On finite-time singularity in the Moffatt-Kimura model for vortex reconnnection of the Navier-Stokes equation

In [1][2] Moffatt and Kimura proposed an interacting vortex ring model for studying the evolution towards finite-time singularity of the Navier-Stokes equation. In [3] it was shown that their model with the neglect of viscosity is an integrable Hamiltoniann system. By this means it was proven that the system indeed has finite-time singularity, within its claimed asymptotic limits. This talk will cover further investigations of the MK model: properties of its integrability, the physical interpretation of invariants, a transformation to special variables that elucidate the singularity, and the effect of dissipation on the dynamics.

[1] Moffatt, H.K. & Kimura, Y., Towards a finite-time singularity of the Navier-Stokes equations. Part 1. Derivation and analysis of dynamical system. J. Fluid Mech. (2019) 861 930-967.

[2] Moffatt, H.K. & Kimura, Y., Towards a finite-time singularity of the Navier-Stokes equations. Part 2. Vortex reconnection and singularity evasion. J. Fluid Mech. (2019) 870 R1.

[3] Morrison, P.J. & Kimura, Y., A Hamiltonian description of finite-time singularity in Euler's fluid equations. arXiv: 2011.10864v1 [physics.flu-dyn].