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

Keith Moffatt, Yoshifumi Kimura

Published 2018-11-08Version 1

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. The maximum vorticity is attained within a finite time and increases as the square of the vortex Reynolds number. The manner in which vortex reconnection occurs at the apex of a pyramid, and singularity thereby averted, is described analytically.