9 results
Energy balances for the collision of gravity currents of equal strengths
- Albert Dai, Yu-Lin Huang, Ching-Sen Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 959 / 25 March 2023
- Published online by Cambridge University Press:
- 17 March 2023, A20
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Collision of two counterflowing gravity currents of equal densities and heights was investigated by means of three-dimensional high-resolution simulations with the goal of understanding the flow structures and energetics in the collision region in more detail. The lifetime of collision is approximately $3 \tilde {H}/\tilde {u}_f$, where $\tilde {H}$ is the depth of heavy and ambient fluids, and $\tilde {u}_f$ is the front velocity of the approaching gravity currents, and the lifetime of collision can be divided into three phases. During Phase I, $-0.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 0.5$, where $\tilde {t}$ is the time, and $\tilde {t}_c$ is the time instance at which the two colliding gravity currents have fully osculated, geometric distortions of the gravity current fronts result in stretching of pre-existing vorticity in the wall-normal direction inside the fronts, and an array of vertical vortices extending throughout the updraught fluid column develop along the interface separating the two colliding gravity currents. The array of vertical vortices is responsible for the mixing between the heavy fluids of the two colliding gravity currents and for the production of turbulent kinetic energy in the collision region. The presence of the top boundary deflects the updraughts into the horizontal direction, and a number of horizontal streamwise vortices are generated close to the top boundary. During Phase II, $0.5 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 1.2$, the horizontal streamwise vortices close to the top boundary induce turbulent buoyancy flux and break up into smaller structures. While the production of turbulent kinetic energy weakens, the rate of transfer of energy to turbulent flow due to turbulent buoyancy flux reaches its maximum and becomes the primary supply in the turbulent kinetic energy in Phase II. During Phase III, $1.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 2.8$, the collided fluid slumps away from the collision region, while the production of turbulent kinetic energy, turbulent buoyancy flux and dissipation of energy attenuate. From the point of view of energetics, the production of turbulent kinetic energy and turbulent buoyancy flux transfers energy away from the mean flow to the turbulent flow during the collision. Our study complements previous experimental investigations on the collision of gravity currents in that the flow structures, spatial distribution and temporal evolution of the mean flow and turbulent flow characteristics in the collision region are presented clearly. It is our understanding that such complete information on the energy budgets in the collision region can be difficult to attain in laboratory experiments.
On the merging and splitting processes in the lobe-and-cleft structure at a gravity current head
- Albert Dai, Yu-Lin Huang
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- Journal:
- Journal of Fluid Mechanics / Volume 930 / 10 January 2022
- Published online by Cambridge University Press:
- 03 November 2021, A6
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High-resolution simulations are performed for gravity currents propagating on a no-slip boundary to study the merging and splitting processes in the lobe-and-cleft structure at a gravity current head. The simulations reproduce the morphological features observed in the laboratory and provide more detailed flow information to elucidate the merging and splitting processes. Our mean lobe width $\tilde {b}$ and mean maximum lobe width $\tilde {b}_{max}$ satisfy the empirical relationships $\tilde {b}/\tilde {d}=7.4 Re^{-0.39}_f$ and $\tilde {b}_{max}/\tilde {d}=12.6 Re^{-0.38}_f$, respectively, over the front Reynolds number in the range $383 \le Re_f \le 3267$, where the front Reynolds number is defined as $Re_f= \tilde {u}_f \tilde {d} / \tilde {\nu }, \tilde {u}_f$ is the front velocity, $\tilde {d}$ is the height of the gravity current head and $\tilde {\nu }$ is the fluid kinematic viscosity. When measured in terms of the viscous length scale $\tilde {\delta }_\nu = \tilde {\nu }/\tilde {u}^*$, where $\tilde {u}^*$ is the shear velocity at the gravity current head, the mean lobe width and the mean maximum lobe width increase with increasing front Reynolds number and asymptotically approach $126 \tilde {\delta }_\nu$ and $230 \tilde {\delta }_\nu$ at $Re_f=3267$, respectively. The vortical structure inside a lobe has an elongated tooth-like shape and a pair of counter-rotating streamwise vortices are positioned on the left- and right-hand sides of each cleft. For the merging process, it requires the interaction of three tooth-like vortices and the middle tooth-like vortex breaks up and reconnects with the two neighbouring tooth-like vortices. Therefore, a cleft may continually merge with another neighbouring cleft but may never disappear. For the splitting process, even before the new cleft appears, a new born streamwise vortex is created by the parent vortex of opposite orientation and the parent vortex can be either the left part or the right part of the existing tooth-like vortex inside the splitting lobe. The new born streamwise vortex then induces the other counter-rotating streamwise vortex as the new cleft develops. The initiation of the splitting process can be attributed to the Brooke–Hanratty mechanism reinforced by the baroclinic production of vorticity. Depending on the orientation of the parent vortex, the resulting new cleft after the splitting process can shift laterally in the positive or negative spanwise direction along the leading edge of the gravity currents as the lobe-and-cleft structure moves forward in the streamwise direction. For gravity currents propagating on a no-slip boundary, the lobe-and-cleft structure is self-sustaining and the manifestations of the merging and splitting processes are in accord with reported laboratory observations.
