Towards a finite-time singularity of the Navier-Stokes equations

2018/11/08 by Keith Moffatt, Moffatt, Keith, Yoshifumi Kimura +1 · 1 citation
Engineering · Mathematics · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1811.03304

openalex publication_date 2018/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution of the vortex core cross-sections. A nonlinear dynamical system is derived for the minimum separation parameter s(τ), the curvature κ(τ), and the radial scale δ(τ) of the vortex cross-section at the points of closest approach, where τ is dimensionless time. The scaling properties of this system are investigated.

Citations

• L 3,∞ -solutions of the Navier-Stokes equations and backward uniqueness
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Dynamics of thin vortex rings

Cited by

• On taming Moffatt-Kimura vortices of doom in the viscous case

Related

• Singularities in Fluid Mechanics
• A model for singularity formation in three-dimensional Euler and\n Navier-Stokes flows
• Finite-Time Euler singularities: A Lagrangian perspective
• A Hamiltonian description of finite-time singularity in Euler's fluid equations
• Interacting vortex pairs in inviscid and viscous planar flows