Discretization of the vorticity field of a planar jet
 Natalie Ross,
 Jean Hertzberg,
 Elizabeth Bradley
 … show all 3 hide
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In data assimilation, information from sensors is used to correct the state variables of a numerical model. This has been used to great advantage by the weather prediction community in the context of direct numerical simulation (DNS) models, but has seen comparatively little use in pointvortex models. This is due in large part to dataprocessing issues. In order to keep up with the speeds necessary for effective data assimilation, one must extract and discretize the vortex structures from velocity field data in a computationally efficient fashion—i.e., using as few discrete vortices as possible to model the measured flow. This paper describes a new strategy for accomplishing this and evaluates the results using data from a laboratoryscale vortexdominated planar jet. Largescale vortex structures are found using a family of variants on traditional vortex extraction methods. By augmenting these methods with simple computational topology techniques, one obtains a new method that finds the boundaries of the coherent structures in a manner that naturally follows the geometry of the flow. This strategy was evaluated in the context of two standard vortex extraction methods, vorticity thresholding and Okubo–Weiss, and tested upon velocity field data from the experimental fluid flow. The largescale structures found in this manner were then modeled with collections of discrete vortices, and the effects of the grain size of the discretization and the parameters of the discrete vortex model were studied. The results were evaluated by comparing the instantaneous velocity field induced by the discrete vortices to that measured in the jet. These comparisons showed that the two extraction techniques were comparable in terms of sensitivity and error, suggesting that the computationally simpler vorticity thresholding method is more appropriate for applications where speed is an issue, like data assimilation. Comparisons of different discretization strategies showed that modeling each largescale vortex structure with a single discrete vortex provided the best compromise between meansquared error and computational effort. These results are of potential interest in any situation where one must balance accuracy and expense while extracting vortices from a snapshot of a flow field; data assimilation is only one example.
 Adrian, R, Christiensen, K, Liu, Z (2000) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29: pp. 275290 CrossRef
 Anderson JL (2010) Personal Communication
 Banks, D, Singer, B (1995) A predictorcorrector technique for visualizing unsteady flow. IEEE Trans Vis Comput Graph 1: pp. 151163 CrossRef
 Barba L (2007) Spectrallike accuracy in space of a meshless vortex method. In: Leitão V (ed) Advances in meshfree techniques. Springer
 Barba, L, Leonard, A, Allen, C (2005) Advances in viscous vortex methods—meshless spatial adaption based on radial basis function interpolation. Int J Numer Methods Fluids 47: pp. 387421 CrossRef
 Camussi, R (2002) Coherent structure identification from wavelet analysis of particle image velocimetry data. Exp Fluids 32: pp. 7686 CrossRef
 Chong, M, Perry, A, Cantwell, B (1990) A general classification of threedimensional flow fields. Phys Fluids 2: pp. 765777 CrossRef
 Chorin, A (1973) Numerical study of slightly viscous flow. J Fluid Mech 57: pp. 785796 CrossRef
 Cottet, GH, Koumoutsakos, P (2000) Vortex methods: theory and practice. Cambridge University Press, Cambridge CrossRef
 Farge, M, Schneider, K, Kevlahan, N (1999) NonGaussianity and coherent vortex simulation for twodimensional turbulence using an adaptive orthogonal wavelet basis. Phys Fluids 11: pp. 21872201 CrossRef
 Farge, M, Schneider, K, Pellegrino, G, Wray, A, Rogallo, R (2003) Coherent vortex extraction in threedimensional homogeneous turbulence: comparison between CVSwavelet and PODFourier decompositions. Phys Fluids 15: pp. 28862896 CrossRef
 Farrell N (2008) PIV analysis of forcing a planar jet using a loudspeaker. Technical Report CUCS (Department of Computer Science) 104308, University of Colorado