Boussinesq and non-Boussinesq gravity currents propagating on unbounded uniform slopes in the deceleration phase
- Albert Dai, Yu-Lin Huang
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- Journal:
- Journal of Fluid Mechanics / Volume 917 / 25 June 2021
- Published online by Cambridge University Press:
- 23 April 2021, A23
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Boussinesq and non-Boussinesq gravity currents produced from a finite volume of heavy fluid propagating into an environment of light ambient fluid on unbounded uniform slopes in the range $0\,^\circ \le \theta \le 12\,^\circ$ are reported. The relative density difference $\epsilon = (\rho _1-\rho _0)/\rho _0$ is varied in the range $0.05 \le \epsilon \le 0.15$ in this study, where $\rho _1$ and $\rho _0$ are the densities of the heavy and light ambient fluids, respectively. Our focus is on the influence of the relative density difference on the deceleration phase of the propagation. In the early deceleration phase, the front location history follows the power relationship ${(x_f+x_0)}^2 = {(K_I B)}^{1/2} (t+t_{I})$, where $(x_f+x_0)$ is the front location measured from the virtual origin, $K_I$ an experimental constant, $B$ the total buoyancy, $t$ the time and $t_I$ the $t$ intercept. The dimensionless constant $K_I$ is influenced by the slope angle and the relative density difference. In the late deceleration phase for the gravity currents on the steeper slopes in this study ($12\,^\circ$, $9\,^\circ$ and $6\,^\circ$), an ‘active’ head separates from the body of the current and the front location history follows the power relationship ${(x_f+x_0)}^{8/3} = K_{VS} {B}^{2/3} V^{2/9}_0 {\nu }^{-1/3} ({t+t_{VS}})$, where $K_{VS}$ is an experimental constant, $V_0$ the total volume of heavy fluid, $\nu$ the kinematic viscosity of fluid and $t_{VS}$ the $t$ intercept. The dimensionless constant $K_{VS}$ is shown to be influenced by the slope angle but not significantly influenced by the relative density difference. In the late deceleration phase for the gravity currents on the milder slopes in this study ($3\,^\circ$ and $0\,^\circ$), the gravity currents maintain an integrated shape without violent mixing with the ambient fluid and the front location history follows the power relationship ${(x_f+x_0)}^{4} = K_{VM} {B}^{2/3} V^{2/3}_0 {\nu }^{-1/3} ({t+t_{VM}})$, where $K_{VM}$ is an experimental constant and $t_{VM}$ the $t$ intercept. The dimensionless constant $K_{VM}$ is shown to be influenced by both the slope angle and the relative density difference. While the influence of the relative density difference on $K_{VM}$ is carried along for the gravity currents on the milder slopes in the late deceleration phase, the relative density difference interestingly has no significant influence on $K_{VS}$ for the gravity currents on the steeper slopes in the late deceleration phase. Our results suggest that the non-Boussinesq gravity currents on the milder slopes may remain non-Boussinesq ones in the late deceleration phase while the non-Boussinesq gravity currents on the steeper slopes may have become Boussinesq ones in the late deceleration phase.
Hair cannabinoid concentrations in emergency patients with cannabis hyperemesis syndrome
- Khala Albert, Marco L.A. Sivilotti, Joey Gareri, Andrew Day, Aaron J. Ruberto, Lawrence C. Hookey
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- Journal:
- Canadian Journal of Emergency Medicine / Volume 21 / Issue 4 / July 2019
- Published online by Cambridge University Press:
- 26 February 2019, pp. 477-481
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- July 2019
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Objectives
Cannabis hyperemesis syndrome is characterized by bouts of protracted vomiting in regular users of cannabis. We wondered whether this poorly understood condition is idiosyncratic, like motion sickness or hyperemesis gravidarum, or the predictable dose-response effect of prolonged heavy use.
