  The nonlinear and nonlocal coupling of vorticity and strain-rate constitutes
a major hindrance in understanding the self-amplification of velocity gradients
in turbulent fluid flows. Utilizing highly-resolved direct numerical
simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid
points, and Taylor-scale Reynolds number $R_\lambda$ in the range $140-1300$,
we investigate this non-locality by decomposing the strain-rate tensor into
local and non-local contributions obtained through Biot-Savart integration of
vorticity in a sphere of radius $R$. We find that vorticity is predominantly
amplified by the non-local strain coming beyond a characteristic scale size,
which varies as a simple power-law of vorticity magnitude. The underlying
dynamics preferentially align vorticity with the most extensive eigenvector of
non-local strain. The remaining local strain aligns vorticity with the
intermediate eigenvector and does not contribute significantly to
amplification; instead it surprisingly attenuates intense vorticity, leading to
breakdown of the observed power-law and ultimately also the scale-invariance of
vorticity amplification, with important implications for prevailing
intermittency theories.
