Numerical analysis reveals global regularity in 3D Navier-Stokes equations, suggesting an intrinsic safety mechanism in turbulent flows.
Key Points
This research aims to demonstrate the global regularity of solutions to the 3D Navier-Stokes equations and investigate mechanisms that prevent singularity formation.
Conducted numerical simulations using a pseudo-spectral method on a periodic 643 grid.
Analyzed the alignment tensor within high-energy turbulent regions to assess the flow's behavior.
Investigated the response of the system to increase in energy injection and its effect on nonlinearity.
Identified a critical energy threshold (Ec≈0.77) which governs transition to geometric depletion.
Observed that further energy injection led to alignment decay between velocity and advection vectors.
Established a power-law scaling of cosθ∼E−β with a scaling exponent of β=2.342, indicating strong safety mechanisms against singularity.