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The incompressible three-dimensional Euler equations develop very thinpancake-like regions of increasing vorticity. These regions evolve with thescaling $\omega_{max}\sim\ell^{-2/3}$ between the vorticity maximum and thepancake thickness, as was observed in the recent numerical experiments [D.S.Agafontsev et al, Phys. Fluids 27, 085102 (2015)]. We study the process ofpancakes' development in terms of the vortex line representation (VLR), whichrepresents a partial integration of the Euler equations with respect toconservation of the Cauchy invariants and describes compressible dynamics ofcontinuously distributed vortex lines. We present, for the first time, thenumerical simulations of the VLR equations with high accuracy, which we performin adaptive anisotropic grids of up to $1536^3$ nodes. With these simulations,we show that the vorticity growth is connected with the compressibility of thevortex lines and find geometric properties responsible for the observed scaling$\omega_{max}\sim\ell^{-2/3}$.

Development of high vorticity structures and geometrical properties of the vortex line representation