Abstract
We focus on the description of point vortices both in inviscid and viscous environments and try to extend the idea of quantification of chaos in inviscid vortex systems of Babiano et al. [1] to viscous environments. In particular, we notice that viscosity can disrupt stable dynamics and cause initially stable trajectories to go through chaotic behavior, before succumbing to viscosity completely. We also find that the logarithms of the duration of this chaotic behavior and the kinematic viscosity coefficient seem to be connected by a linear relationship. Most approaches to control of point vortices don’t take viscosity into account. However, viscosity exists in most real fluids. As such, it is important to take it into account to try to obtain better descriptions of real world problems.
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Acknowledgements
This work was partially supported by CMUP (GM, MJR, SG), which is financed by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the project with reference UIDB/00144/2020; by Project STRIDE NORTE-01-0145-FEDER-000033 (SG), funded by ERDF NORTE 2020; and by project MAGIC POCI-01-0145- FEDER-032485 (SG), funded by FEDER via COMPETE 2020 - POCI and by FCT/MCTES via PIDDAC.
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Marques, G., Rodrigues, M.J., Gama, S. (2021). Passive Particle Dynamics in Viscous Vortex Flow. In: Gonçalves, J.A., Braz-César, M., Coelho, J.P. (eds) CONTROLO 2020. CONTROLO 2020. Lecture Notes in Electrical Engineering, vol 695. Springer, Cham. https://doi.org/10.1007/978-3-030-58653-9_34
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