3,414
Views
29
CrossRef citations to date
0
Altmetric
Research papers

Implications of the selection of a particular modal decomposition technique for the analysis of shallow flows

, &
Pages 796-805 | Received 22 Mar 2017, Accepted 15 Nov 2017, Published online: 26 Mar 2018

References

  • Aubry, N. (1991). On the hidden beauty of the proper orthogonal decomposition. Theoretical and Computational Fluid Dynamics, 2(5-6), 339–352. doi: 10.1007/BF00271473
  • Berkooz, G., Holmes, P., & Lumley, J. L. (1993). The proper orthogonal decomposition in the analysis of turbulent flows. Annual Review of Fluid Mechanics, 25(1), 539–575. doi: 10.1146/annurev.fl.25.010193.002543
  • Brevis, W., & García-Villalba, M. (2011). Shallow-flow visualization analysis by proper orthogonal decomposition. Journal of Hydraulic Research, 49(5), 586–594. doi: 10.1080/00221686.2011.585012
  • Chen, D., & Jirka, G. H. (1997). Absolute and convective instabilities of plane turbulent wakes in a shallow water layer. Journal of Fluid Mechanics, 338, 157–172. doi: 10.1017/S0022112097005041
  • Chen, K. K., Tu, J. H., & Rowley, C. W. (2012). Variants of dynamic mode decomposition: Boundary condition, Koopman, and Fourier analyses. Journal of Nonlinear Science, 22(6), 887–915. doi: 10.1007/s00332-012-9130-9
  • Constantinescu, G., Sukhodolov, A., & McCoy, A. (2009). Mass exchange in a shallow channel flow with a series of groynes: LES study and comparison with laboratory and field experiments. Environmental fluid mechanics, 9(6), 587–615. doi: 10.1007/s10652-009-9155-2
  • Fox, J. F., & Belcher, B. J. (2011). Comparison of macroturbulence measured using decomposition of PIV, ADV and LSPIV data. Journal of Hydraulic Research, 49(1), 122–126. doi: 10.1080/00221686.2010.535704
  • Ghidaoui, M. S., Kolyshkin, A. A., Liang, J. H., Chan, F. C., Li, Q., & Xu, K. (2006). Linear and nonlinear analysis of shallow wakes. Journal of Fluid Mechanics, 548, 309–340. doi: 10.1017/S0022112005007731
  • Higham, J., & Brevis, W. (2018). Modification of the modal characteristics of a square cylinder wake obstructed by a multi-scale array of obstacles. Experimental Thermal and Fluid Science, 90, 212–219. doi: 10.1016/j.expthermflusci.2017.09.019
  • Higham, J. E., Brevis, W., & Keylock, C. J. (2016). A rapid non-iterative proper orthogonal decomposition based outlier detection and correction for PIV data. Measurement Science and Technology, 27(12), 125303. doi: 10.1088/0957-0233/27/12/125303
  • Higham, J. E., Brevis, W., Keylock, C. J., & Safarzadeh, A. (2017). Using modal decompositions to explain the sudden expansion of the mixing layer in the wake of a groyne in a shallow flow. Advances in Water Resources, 107, 451–459. doi: 10.1016/j.advwatres.2017.05.010
  • Hinterberger, C., Fröhlich, J., & Rodi, W. (2007). Three-dimensional and depth-averaged large-eddy simulations of some shallow water flows. Journal of Hydraulic Engineering, 133(8), 857–872. doi: 10.1061/(ASCE)0733-9429(2007)133:8(857)
  • Jirka, G. H. (2001). Large scale flow structures and mixing processes in shallow flows. Journal of Hydraulic Research, 39(6), 567–573. doi: 10.1080/00221686.2001.9628285
  • Jirka, G. H., & Uijttewaal, W. S. (2004). Shallow flows: A definition. In G. H Jirka & W. S. Uijttewaal (Eds.), Shallow flows (pp. 3–11). London: Taylor and Francis Group.
  • Jovanović, M. R., Schmid, P. J., & Nichols, J. W. (2014). Sparsity-promoting dynamic mode decomposition. Physics of Fluids, 26(2), 024103. doi: 10.1063/1.4863670
  • Karhunen, K. (1946). Zur spektral theorie stochastischer prozesse. Annales Academiæ Scientiarum Fennicæ, A1, 34.
  • Kosambi, D. (1943). Statistics in function space. Journal of Indian Mathematical Society, 7, 76–88.
  • Loève, M. (1945). Functions aleatoire de second ordre. Comptes Rendus de l'Académie des Sciences, 220.
  • Lumley, J., Holmes, P., & Berkooz, G. (1996). Turbulence, coherent structures, dynamical systems and symmetry. Cambridge: Cambridge University Press.
