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Symmetry breaking for extreme vorticity and strain in the 3D Navier-Stokes equations
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Schorlepp, Timo, Grafke, Tobias, May, Sandra and Grauer, Rainer (2022) Symmetry breaking for extreme vorticity and strain in the 3D Navier-Stokes equations. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 380 (2226). doi:10.1098/rsta.2021.0051 ISSN 1364-503X.
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Official URL: https://doi.org/10.1098/rsta.2021.0051
Abstract
We investigate the spatio-temporal structure of the most likely configurations realizing extremely high vorticity or strain in the stochastically forced three-dimensional incompressible Navier–Stokes equations. Most likely configurations are computed by numerically finding the highest probability velocity field realizing an extreme constraint as solution of a large optimization problem. High-vorticity configurations are identified as pinched vortex filaments with swirl, while high-strain configurations correspond to counter-rotating vortex rings. We additionally observe that the most likely configurations for vorticity and strain spontaneously break their rotational symmetry for extremely high observable values. Instanton calculus and large deviation theory allow us to show that these maximum likelihood realizations determine the tail probabilities of the observed quantities. In particular, we are able to demonstrate that artificially enforcing rotational symmetry for large strain configurations leads to a severe underestimate of their probability, as it is dominated in likelihood by an exponentially more likely symmetry-broken vortex-sheet configuration.
Item Type: | Journal Article | |||||||||
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Alternative Title: | ||||||||||
Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Large deviations , Deviation (Mathematics) , Instantons , Control theory, Navier-Stokes equations , Vortex-motion -- Mathematical models | |||||||||
Journal or Publication Title: | Philosophical Transactions A: Mathematical, Physical and Engineering Sciences | |||||||||
Publisher: | Royal Society Publishing | |||||||||
ISSN: | 1364-503X | |||||||||
Official Date: | 27 June 2022 | |||||||||
Dates: |
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Volume: | 380 | |||||||||
Number: | 2226 | |||||||||
DOI: | 10.1098/rsta.2021.0051 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 21 June 2022 | |||||||||
Date of first compliant Open Access: | 21 June 2022 | |||||||||
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