# Discretization of the vorticity field of a planar jet

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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 point-vortex models. This is due in large part to data-processing 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 laboratory-scale vortex-dominated planar jet. Large-scale 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 large-scale 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 large-scale vortex structure with a single discrete vortex provided the best compromise between mean-squared 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.

## Notes

### Acknowledgments

the authors wish to thank Jeffrey Anderson, Matthew Culbreth, Nathan Farrell, and Mark Rast for their input to this project.

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