MethodsAdults with an emergency department visit diagnosed as cannabis hyperemesis syndrome, near-daily use of cannabis for ≥6 months, and ≥2 episodes of severe vomiting in the previous year were age- and sex-matched to two control groups: RU controls (recreational users without vomiting), and ED controls (patients in the emergency department for an unrelated condition). Δ9-Tetrahydrocannabinol (THC), cannabinol (CBN), cannabidiol, and 11-nor-9-carboxy-THC concentrations in scalp hair were compared for subjects with positive urine THC.
ResultsWe obtained satisfactory hair samples from 46 subjects with positive urine THC: 16 cases (age 26.8 ± 9.2 years; 69% male), 16 RU controls and 14 ED controls. Hair cannabinoid concentrations were similar between all three groups (e.g. cases THC 220 [median; IQR 100,730] pg/mg hair, RU controls 150 [71,320] and ED controls 270 [120,560]). Only the THC:CBN ratio was different between groups, with a 2.6-fold (95%CI 1.3,5.7) lower age- and sex-adjusted ratio in cases than RU controls. Hair cannabidiol concentrations were often unquantifiably low in all subjects.
ConclusionsSimilar hair cannabinoid concentrations in recreational users with and without hyperemesis suggest that heavy use is necessary but not sufficient for hyperemesis cannabis. Our results underline the high prevalence of chronic heavy cannabis use in emergency department patients and our limited understanding of this plant's adverse effects.
High-resolution simulations of cylindrical gravity currents in a rotating system
- Albert Dai, Ching-Sen Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 806 / 10 November 2016
- Published online by Cambridge University Press:
- 29 September 2016, pp. 71-101
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Cylindrical gravity currents, produced by a full-depth lock release, in a rotating system are investigated by means of three-dimensional high-resolution simulations of the incompressible variable-density Navier–Stokes equations with the Coriolis term and using the Boussinesq approximation for a small density difference. Here, the depth of the fluid is chosen to be the same as the radius of the cylindrical lock and the ambient fluid is non-stratified. Our attention is focused on the situation when the ratio of Coriolis to inertia forces is not large, namely $0.1\leqslant {\mathcal{C}}\leqslant 0.3$, and the non-rotating case, namely ${\mathcal{C}}=0$, is also briefly considered. The simulations reproduce the major features observed in the laboratory and provide more detailed flow information. After the heavy fluid contained in a cylindrical lock is released in a rotating system, the influence of the Coriolis effects is not significant during the initial one-tenth of a revolution of the system. During the initial one-tenth of a revolution of the system, Kelvin–Helmholtz vortices form and the rotating cylindrical gravity currents maintain nearly perfect axisymmetry. Afterwards, three-dimensionality of the flow quickly develops and the outer rim of the spreading heavy fluid breaks away from the body of the current, which gives rise to the maximum dissipation rate in the system during the entire adjustment process. The detached outer rim of heavy fluid then continues to propagate outward until a maximum radius of propagation is attained. The body of the current exhibits a complex contraction–relaxation motion and new outwardly propagating pulses form regularly in a period slightly less than half-revolution of the system. Depending on the ratio of Coriolis to inertia forces, such a contraction–relaxation motion may be initiated after or before the attainment of a maximum radius of propagation. In the contraction–relaxation motion of the heavy fluid, energy is transformed between potential energy and kinetic energy, while it is mainly the kinetic energy that is consumed by the dissipation. As a new pulse initially propagates outward, the potential energy in the system increases at the expense of decreasing kinetic energy, until a local maximum of potential energy is reached. During the latter part of the new pulse propagation, the kinetic energy in the system increases at the expense of decreasing potential energy, until a local minimum of potential energy is reached and another new pulse takes form. With the use of three-dimensional high-resolution simulations, the lobe-and-cleft structure at the advancing front can be clearly observed. The number of lobes is maintained only for a limited period of time before merger between existing lobes occurs when a maximum radius of propagation is approached. The high-resolution simulations complement the existing shallow-water formulation, which accurately predicts many important features and provides insights for rotating cylindrical gravity currents with good physical assumptions and simple mathematical models.
