related malformation (n=55 patients with HLHS who underwent 64 extracorporeal membrane oxygenation runs). For respiratory extracorporeal membrane oxygenation, the most frequent diagnosis was congenital diaphragmatic hernia (n=22). A total of 24 patients underwent 26 ventricular assist device runs. Median support time was 7 days, ranging from 0 to 75 days, with a mean of 15.3±18.8 days. Mean age at initiation of ventricular assist device was 2530.8±660.2 days (6.93±1.81 years). Cardiomyopathy/myocarditis was the most frequent indication for ventricular assist device placement (n=14; 53.8%). Survival to discharge was 42.2% for extracorporeal membrane oxygenation patients and 54.2% for ventricular assist device patients. Kaplan–Meier 1-year survival was as follows: all patients, 41.0%; extracorporeal membrane oxygenation patients, 41.0%; and ventricular assist device patients, 43.2%. Kaplan–Meier 5-year survival was as follows: all patients, 39.7%; extracorporeal membrane oxygenation patients, 39.7%; and ventricular assist device patients, 43.2%.
ConclusionsThis single-institutional 18-year review documents the differential probability of survival for various sub-groups of patients who require support with extracorporeal membrane oxygenation or ventricular assist device. The indication for mechanical circulatory support, underlying diagnosis, age, and setting in which cannulation occurs may affect survival after extracorporeal membrane oxygenation and ventricular assist device. The Kaplan–Meier analyses in this study demonstrate that patients who survive to hospital discharge have an excellent chance of longer-term survival.
Numerical Simulation of Powder-Snow Avalanches
- Yusuke Fukushima, Gary Parker
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- Journal:
- Journal of Glaciology / Volume 36 / Issue 123 / 1990
- Published online by Cambridge University Press:
- 20 January 2017, pp. 229-237
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Appropriate expressions describing the motion of powder-snow avalanches are derived. The model consists of four equations, i.e. the conservation equations of fluid mass, snow-particle mass, momentum of the cloud, and kinetic energy of the turbulence. Insofar as the density difference between the avalanche and the ambient air becomes rather large compared with the density of the ambient air, the Boussinesq approximation, which is typically used to analyze density currents, cannot be adopted in the present case. As opposed to previous models, the total buoyancy of a powder-snow avalanche is allowed to change freely via erosion from and deposition on to a static snow layer on a slope. In the model, the snow-particle entrainment rate from the slope is directly linked to the level of turbulence.
A discontinuous, large-scale powder-snow avalanche occurred on 26 January 1986 near Maseguchi, Niigata Prefecture, Japan. The avalanche appears to have had a dense core at its base. The present model is employed to simulate that part of the avalanche above any dense core. The depth of the layer of fresh snow is considered to be an important parameter in the model. The larger the depth of fresh snow, the larger is the concentration of snow attained in the avalanche, and the faster its speed. It is seen that the model provides a reasonable description of the powder-snow avalanche generated near Maseguchi. In particular, the model prediction that a powder-snow avalanche strong enough to reach Maseguchi requires a depth of fresh snow of at least 2 m is in agreement with the observed depth just before the event.
FLAIR II Spectroscopy of Two DENIS J Band Galaxy Samples
- Gary A. Mamon, Quentin A. Parker, Dominique Proust
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- Journal:
- Publications of the Astronomical Society of Australia / Volume 18 / Issue 3 / 2001
- Published online by Cambridge University Press:
- 05 March 2013, pp. 232-242
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As a pilot survey for the forthcoming 6dF Galaxy Redshift Survey, spectroscopy of galaxies selected in the 1.2 micron J waveband with the DENIS imaging survey was performed at the UKST using the FLAIR II multi-object spectroscope. Sixty-nine galaxy redshifts were obtained in a high galactic latitude field and an additional 12 redshifts in a low galactic latitude (b = 17˚), obscured field. This spectroscopic followup of NIR selected galaxies illustrates the feasibility of obtaining redshifts with optical spectra on galaxies selected at much longer wavelengths. It validated a very preliminary algorithm for star/galaxy separation for high galactic latitude DENIS objects, with 99% reliability for J <13.9. The FLAIR II redshifts are in excellent agreement with those, previously published, of 20 common galaxies. However, the FLAIR II redshift determinations presented here required substantially longer integration times to achieve 90% completeness than expected from previous optical surveys at comparable depth. This is mainly due to a degradation in overall fibre throughput due to known problems with ageing of the prism–cement–fibre interface with exposure to UV light. In comparison to our high galactic latitude field, our low latitude (high extinction) field required 2.5 times more exposure time for less than 50% of successful redshift measurements.
