How Fast can Vorticity Stretch itself?

We review some examples of computing or bounding the long-time growth of vorticity in Euler flows under various assump- tions. Estimates for axisymmetric flow without swirl, obtained under constraints on vorticity volume and and kinetic energy, are discussed. Axisymmetric flow with swirl is treated under a truncation equivalent to an axisymmetric ‘stretched’ version of the Taylor-Green problem. The close relation of flows with swirl to 2D Boussinesq convection is used to give some examples of peri- odic flows developing arbitrarily large vorticity in a bounded domain. Finally, a moving line problem is introduced which produces finite time singularities. It is noted that locally 2D vortex structures of the kind obtained in the growth estimates without swirl motion could be consistent with the equations of motion of the line, but no computable examples of this are known.