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Frequency–wavenumber spectral analysis of spatio-temporal flows
- Christopher J. Geoga, Charlotte L. Haley, Andrew R. Siegel, Mihai Anitescu
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- Journal:
- Journal of Fluid Mechanics / Volume 848 / 10 August 2018
- Published online by Cambridge University Press:
- 08 June 2018, pp. 545-559
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We propose a fully spatio-temporal approach for identifying spatially varying modes of oscillation in fluid dynamics simulation output by means of multitaper frequency–wavenumber spectral analysis. One-dimensional spectrum estimation has proven to be a valuable tool in the analysis of turbulence data applied spatially to determine the rate of energy transport between spatial scales, or temporally to determine frequencies of oscillatory flows. It also allows for the quantitative comparison of flow characteristics between two scenarios using a standard basis. It has the limitation, however, that it neglects coupling between spatial and temporal structures. Two-dimensional frequency–wavenumber spectral analysis allows one to decompose waveforms into standing or travelling variety. The extended higher-dimensional multitaper method proposed here is shown to have improved statistical properties over conventional non-parametric spectral estimators, and is accompanied by confidence intervals which estimate their uncertainty. Multitaper frequency–wavenumber analysis is applied to a canonical benchmark problem, namely, a direct numerical simulation of von Kármán vortex shedding off a square wall-mounted cylinder with two inflow scenarios with matching momentum-thickness Reynolds numbers $Re_{\unicode[STIX]{x1D703}}\approx 1000$ at the obstacle. Frequency–wavenumber analysis of a two-dimensional section of these data reveals that although both the laminar and turbulent inflow scenarios show a turbulent $-5/3$ cascade in wavenumber ($\unicode[STIX]{x1D708}$) and frequency ($f$), the flow characteristics differ in that there is a significantly more prominent discrete harmonic oscillation near $(f,\unicode[STIX]{x1D708})=(0.2,0.21)$ in wavenumber and frequency in the laminar inflow scenario than the turbulent scenario. This frequency–wavenumber pair corresponds to a travelling wave with velocity near one near the centre path of the vortex street.
Contributors
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- By Giustino Albanese, Andrew Amaranto, Brandon H. Backlund, Alexander Baxter, Abraham Berger, Mark Bernstein, Marian E. Betz, Omar Bholat, Suzanne Bigelow, Carl Bonnett, Elizabeth Borock, Christopher B. Colwell, Alasdair Conn, Moira Davenport, David Dreitlein, Aaron Eberhardt, Ugo A. Ezenkwele, Diana Felton, Spiros G. Frangos, John E. Frank, Jonathan S. Gates, Lewis Goldfrank, Pinchas Halpern, Jean Hammel, Kristin E. Harkin, Jason S. Haukoos, E. Parker Hays, Aaron Hexdall, James F. Holmes, Debra Houry, Jennifer Isenhour, Andy Jagoda, John L. Kendall, Erica Kreisman, Nancy Kwon, Eric Legome, Matthew R. Levine, Phillip D. Levy, Charles Little, Marion Machado, Heather Mahoney, Vincent J. Markovchick, Nancy Martin, John Marx, Julie Mayglothling, Ron Medzon, Maurizio A. Miglietta, Elizabeth L. Mitchell, Ernest Moore, Maria E. Moreira, Sassan Naderi, Salvatore Pardo, Sajan Patel, David Peak, Christine Preblick, Niels K. Rathlev, Charles Ray, Phillip L. Rice, Carlo L. Rosen, Peter Rosen, Livia Santiago-Rosado, Tamara A. Scerpella, David Schwartz, Fred Severyn, Kaushal Shah, Lee W. Shockley, Mari Siegel, Matthew Simons, Michael Stern, D. Matthew Sullivan, Carrie D. Tibbles, Knox H. Todd, Shawn Ulrich, Neil Waldman, Kurt Whitaker, Stephen J. Wolf, Daniel Zlogar
- Edited by Eric Legome, Lee W. Shockley
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- Book:
- Trauma
- Published online:
- 07 September 2011
- Print publication:
- 16 June 2011, pp ix-xiv
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Contributors
