Discretization of the vorticity field of a planar jet
 Natalie Ross,
 Jean Hertzberg,
 Elizabeth Bradley
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Abstract
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.
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 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