Among the J ≤ 13.9 galaxies with measured redshifts, only 376% display emission lines, in comparison with 60% of emission line galaxies in optical samples of comparable depth. These galaxies are, on average, half a magnitude bluer in B-J than galaxies of the same luminosity without emission lines. We confirm a previous optically-based result that the fraction of galaxies with emission lines increases rapidly with decreasing galaxy luminosity. The J band luminosity function is estimated. Our high latitude field displays a concentration of galaxies at cz ≲ 38 000 km s−1 suggesting a possible supercluster.A radial velocity is reported for a galaxy lying near the projected centre of the Abell 1434 cluster of galaxies, for which no cluster redshift is currently available.
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
- Published online:
- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Conditions under which a supercritical turbidity current traverses an abrupt transition to vanishing bed slope without a hydraulic jump
- SVETLANA KOSTIC, GARY PARKER
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- Journal of Fluid Mechanics / Volume 586 / 10 September 2007
- Published online by Cambridge University Press:
- 14 August 2007, pp. 119-145
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Turbidity currents act to sculpt the submarine environment through sediment erosion and deposition. A sufficiently swift turbidity current on a steep slope can be expected to be supercritical in the sense of the bulk Richardson number; a sufficiently tranquil turbidity current on a mild slope can be expected to be subcritical. The transition from supercritical to subcritical flow is accomplished through an internal hydraulic jump. Consider a steady turbidity current flowing from a steep canyon onto a milder fan, and then exiting the fan down another steep canyon. The flow might be expected to undergo a hydraulic jump to subcritical flow near the canyon–fan break, and then accelerate again to critical flow at the fan–canyon break downstream. The problem of locating the hydraulic jump is here termed the ‘jump problem’. Experiments with fine-grained sediment have confirmed the expected behaviour outlined above. Similar experiments with coarse-grained sediment suggest that if the deposition rate is sufficiently high, this ‘jump problem’ may have no solution with the expected behaviour, and in particular no solution with a hydraulic jump. In such cases, the flow either transits the length of the low-slope fan as a supercritical flow and shoots off the fan–canyon break without responding to it, or dissipates as a supercritical flow before exiting the fan. The analysis presented below confirms the existence of a range associated with rapid sediment deposition where no solution to the ‘jump problem’ can be found. The criterion for this range is stated in terms of an order-one dimensionless parameter involving the fall velocity of the sediment. The criterion is tested and confirmed against the experiments mentioned above. A sample field application is presented.
Nearly pure sorting waves and formation of bedload sheets
- Giovanni Seminara, Marco Colombini, Gary Parker
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- Journal:
- Journal of Fluid Mechanics / Volume 312 / 10 April 1996
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- 26 April 2006, pp. 253-278
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Bedload sheets are coherent migrating patterns of bed material recently observed both in flume studies and in field streams with beds of coarse sand and fine gravel. This newly recognized feature is inherently associated with the heterogeneous character of the sediment and consists of sorting waves with distinct coarse fronts only one or two coarse grains high.
The question of the formation of bedload sheets poses an interesting and peculiar stability problem for the grain size distribution. Sorting waves are essentially two-dimensional migrating perturbations associated with variations of this distribution. We show that their growth is strictly associated with grain sorting. In fact the latter gives rise to perturbations of bedload transport which drive small perturbations of bottom elevation the amplitude of which scales with grain size. The sorting wave also induces spatial variations of bottom roughness, and consequently alters the fluid motion, which conversely exerts a spatially varying stress on the bed. The feature of bedload sheets which allows them to be distinguished from dunes over beds with coarse sand or fine gravel is then the fact that sorting is the dominant effect controlling their growth, rather than being a relatively small perturbation of the mechanism which gives rise to dunes in the case of uniform sediment.
