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arXiv · 1307.3589

Vortices, Maximum Growth and the Problem of Finite-Time Singularity Formation

Diego Ayala·Bartosz Protas
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Abstract

In this work we are interested in extreme vortex states leading to the maximum possible growth of palinstrophy in 2D viscous incompressible flows on periodic domains. This study is a part of a broader research effort motivated by the question about the finite-time singularity formation in the 3D Navier-Stokes system and aims at a systematic identification of the most singular flow behaviors. We extend the results reported in Ayala & Protas (2013) where extreme vortex states were found leading to the growth of palinstrophy, both instantaneously and in finite-time, which saturates the estimates obtained with rigorous methods of mathematical analysis. Here we uncover the vortex dynamics mechanisms responsible for such extreme behavior in time-dependent 2D flows. While the maximum palinstrophy growth is achieved at short times, the corresponding long-time evolution is characterized by some nontrivial features, such as vortex scattering events.

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Diego Ayala, Bartosz Protas. 2013-12-18. Vortices, Maximum Growth and the Problem of Finite-Time Singularity Formation. https://doi.org/10.1088/0169-5983%2F46%2F3%2F031404

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