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. Hull, Patricia Huntington, Thomas Hurka, Paul Hurley, Rosalind Hursthouse, Guillermo Hurtado, Ronald E. Hustwit, Sarah Hutton, Jonathan Jenkins Ichikawa, Harry A. Ide, David Ingram, Philip J. Ivanhoe, Alfred L. Ivry, Frank Jackson, Dale Jacquette, Joseph Jedwab, Richard Jeffrey, David Alan Johnson, Edward Johnson, Mark D. Jordan, Richard Joyce, Hwa Yol Jung, Robert Hillary Kane, Tomis Kapitan, Jacquelyn Ann K. Kegley, James A. Keller, Ralph Kennedy, Sergei Khoruzhii, Jaegwon Kim, Yersu Kim, Nathan L. King, Patricia Kitcher, Peter D. Klein, E. D. Klemke, Virginia Klenk, George L. Kline, Christian Klotz, Simo Knuuttila, Joseph J. Kockelmans, Konstantin Kolenda, Sebastian Tomasz Kołodziejczyk, Isaac Kramnick, Richard Kraut, Fred Kroon, Manfred Kuehn, Steven T. Kuhn, Henry E. Kyburg, John Lachs, Jennifer Lackey, Stephen E. Lahey, Andrea Lavazza, Thomas H. Leahey, Joo Heung Lee, Keith Lehrer, Dorothy Leland, Noah M. Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. Mendola, Christopher Menzel, Michael J. Meyer, Christian B. Miller, David W. Miller, Peter Millican, Robert N. Minor, Phillip Mitsis, James A. Montmarquet, Michael S. Moore, Tim Moore, Benjamin Morison, Donald R. Morrison, Stephen J. Morse, Paul K. Moser, Alexander P. D. Mourelatos, Ian Mueller, James Bernard Murphy, Mark C. Murphy, Steven Nadler, Jan Narveson, Alan Nelson, Jerome Neu, Samuel Newlands, Kai Nielsen, Ilkka Niiniluoto, Carlos G. Noreña, Calvin G. Normore, David Fate Norton, Nikolaj Nottelmann, Donald Nute, David S. Oderberg, Steve Odin, Michael O’Rourke, Willard G. Oxtoby, Heinz Paetzold, George S. Pappas, Anthony J. Parel, Lydia Patton, R. P. Peerenboom, Francis Jeffry Pelletier, Adriaan T. Peperzak, Derk Pereboom, Jaroslav Peregrin, Glen Pettigrove, Philip Pettit, Edmund L. Pincoffs, Andrew Pinsent, Robert B. Pippin, Alvin Plantinga, Louis P. Pojman, Richard H. Popkin, John F. Post, Carl J. Posy, William J. Prior, Richard Purtill, Michael Quante, Philip L. Quinn, Philip L. Quinn, Elizabeth S. Radcliffe, Diana Raffman, Gerard Raulet, Stephen L. Read, Andrews Reath, Andrew Reisner, Nicholas Rescher, Henry S. Richardson, Robert C. Richardson, Thomas Ricketts, Wayne D. Riggs, Mark Roberts, Robert C. Roberts, Luke Robinson, Alexander Rosenberg, Gary Rosenkranz, Bernice Glatzer Rosenthal, Adina L. Roskies, William L. Rowe, T. M. Rudavsky, Michael Ruse, Bruce Russell, Lilly-Marlene Russow, Dan Ryder, R. M. Sainsbury, Joseph Salerno, Nathan Salmon, Wesley C. Salmon, Constantine Sandis, David H. Sanford, Marco Santambrogio, David Sapire, Ruth A. Saunders, Geoffrey Sayre-McCord, Charles Sayward, James P. Scanlan, Richard Schacht, Tamar Schapiro, Frederick F. Schmitt, Jerome B. Schneewind, Calvin O. Schrag, Alan D. Schrift, George F. Schumm, Jean-Loup Seban, David N. Sedley, Kenneth Seeskin, Krister Segerberg, Charlene Haddock Seigfried, Dennis M. Senchuk, James F. Sennett, William Lad Sessions, Stewart Shapiro, Tommie Shelby, Donald W. Sherburne, Christopher Shields, Roger A. Shiner, Sydney Shoemaker, Robert K. Shope, Kwong-loi Shun, Wilfried Sieg, A. John Simmons, Robert L. Simon, Marcus G. Singer, Georgette Sinkler, Walter Sinnott-Armstrong, Matti T. Sintonen, Lawrence Sklar, Brian Skyrms, Robert C. Sleigh, Michael Anthony Slote, Hans Sluga, Barry Smith, Michael Smith, Robin Smith, Robert Sokolowski, Robert C. Solomon, Marta Soniewicka, Philip Soper, Ernest Sosa, Nicholas Southwood, Paul Vincent Spade, T. L. S. Sprigge, Eric O. Springsted, George J. Stack, Rebecca Stangl, Jason Stanley, Florian Steinberger, Sören Stenlund, Christopher Stephens, James P. Sterba, Josef Stern, Matthias Steup, M. A. Stewart, Leopold Stubenberg, Edith Dudley