The requirement that perturbations should not alter the sediment budget leads to an integral condition which gives rise to an integro-differential mathematical problem. With the help of recently developed bedload relationships suitable for mixtures, as well as appropriate modelling of turbulent channel flow over a bed with spatially periodic perturbations of bottom elevation and roughness we are able to derive a general dispersion relation which can be readily solved in terms of undisturbed size densities in the form of sums of Dirac distributions.
Perturbations are found to be unstable within a range of wavenumbers depending on the relative roughness and Froude number. We show that when the effects of perturbations of bottom elevation are neglected the unstable region corresponds to the range of conditions where the bottom stress leads bottom roughness, a range distinct from that which characterizes the formation of dunes. This result is given a physical explanation which depends crucially on the deviation from equal mobility of different grain sizes in the surface layer. The effect of perturbations of bottom elevation is however not negligible when the bottom roughness is fairly large compared to depth. In the latter case perturbations of bottom elevation and of bottom roughness are equally important, and gravel sheets are not easily distinguished from small-amplitude dunes.
Comparison with the field observations of Whiting et al. (1985, 1988) is satisfactory insofar as the bedload sheet mode is unstable under the conditions of the experiments, and the predicted wavelengths fall within the experimental range. The laboratory observations of Kuhnle & Southard (1988), on the other hand, appear to fall within a range of bottom roughness where the observed bedforms do not exhibit features unambiguously distinct from those of small-amplitude dunes.
Longitudinal streaks
- Marco Colombini, Gary Parker
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- Journal:
- Journal of Fluid Mechanics / Volume 304 / 10 December 1995
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- 26 April 2006, pp. 161-183
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A commonly observed bedform in wide erodible-bed channels consists of rows of streaks or stripes parallel to the flow. These stripes can be manifested in terms of transverse variation of bed elevation, characteristic grain size (and thus roughness or both. The former case is manifested most strongly in sediment with a nearly uniform size distribution and the latter most strongly in sediment with substantial heterogeneity in size. The amplitude of stripes is rarely larger than one or two grain diameters, and the transverse spacing is invariably of the order of the flow depth. They are closely linked to a pattern of paired cells of secondary flow in the flow cross-section.
An existing theory of streak formation for the case of uniform sediment relies on a second-order turbulence closure which explicitly links the streamwise flow to transverse variations in bed elevation. The theory successfully predicts the formation of streaks, but only at rather high values of the Shields stress, i.e. rather strong sediment transport. Streaks are commonly observed, however, at Shields stresses as low as only slightly above the threshold of motion.
In the present analysis the previous flow model is adapted to the case of transverse variation of roughness as well as elevation, and the constraint of uniform sediment is removed. The theory indicates that allowance for even slight heterogeneity of bed sediment results in the formation of streaks at any Shields stress above the threshold of motion. The resulting streaks are hybrid in the sense that they show transverse variation in both elevation and roughness. The model thus provides a general theory of streak formation.
Inception of channelization and drainage basin formation: upstream-driven theory
- Norihiro Izumi, Gary Parker
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- Journal:
- Journal of Fluid Mechanics / Volume 283 / 25 January 1995
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- 26 April 2006, pp. 341-363
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The ubiquitous presence of river drainage basins in the terrestrial environment suggests that distributed overland flow generated by rainfall tends to spontaneously organize itself into dendritic systems of discrete channels. Several recent numerical models describe the evolution of complete drainage basins from the initial condition of rainfall on a flat, tilted plateau, the surface of which has been provided with random elevation perturbations. These analyses model overland flow via the assumption of a perfect balance between gravitational and frictional terms, i.e. in terms of normal flow.
Linear stability analysis applied to the normal flow model has been shown, however, to fail to select a wavelength corresponding to a finite distance of separation between incipient basins. This suggests that the normal flow model may not be a sufficient basis for studying drainage basin development, especially at the finest scales of morphologic significance.
Here the concept of a threshold condition for bed erosion is combined with an analysis of the full equations of shallow overland flow in order to study wavelength selection. Classical linear stability analysis is shown to be inadequate to analyse the problem at the level of inception. An alternative linear analysis of bed perturbations based on the threshold condition is developed, and shown to lead to the selection of finite wavelength of the correct order of magnitude.