 Gustafson, K, Sethian, J (1991) Vortex methods and vortex motion. Society for Industrial & Applied Mathematics, Philadelphia
 Hald, O Convergence of vortex methods. In: Gustafson, K, Sethian, J eds. (1991) Vortex methods and vortex motion. Society for Industrial & Applied Mathematics, Philadelphia
 Haller, G (2005) An objective definition of a vortex. J Fluid Mech 525: pp. 126 CrossRef
 Harms, D, Raman, S, Madala, R (1992) An examination of fourdimensional dataassimilation techniques for numerical weather prediction. Bull AMS 73: pp. 425440
 Hua, B, Klein, P (1998) An exact criterion for the stirring properties of nearly twodimensional turbulence. Physica D 113: pp. 98110 CrossRef
 Hua, BL, McWilliams, J, Klein, P (1998) Lagrangian accelerations in geostrophic turbulence. J Fluid Mech 366: pp. 87108 CrossRef
 Hunt J, Wray A, Moin P (1988) Eddies, streams, and convergence zones in turbulent flows. In: Proceedings of the summer program, vol CTRS88. Stanford University Center for Turbulence Research Report, pp 193–208
 Ide, K, Ghil, M (1997) Extended Kalman filtering for vortex systems. Part I: methodology and point vortices. Dyn Atmos Oceans 27: pp. 301332 CrossRef
 Ide, K, Kuznetsov, L, Jones, C (2002) Lagrangian data assimilation for point vortex systems. J Turb 3: pp. 17
 Jeong, J, Hussain, F (1995) On the identification of a vortex. J Fluid Mech 285: pp. 6994 CrossRef
 Joseph R, Viglione S, Wolf H (1964) Cloud pattern recognition. In: Proceedings of the 19th ACM national conference. pp 42.301–42.3017
 Lugt, H The dilemma of defining a vortex. In: Muller, U, Roesner, K, Schmidt, B eds. (1979) Recent developments in theoretical and experimental fluid mechanics. Springer, London, pp. 309321
 Okubo, A (1970) Horizontal dispersion of floatable trajectories in the vicinity of velocity singularities such as convergencies. Deep Sea Res 17: pp. 445454
 Palacios, A, Armbruster, D, Kostelich, E, Stone, E (1996) Analyzing the dynamics of cellular flames. Physica D 96: pp. 132161 CrossRef
 Pemberton, R, Turnock, S, Dodd, T, Rogers, E (2002) A novel method for identifying vortical structures. J Fluids Struc 16: pp. 10511057 CrossRef
 Preisendorfer, R (1988) Principal component analysis in meteorology and oceanography. Elsevier, NY
 Raffel, M, Willert, C, Kompenhans, J (1998) Particle image velocimetry: a practical guide. Springer, NY
 Robins, V, Abernethy, J, Rooney, N, Bradley, E (2004) Topology and intelligent data analysis. Intell Data Anal 8: pp. 505515
 Robins, V, Meiss, J, Bradley, E (1998) Computing connectedness: an exercise in computational topology. Nonlinearity 11: pp. 913922 CrossRef
 Robins, V, Rooney, N, Bradley, E (2004) Topologybased signal separation. Chaos 14: pp. 305316 CrossRef
 Ross N (2008) Understanding the dynamics of pointvortex data assimilation. PhD thesis, University of Colorado
 Scarano, F, Benocci, C, Riethmuller, M (1999) Pattern recognition analysis of the turbulent flow past a backward facing step. Phys Fluids 11: pp. 38083818 CrossRef
 Segur H (1998) Evolution of a tracer gradient in an incompressible, twodimensional flow. In: IUTAM symposium on developments in geophysical turbulence
 Seigel, A, Weiss, J (1997) A waveletpacket census algorithm for calculating vortex statistics. Phys Fluids 9: pp. 19881999 CrossRef
 Shadden, S, Lekien, F, Marsden, J (2005) Definition and properties of Lagrangian coherent structures from finitetime Lyapunov exponents in twodimensional aperiodic flows. Physica D 212: pp. 271304 CrossRef
 Vollmers, H (2001) Detection of vortices and quantitative evaluation of their main parameters from experimental velocity data. Measure Sci Technol 12: pp. 11991207 CrossRef
 Weiss, J (1991) The dynamics of enstrophy transfer in 2dimensional hydrodynamics. Physica D 48: pp. 273294 CrossRef
 Title
 Discretization of the vorticity field of a planar jet
 Journal

Experiments in Fluids
Volume 49, Issue 5 , pp 11611175
 Cover Date
 20101101
 DOI
 10.1007/s0034801008628
 Print ISSN
 07234864
 Online ISSN
 14321114
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Natalie Ross ^{(1)}
 Jean Hertzberg ^{(2)}
 Elizabeth Bradley ^{(1)}
 Author Affiliations

 1. Department of Computer Science, University of Colorado, Boulder, CO, 803090430, USA
 2. Department of Mechanical Engineering, University of Colorado, Boulder, CO, 803090427, USA