Sulla, Frederick Suppe, Jere Paul Surber, David George Sussman, Sigrún Svavarsdóttir, Zeno G. Swijtink, Richard Swinburne, Charles C. Taliaferro, Robert B. Talisse, John Tasioulas, Paul Teller, Larry S. Temkin, Mark Textor, H. S. Thayer, Peter Thielke, Alan Thomas, Amie L. Thomasson, Katherine Thomson-Jones, Joshua C. Thurow, Vzalerie Tiberius, Terrence N. Tice, Paul Tidman, Mark C. Timmons, William Tolhurst, James E. Tomberlin, Rosemarie Tong, Lawrence Torcello, Kelly Trogdon, J. D. Trout, Robert E. Tully, Raimo Tuomela, John Turri, Martin M. Tweedale, Thomas Uebel, Jennifer Uleman, James Van Cleve, Harry van der Linden, Peter van Inwagen, Bryan W. Van Norden, René van Woudenberg, Donald Phillip Verene, Samantha Vice, Thomas Vinci, Donald Wayne Viney, Barbara Von Eckardt, Peter B. M. Vranas, Steven J. Wagner, William J. Wainwright, Paul E. Walker, Robert E. Wall, Craig Walton, Douglas Walton, Eric Watkins, Richard A. Watson, Michael V. Wedin, Rudolph H. Weingartner, Paul Weirich, Paul J. Weithman, Carl Wellman, Howard Wettstein, Samuel C. Wheeler, Stephen A. White, Jennifer Whiting, Edward R. Wierenga, Michael Williams, Fred Wilson, W. Kent Wilson, Kenneth P. Winkler, John F. Wippel, Jan Woleński, Allan B. Wolter, Nicholas P. Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- The Cambridge Dictionary of Philosophy
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- 05 August 2015
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- 27 April 2015, pp ix-xxx
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Non-Boussinesq gravity currents propagating on different bottom slopes
- Albert Dai
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- Journal of Fluid Mechanics / Volume 741 / 25 February 2014
- Published online by Cambridge University Press:
- 13 February 2014, pp. 658-680
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Experiments on the non-Boussinesq gravity currents generated from an instantaneous buoyancy source propagating on an inclined boundary in the slope angle range $0^{\circ } \le \theta \le 9^{\circ }$ with relative density difference in the range of $0.05 \le \epsilon \le 0.17$ are reported, where $\epsilon = (\rho _1-\rho _0)/\rho _0$, with $\rho _1$ and $\rho _0$ the densities of the heavy and light ambient fluids, respectively. We showed that a $3/2$ power-law, ${(x_f+x_0)}^{3/2}= K_M^{3/2} {B_0'}^{1/2} (t+t_{I0})$, exists between the front location measured from the virtual origin, $(x_f+x_0)$, and time, $t$, in the early deceleration phase for both the Boussinesq and non-Boussinesq cases, where $K_M$ is a measured empirical constant, $B_0'$ is the total released buoyancy, and $t_{I0}$ is the $t$-intercept. Our results show that $K_M$ not only increases as the relative density difference increases but also assumes its maximum value at $\theta \approx 6^{\circ }$ for sufficiently large relative density differences. In the late deceleration phase, the front location data deviate from the $3/2$ power-law and the flow patterns on $\theta =6^{\circ },9^{\circ }$ slopes are qualitatively different from those on $\theta =0^{\circ },2^{\circ }$. In the late deceleration phase, we showed that viscous effects could become more important and another power-law, ${(x_f+x_0)}^{2}= K_{V}^{2} {B_0'}^{2/3} {{A}^{1/3}_0} {\nu }^{-1/3} (t+t_{V0})$, applies for both the Boussinesq and non-Boussinesq cases, where $K_V$ is an empirical constant, $A_0$ is the initial volume of heavy fluid per unit width, $\nu $ is the kinematic viscosity of the fluids, and $t_{V0}$ is the $t$-intercept. Our results also show that $K_V$ increases as the relative density difference increases and $K_V$ assumes its maximum value at $\theta \approx 6^{\circ }$.