The analysis here is driven from the upstream direction in that bed erosion is first caused only when sufficient flow has gathered from upstream due to rainfall. A downstream-driven theory of incipient channelization that is not necessarily dependent upon rainfall is presented in Izumi (1993), and is presently in preparation for publication.
A new vectorial bedload formulation and its application to the time evolution of straight river channels
- Agnes Kovacs, Gary Parker
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- Journal:
- Journal of Fluid Mechanics / Volume 267 / 25 May 1994
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- 26 April 2006, pp. 153-183
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The derivation of a new vectorial bedload formulation for the transport of coarse sediment by fluid flow is presented in the first part of the paper. This relation has been developed for slopes up to the angle of repose both in the streamwise and transverse directions. The pressure distribution is assumed to be hydrostatic. The bed shear stress for the onset of particle motion and mean particle velocity are obtained from the mean force balance on a particle. A new generalized Bagnold hypothesis is introduced to calculate the sediment content of the bedload layer. The new formulation possesses two innovative features. It is fully nonlinear and vectorial in nature, in addition, it behaves smoothly up to the angle of repose.
A mathematical model of the time evolution of straight river channels is presented in the second half of the paper. This study focuses on the evolution process due to bank erosion in the presence of bedload only. The bed and bank material is taken to be coarse, non-cohesive and uniform in size. The sediment continuity and the fluid momentum conservation equations describe the time evolution of the bed topography and flow field. These equations are coupled through the fluid shear stress acting on the bed. This bed shear stress distribution is predicted with the aid of a simple algebraic turbulent closure model. As regards the computation of the sediment flux, the new fully nonlinear vectorial formulation is found to perform well and renders the evolution model fully mechanistic.
The formation of an erosional front in the time development of straight river channels has been so far obscured in physical experiments. Herein, with the help of the new bedload formulation, the existence and migration speed of the front of erosion are inferred from the analysis of the sediment continuity equation.
The model successfully describes the time relaxation of an initially trapezoidal channel toward an equilibrium cross-sectional shape, as evidenced by comparison with experimental data. This equilibrium is characterized by a constant width, vanishing sediment transport in the transverse direction, and a small but non-vanishing streamwise transport rate of bed sediment.
On the time development of meander bends
- Gary Parker, Edmund D. Andrews
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- Journal:
- Journal of Fluid Mechanics / Volume 162 / January 1986
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- 21 April 2006, pp. 139-156
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According to the theory of Ikeda, Parker & Sawai (1981), meander migration rate at a point depends on a convolution integral of channel curvature from that point upstream. The problem can be quantified in terms of the bend equation. The time development of periodic bend trains of finite amplitude is analysed using the method of two-timing. The results apply near the critical wavenumber for the growth of bends of infinitesimal amplitude.
A finite-amplitude equilibrium state bifurcating from the null state at the critical wavenumber was delineated by Parker, Diplas & Akiyama (1983): they called the resulting solution the Kinoshita curve. It is found herein that this equilibrium state is unstable. Bends of longer Cartesian wavelength grow to cutoff. Shorter bends are obliterated. Nevertheless, in either case, the bend train tends towards the shape of the Kinoshita curve.
The theory suggests that some growing bends may be stabilized by local obstructions to downstream migration. The obstructions would cause an effective reduction in Cartesian wavelength, moving the bend from the unstable regime to the stable regime. A rather crude check of bend shape and rates of deformation generally lends support to the analysis.
Self-accelerating turbidity currents
- Gary Parker, Yusuke Fukushima, Henry M. Pantin
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- Journal:
- Journal of Fluid Mechanics / Volume 171 / October 1986
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- 21 April 2006, pp. 145-181
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Approximate layer-averaged equations describing the mechanics of turbid underflows are derived. Closure of the equations describing the balance of fluid mass, sediment mass, and mean flow momentum provides for the delineation of a three-equation model. A description of sediment exchange with the bed allows for the possibility of a self-accelerating turbidity current in which sediment entrainment from the bed is linked to flow velocity. A consideration of the balance of the mean energy of the turbulence yields a constraint on physically realistic solutions to the three-equation model. It is shown that the self-acceleration predicted by the three-equation model is so strong that the energy constraint fails to be satisfied. In particular, the turbulent energy consumed in entraining new bed sediment exceeds the supply of energy to the turbulence, so that the turbulence, and thus the turbidity current, must die. The problem is rectified by the formulation of a four-equation model, in which an explicit accounting is made of the mean energy of the turbulence. Sediment entrainment from the bed is linked to the level of turbulence in the four-equation model. Self-acceleration is again predicted, although it is somewhat subdued compared with that predicted by the three-equation model. The predictions of both models are summarized over a wide range of conditions.
