Michael Jolly Indiana University Bounding curves in the energy,enstrophy-plane are derived for the 3D Navier-Stokes equations under an assumption on coherence of the vorticity direction. The analysis in the critical case where the direction is H\"older continuous with exponent r=1/2 results in a curve with extraordinarily large maximal enstrophy, in marked contrast to the subcritical case, r>1/2. Joint work with R. Dascaluic and Z. Grujic.