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