Bend theory of river meanders. Part 1. Linear development
- Syunsuke Ikeda, Gary Parker, Kenji Sawai
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- Journal:
- Journal of Fluid Mechanics / Volume 112 / November 1981
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- 20 April 2006, pp. 363-377
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Instability of the alternate-bar type in straight channels has long been identified as the cause of fluvial meandering. The condition of inerodible sidewalls, however, does not allow a meandering channel to develop. Herein a stability analysis of a sinuous channel with erodible banks allows for delineation of a ‘bend’ instability that does not occur in straight channels, and differs from the alternate-bar instability.
In the case of alluvial meanders, the two mechanisms are shown to operate at similar characteristic wavelengths. This provides a rationale for the continuous evolution of alternate bars into true bends such that each bend contains one alternate bar.
The same bend instability applies to incised meanders. A mechanism for incised alternate bars which differs from that for the alluvial case appears to operate at different characteristic wavelengths than that of bend instability. Analysis of data suggests that meandering in supraglacial meltwater streams is primarily due to the alternate bar mechanism, whereas the meandering of rills incised in cohesive material and of caves is likely due to the bend mechanism.
The meander wavelength of incised reaches of meandering streams is often longer than that of adjacent alluvial reaches. An explanation is offered in terms of bend instability.
Bend theory of river meanders. Part 2. Nonlinear deformation of finite-amplitude bends
- Gary Parker, Kenji Sawai, Syunsuke Ikeda
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- Journal:
- Journal of Fluid Mechanics / Volume 115 / February 1982
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- 20 April 2006, pp. 303-314
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Meander bends typically show certain systematic deviations from simple Cartesian sinusoidal forms. Bends tend to be round and full, or ‘fat’, often to the point of possessing double-valued plan-forms, as Langbein & Leopold (1966) have noted. Bends also tend to be characteristically skewed in such a fashion that their direction of migration can be determined directly from an aerial photograph of the planform; the water margin of the downstream accreting half of a point bar describes a convex planform, whereas the upstream eroding side has a concave shape.
In the present paper a generalized nonlinear equation of bend migration is treated based on the analysis of Part 1 (Ikeda, Parker & Sawai 1981). An expansion technique reminiscent of the Stokes expansion for water waves is developed to perform a nonlinear stability analysis. This analysis provides an explanation of skewing and fattening, and also indicates that lateral and downstream migration rates should increase as bend amplitude develops. These results agree qualitatively with field observations.
Self-formed straight rivers with equilibrium banks and mobile bed. Part 1. The sand-silt river
- Gary Parker
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- Journal:
- Journal of Fluid Mechanics / Volume 89 / Issue 1 / 14 November 1978
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- 19 April 2006, pp. 109-125
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Rivers and canals with perimeters composed of non-cohesive sand and silt have self-formed active beds and banks. They thus provide a most interesting fluid flow problem, for which one must determine the container as well as the flow. If bed load alone occurs across the perimeter of a wide channel, gravity will pull particles down the lateral slope of the banks; bank erosion is accomplished and the channel widens. In order to maintain equilibrium, this export of material from the banks must be countered by an import of sediment from the channel centre.
The mechanism postulated for this import is lateral diffusion of suspended sediment, which overloads the flow near the banks and causes deposition. The model is formulated analytically with the aid of a series of approximate but reasonable assumptions. Singular perturbation techniques are used to define the channel geometry and obtain rational regime relations for straight channels. A comparison with data lends credence to the model.