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- By Jane E. Adcock, Yahya Aghakhani, A. Anand, Eva Andermann, Frederick Andermann, Alexis Arzimanoglou, Sandrine Aubert, Nadia Bahi-Buisson, Carman Barba, Agatino Battaglia, Geneviève Bernard, Nadir E. Bharucha, Laurence A. Bindoff, William Bingaman, Francesca Bisulli, Thomas P. Bleck, Stewart G. Boyd, Andreas Brunklaus, Harry Bulstrode, Jorge G. Burneo, Laura Canafoglia, Laura Cantonetti, Roberto H. Caraballo, Fernando Cendes, Kevin E. Chapman, Patrick Chauvel, Richard F. M. Chin, H. T. Chong, Fahmida A. Chowdhury, Catherine J. Chu-Shore, Rolando Cimaz, Andrew J. Cole, Bernard Dan, Geoffrey Dean, Alessio De Ciantis, Fernando De Paolis, Rolando F. Del Maestro, Irissa M. Devine, Carlo Di Bonaventura, Concezio Di Rocco, Henry B. Dinsdale, Maria Alice Donati, François Dubeau, Michael Duchowny, Olivier Dulac, Monika Eisermann, Brent Elliott, Bernt A. Engelsen, Kevin Farrell, Natalio Fejerman, Rosalie E. Ferner, Silvana Franceschetti, Robert Friedlander, Antonio Gambardella, Hector H. Garcia, Serena Gasperini, Lorenzo Genitori, Gioia Gioi, Flavio Giordano, Leif Gjerstad, Daniel G. Glaze, Howard P. Goodkin, Sidney M. Gospe, Andrea Grassi, William P. Gray, Renzo Guerrini, Marie-Christine Guiot, William Harkness, Andrew G. Herzog, Linda Huh, Margaret J. Jackson, Thomas S. Jacques, Anna C. Jansen, Sigmund Jenssen, Michael R. Johnson, Dorothy Jones-Davis, Reetta Kälviäinen, Peter W. Kaplan, John F. Kerrigan, Autumn Marie Klein, Matthias Koepp, Edwin H. Kolodny, Kandan Kulandaivel, Ruben I. Kuzniecky, Ahmed Lary, Yolanda Lau, Anna-Elina Lehesjoki, Maria K. Lehtinen, Holger Lerche, Michael P. T. Lunn, Snezana Maljevic, Mark R. Manford, Carla Marini, Bindu Menon, Giulia Milioli, Eli M. Mizrahi, Manish Modi, Márcia Elisabete Morita, Manuel Murie-Fernandez, Vivek Nambiar, Lina Nashef, Vincent Navarro, Aidan Neligan, Ruth E. Nemire, Charles R. J. C. Newton, John O'Donavan, Hirokazu Oguni, Teiichi Onuma, Andre Palmini, Eleni Panagiotakaki, Pasquale Parisi, Elena Parrini, Liborio Parrino, Ignacio Pascual-Castroviejo, M. Scott Perry, Perrine Plouin, Charles E. Polkey, Suresh S. Pujar, Karthik Rajasekaran, R. Eugene Ramsey, Rahul Rathakrishnan, Roberta H. Raven, Guy M. Rémillard, David Rosenblatt, M. Elizabeth Ross, Abdulrahman Sabbagh, P. Satishchandra, Swati Sathe, Ingrid E. Scheffer, Philip A. Schwartzkroin, Rod C. Scott, Frédéric Sedel, Michelle J. Shapiro, Elliott H. Sherr, Michael Shevell, Simon D. Shorvon, Adrian M. Siegel, Gagandeep Singh, S. Sinha, Barbara Spacca, Waney Squier, Carl E. Stafstrom, Bernhard J. Steinhoff, Andrea Taddio, Gianpiero Tamburrini, C. T. Tan, Raymond Y. L. Tan, Erik Taubøll, Robert W. Teasell, Mario Giovanni Terzano, Federica Teutonico, Suzanne A. Tharin, Elizabeth A. Thiele, Pierre Thomas, Paolo Tinuper, Dorothée Kasteleijn-Nolst Trenité, Sumeet Vadera, Pierangelo Veggiotti, Jean-Pierre Vignal, J. M. Walshe, Elizabeth J. Waterhouse, David Watkins, Ruth E. Williams, Yue-Hua Zhang, Benjamin Zifkin, Sameer M. Zuberi
- Edited by Simon D. Shorvon, Frederick Andermann, Renzo Guerrini
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- Book:
- The Causes of Epilepsy
- Published online:
- 05 March 2012
- Print publication:
- 14 April 2011, pp ix-xvi
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Long-Term Behavior of Yield Curves
- Andrew F. Siegel, Charles R. Nelson
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- Journal:
- Journal of Financial and Quantitative Analysis / Volume 23 / Issue 1 / March 1988
- Published online by Cambridge University Press:
- 06 April 2009, pp. 105-110
- Print publication:
- March 1988
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The flattening of yield curves at long-term maturities is proven to be approximately proportional to the reciprocal of the time to maturity under general conditions. This is a consequence of the persistence of earlier forward rates in the averaging process, which produces yields from forward rates. This relationship suggests the use of a “reciprocal maturity yield curve,” which significantly facilitates the interpretation of the behavior of long-term yields by linearizing them for display over a shorter interval. This is illustrated using a yield curve for U.S. Treasury bills.