Experiments on gravity currents propagating on different bottom slopes
- Albert Dai
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- Journal:
- Journal of Fluid Mechanics / Volume 731 / 25 September 2013
- Published online by Cambridge University Press:
- 14 August 2013, pp. 117-141
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Experiments for gravity currents generated from an instantaneous buoyancy source propagating on an inclined boundary in the slope angle range ${0}^{\circ } \leq \theta \leq {9}^{\circ } $ are reported. While the flow patterns for gravity currents on $\theta = {6}^{\circ } , {9}^{\circ } $ are qualitatively different from those on $\theta = {0}^{\circ } $, similarities are observed in the acceleration phase for the flow patterns between $\theta = {2}^{\circ } $ and $\theta = {6}^{\circ } , {9}^{\circ } $ and in the deceleration phase, the patterns for gravity currents on $\theta = {2}^{\circ } $ are found similar to those on $\theta = {0}^{\circ } $. Previously, it was known that the front location history in the deceleration phase obeys a power-relationship, which is essentially an asymptotic form of the solution to thermal theory. We showed that this power-relationship applies only in the early stage of the deceleration phase, and when gravity currents propagate into the later stage of the deceleration phase, viscous effects become more important and the front location data deviate from this relationship. When the power-relationship applies, it is found that at $\theta = {9}^{\circ } $, ${u}_{f} {({x}_{f} + {x}_{0} )}^{1/ 2} / {{ B}_{0}^{\prime } }^{1/ 2} \approx 2. 8{ 8}_{- 0. 17}^{+ 0. 19} $, which changes to $2. 8{ 6}_{- 0. 13}^{+ 0. 13} $ at $\theta = {6}^{\circ } $, $2. 5{ 4}_{- 0. 07}^{+ 0. 08} $ at $\theta = {2}^{\circ } $, and $1. 5{ 1}_{- 0. 07}^{+ 0. 07} $ on a horizontal boundary, where ${u}_{f} $ is the front velocity, $({x}_{f} + {x}_{0} )$ is the front location measured from the virtual origin, and ${ B}_{0}^{\prime } $ is the released buoyancy. Our results indicate that in the slope angle range ${6}^{\circ } \leq \theta \leq {9}^{\circ } $, the asymptotic relationship between the front velocity and front location in the deceleration phase is not sensitive to the variation of slope angle. In the late deceleration phase when the front location data deviate from the power-relationship, we found that the flow patterns for $\theta = {6}^{\circ } , {9}^{\circ } $ are dramatically different from those for $\theta = {0}^{\circ } , {2}^{\circ } $. For high slope angles, i.e. $\theta = {6}^{\circ } , {9}^{\circ } $, the edge of the gravity current head experiences a large upheaval and enrolment by ambient fluid towards the end of the deceleration phase, while for low slope angles, i.e. $\theta = {0}^{\circ } , {2}^{\circ } $, the gravity current head maintains a more streamlined shape without violent mixing with ambient fluid throughout the course of gravity current propagation. Our findings indicate two plausible routes to the finale of a gravity current event.
Polarization switching mechanisms and electromechanical properties of La-modified lead zirconate titanate ceramics
- Jie-Fang Li, Xunhu Dai, Albert Chow, Dwight Viehland
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- Journal:
- Journal of Materials Research / Volume 10 / Issue 4 / April 1995
- Published online by Cambridge University Press:
- 03 March 2011, pp. 926-938
- Print publication:
- April 1995
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- Article
- Export citation
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The electromechanical properties of (Pb1−xLax)(ZryTi1−y)O3 [PLZT x/y/(1 - y)] have been investigated in the compositional range 0 < x < 0.10 for y = 0.65 (rhombohedral PLZT) and 0 < x < 0.18 for y = 0.40 (tetragonal PLZT). Both field-induced strains (∊-E) associated with polarization switching and piezoelectric responses (d33) were studied. Transmission electron microscopy (TEM) and dielectric investigations were also performed. Room temperature TEM investigations revealed common trends in the domain structure with increasing La content for both PLZT x/65/35 and x/40/60, including a micron-sized domain structure, a subdomain tweed-like structure, and a nanopolar domain state. Changes in the field-induced strains and piezoelectric properties were then related to these microstructural trends. The dominant electromechanical coupling mechanism in the micron-sized domain state was found to be piezoelectricity. However, an electrostrictive coupling became apparent with the appearance of the subdomain tweed-like structures, and became stronger in the nanopolar domain state. It is believed that polarization switching can-occur through 70°or 110°domains, the subdomain tweed-like structure, or nanopolar domains depending on La content.