It is hoped that a first step has been made towards a more general treatment, which would include various complicating factors that are important features of natural rivers but are not essential to the maintenance of channel width. Among these factors are meandering, sediment sorting and seepage.
Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river
- Gary Parker
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- Journal:
- Journal of Fluid Mechanics / Volume 89 / Issue 1 / 14 November 1978
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- 19 April 2006, pp. 127-146
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Rivers are capable of transporting their own bed material without altering their width. However, a naive extension of the threshold theory of canals in coarse alluvium to straight reaches of gravel rivers leads to the stable-channel paradox: transport of bed material is incompatible with a stable width. In this paper singular perturbation techniques are used to obtain a bed stress distribution which allows a mobile bed but immobile banks at bankfull or dominant discharge. This result is used to obtain regime relations for straight rivers with bed and banks composed of coarse gravel.
The analysis, although dependent on a series of approximate assumptions for Reynolds-stress closure and sediment transport, provides reasonable agreement with data.
On the cause and characteristic scales of meandering and braiding in rivers
- Gary Parker
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- Journal:
- Journal of Fluid Mechanics / Volume 76 / Issue 3 / 11 August 1976
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- 11 April 2006, pp. 457-480
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A stability analysis of meandering and braiding perturbations in a model alluvial river is described. A perturbation technique, involving a small parameter representing the ratio of sediment transport to water transport, is used to obtain the following results.
Under appropriate conditions, the existence of sediment transport and friction are necessary conditions for the occurrence of instability in the flow and on the bed; thus instability is not inherent in the flow alone. An Anderson-type scale relation for longitudinal instability is obtained for meandering. A relation estimating the number of braids and differentiating between meandering and braided regimes is derived. These relations are independent of sediment transport.
Purely erosional cyclic and solitary steps created by flow over a cohesive bed
- GARY PARKER, NORIHIRO IZUMI
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- Journal:
- Journal of Fluid Mechanics / Volume 419 / 25 September 2000
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- 20 October 2000, pp. 203-238
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An erodible surface exposed to supercritical flow often devolves into a series of steps that migrate slowly upstream. Each step delineates a headcut with an associated hydraulic jump. These steps can form in a bed of cohesive material which, once eroded, is carried downstream as washload without redeposition. Here the case of purely erosional, one-dimensional periodic, or cyclic steps in cohesive material is considered. The St. Venant shallow-water equations combined with a formulation for sediment erosion are used to construct a complete theory of the erosional case. The solution allows wavelength, wave height, migration speed and bed and water surface profiles to be determined as functions of imposed parameters. The analysis also admits a solution for a solitary step, or single headcut of self-preserving form.
Linear stability analysis of channel inception: downstream-driven theory
- NORIHIRO IZUMI, GARY PARKER
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- Journal:
- Journal of Fluid Mechanics / Volume 419 / 25 September 2000
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- 20 October 2000, pp. 239-262
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A linear stability analysis of incipient channellization on hillslopes is performed using the shallow-water equations and a description of the erosion of a cohesive bed. The base state consists of a laterally uniform Froude-subcritical sheet flow down a smooth, downward-concave hillslope profile. The downstream boundary condition consists of the imposition of a Froude number of unity. The process of channellization is thus driven from the downstream end. The flow and bed profiles describe a base state that migrates at constant, slow speed in the upstream direction due to bed erosion. Transverse perturbations corresponding to a succession of parallel incipient channels are introduced. It is found that these perturbations grow in time, so describing incipient channellization, only when the characteristic spacing between incipient channels is on the order of 6–100 times the Froude-critical depth divided by the resistance coefficient. The characteristic wavelength associated with maximum perturbation growth rate is found to scale as 10 times the Froude-critical depth divided by the resistance coefficient. Evaluating the friction coefficient as on the order of 0.01, an estimate of incipient channel spacing on the order of 1000 times the Froude-critical depth is obtained. The analysis reveals that downstream-driven channellization becomes more difficult as (a) the critical shear stress required to erode the bed becomes so large that it approaches the Froude-critical shear stress reached at the downstream boundary and (b) the Froude number of the subcritical equilibrium flow attained far upstream approaches unity. Alternative mechanisms must be invoked to explain channellization on slopes high enough to maintain Froude-supercritical sheet flow.