How turbulent flows grow vorticity at a point
Abstract
We describe how strong vorticity fluctuations appear in three-dimensional incompressible turbulence driven by a large-scale random force. By combining analytical and numerical methods, we construct a vorticity instanton: the most probable force history driving the flow to a prescribed large vorticity at a given point and time. We show how the smooth, large-scale force produces a long vortex filament with a thin, viscous-scale core. Our main finding is that the standard mechanism of amplifying a vortex tube through radial compression and axial stretching is only effective up to a threshold value. Producing vorticity above the threshold requires an additional ingredient: vorticity waves propagating along the tube. The final vorticity is the result of two colliding waves. This mechanism has striking similarities to the one recently suggested by OpenAI for creating infinite vorticity in finite-time Navier--Stokes blow-up.
Related
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BibTeX
@misc{schorlepp2026turbulent,
title = {{How turbulent flows grow vorticity at a point}},
author = {Timo Schorlepp and Vladimir Rosenhaus and Gregory Falkovich},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13056},
eprint = {2609.13056},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13056},
}
RIS
TY - UNPB
TI - How turbulent flows grow vorticity at a point
AU - Timo Schorlepp
AU - Vladimir Rosenhaus
AU - Gregory Falkovich
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13056
UR - https://arxiv.org/abs/2609.13056
AB - We describe how strong vorticity fluctuations appear in three-dimensional incompressible turbulence driven by a large-scale random force. By combining analytical and numerical methods, we construct a vorticity instanton: the most probable force history driving the flow to a prescribed large vorticity at a given point and time. We show how the smooth, large-scale force produces a long vortex filament with a thin, viscous-scale core. Our main finding is that the standard mechanism of amplifying a vortex tube through radial compression and axial stretching is only effective up to a threshold value. Producing vorticity above the threshold requires an additional ingredient: vorticity waves propagating along the tube. The final vorticity is the result of two colliding waves. This mechanism has striking similarities to the one recently suggested by OpenAI for creating infinite vorticity in finite-time Navier--Stokes blow-up.
ER -