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.
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