Finite-time singularities in the axisymmetric three-dimension Euler equations

For pointlike singularities localized well away from the symmetry axis, axisymmetric flows with swirl are arbitrarily well approximated by two-dimensional Boussinesq convection. An adaptive mesh simulation of the latter equations was continued until the maximum three-dimensional vorticity showed a factor of ${10}^7$ increase, allowing a reasonable determination of exponents, and elucidation of the mechanism of blowup.