  • Mezić, I. (2005). Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dynamics, 41(1-3), 309–325. doi: 10.1007/s11071-005-2824-x
  • Muld, T. W., Efraimsson, G., & Henningson, D. S. (2012). Flow structures around a high-speed train extracted using proper orthogonal decomposition and dynamic mode decomposition. Computers & Fluids, 57, 87–97. doi: 10.1016/j.compfluid.2011.12.012
  • Obukbov, A. M. (1954). Statistical description of continuous fields. Trudy Geofizicheskogo Instituta, Akademiya Nauk SSSR, 24, 3–42.
  • Peltier, Y., Erpicum, S., Archambeau, P., Pirotton, M., & Dewals, B. (2014). Meandering jets in shallow rectangular reservoirs: POD analysis and identification of coherent structures. Experiments in Fluids, 55(6), 1740. doi: 10.1007/s00348-014-1740-6
  • Pougachev, V. S. (1953). General theory of the correlations of random functions. Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya. Bulletin de l'Académie des Sciences de l'URSS.
  • Rempfer, D., & Fasel, H. F. (1994). Evolution of three-dimensional coherent structures in a flat-plate boundary layer. Journal of Fluid Mechanics, 260, 351–375. doi: 10.1017/S0022112094003551
  • Rodi, W. (2017). Turbulence modeling and simulation in hydraulics: A historical review. Journal of Hydraulic Engineering, 143, 03117001. doi: 10.1061/(ASCE)HY.1943-7900.0001288
  • Roussinova, V., Shinneeb, A.-M., & Balachandar, R. (2010). Investigation of fluid structures in a smooth open-channel flow using proper orthogonal decomposition. Journal of Hydraulic Engineering, 136(3), 143–154. doi: 10.1061/(ASCE)HY.1943-7900.0000155
  • Ruhe, A. (1984). Rational Krylov sequence methods for eigenvalue computation. Linear Algebra and its Applications, 58, 391–405. doi: 10.1016/0024-3795(84)90221-0
  • Scarano, F. (2002). Iterative image deformation methods in PIV. Measurement Science and Technology, 13(1), R1–R19. doi: 10.1088/0957-0233/13/1/201
  • Schmid, P. J. (2010). Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics, 656, 5–28. doi: 10.1017/S0022112010001217
  • Schmid, P. J., Meyer, K. E., & Pust, O. (2009). Dynamic mode decomposition and proper orthogonal decomposition of flow in a lid-driven cylindrical cavity. In 8th international symposium on particle image velocimetry-PIV09 (number 3, pp. 1–4), Monash University.
  • Taira, K., CBrunton, S. L., Dawson, S., Rowley, C. W., Colonius, T., McKeon, B. J., …Ukeiley, L. S. (2017). Modal analysis of fluid flows: An overview. arXiv preprint arXiv:1702.01453.
  • Talstra, H. (2011). Large-scale turbulence structures in shallow separating flows. TU Delft, Delft University of Technology.
  • Thielicke, W., & Stamhuis, E. J. (2014). PIVlab -- towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. Journal of Open Research Software, 2(1), e30. doi: 10.5334/jors.bl
  • Tu, J. H., Rowley, C. W., Luchtenburg, D. M., Brunton, S. L., & Kutz, J. N. (2013). On dynamic mode decomposition: Theory and applications. arXiv preprint arXiv:1312.0041.
  • Uijttewaal, W. S. J. (2005). Effects of groyne layout on the flow in groyne fields: Laboratory experiments. Journal of Hydraulic Engineering, 131(9), 782–791. doi: 10.1061/(ASCE)0733-9429(2005)131:9(782)
  • Uijttewaal, W. S. J. (2014). Hydrodynamics of shallow flows: Application to rivers. Journal of Hydraulic Research, 52(2), 157–172. doi: 10.1080/00221686.2014.905505
  • Uijttewaal, W. S. J., & Jirka, G. H. (2003). Grid turbulence in shallow flows. Journal of Fluid Mechanics, 489, 325–344. doi: 10.1017/S0022112003005020
  • Weitbrecht, V., Kühn, G., & Jirka, G. H. (2002). Large scale PIV-measurements at the surface of shallow water flows. Flow Measurement and Instrumentation, 13(5), 237–245. doi: 10.1016/S0955-5986(02)00059-6
  • Wynn, A., Pearson, D. S., Ganapathisubramani, B., & Goulart, P. J. (2013). Optimal mode decomposition for unsteady flows. Journal of Fluid Mechanics, 733, 473–503. doi: 10.1017/jfm.2013.426