2021
DOI: 10.48550/arxiv.2107.06153
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Spontaneous Symmetry Breaking for Extreme Vorticity and Strain in the 3D Navier-Stokes Equations

Timo Schorlepp,
Tobias Grafke,
Sandra May
et al.

Abstract: We investigate the spatio-temporal structure of the most likely configurations realising extremely high vorticity or strain in the stochastically forced 3D incompressible Navier-Stokes equations. Most likely configurations are computed by numerically finding the highest probability velocity field realising an extreme constraint as solution of a large optimisation problem. High-vorticity configurations are identified as pinched vortex filaments with swirl, while high-strain configurations correspond to counter-… Show more

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Cited by 2 publications
(3 citation statements)
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“…At this Re, vorticity is more likely to be at an angle against the strain axis. Note that while we do not believe that the RFD model remains a valid description of 3D NSE turbulence in this regime, we remark that symmetry breaking has recently been observed for extreme strain events in full 3D Navier-Stokes [26].…”
Section: B Numerical Results For Symmetry Breaking Of the Rfd Modelmentioning
confidence: 63%
See 1 more Smart Citation
“…At this Re, vorticity is more likely to be at an angle against the strain axis. Note that while we do not believe that the RFD model remains a valid description of 3D NSE turbulence in this regime, we remark that symmetry breaking has recently been observed for extreme strain events in full 3D Navier-Stokes [26].…”
Section: B Numerical Results For Symmetry Breaking Of the Rfd Modelmentioning
confidence: 63%
“…In practice, we do so by numerically solving the instanton equations (28). This comes of a significant performance benefit over computing the instanton for the full model (26), allowing us to compute the minimizer faster. For example the average speed-up factor for Re = 100 and z ∈ [2, 10] is 54.…”
Section: B Extreme Configurations Of the Passive Scalar Gradientmentioning
confidence: 99%
“…At this r, vorticity is more likely to be at an angle against the strain axis. Note that while we do not believe that the RFD model remains a valid description of 3D NSE turbulence in this regime; we remark that symmetry breaking has recently been observed for extreme strain events in full 3D Navier-Stokes [57].…”
Section: B Numerical Results For Symmetry Breaking Of the Rfd Modelmentioning
confidence: 71%