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The aim is to refine the criteria for maximum vorticity growth in the 3D Navier-Stokes equations by considering both amplitude and directional effects of viscosity.

July 24, 2026Open Access

An Angularly Corrected Maximum-Vorticity Continuation Criterion for the 3D Navier–Stokes Equations

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The aim is to refine the criteria for maximum vorticity growth in the 3D Navier-Stokes equations by considering both amplitude and directional effects of viscosity.
Developed a two-channel diagnostic approach for vorticity evolution in fluids.
Applied classical equations and derived an exact identity linking maximum vorticity growth to an effective rate.
Utilized direct numerical simulation (DNS) data for measurement validation.
Established that maximum vorticity growth requires both angular and amplitude damping to remain finite over time.
Defined conditions for finite-time blow-up related to the geometry of maximum vorticity.
Provided an analytic validation via a Beltrami solution.

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This note demonstrates a new criterion for vorticity growth in fluids, indicating implications for turbulence analysis.

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Thierry Marechal (2026) studied this question.

synapsesocial.com/papers/6a630201395161722cd16619 https://doi.org/10.5281/zenodo.21495160

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An Angularly Corrected Maximum-Vorticity Continuation Criterion for the 3D Navier–Stokes Equations

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Cite This Study

An Angularly Corrected Maximum-Vorticity Continuation Criterion for the 3D Navier–Stokes Equations

Key Points

Discussion

Implication

Cite This Study

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