  Small scale characteristics of turbulence such as velocity gradients and
vorticity fluctuate rapidly in magnitude and oscillate in sign. Much work
exists on the characterization of magnitude variations, but far less on sign
oscillations. While averages performed on large scales tend to zero because of
the oscillatory character, those performed on increasingly smaller scales will
vary with the averaging scale in some characteristic way. This characteristic
variation at high Reynolds numbers is captured by the so-called cancellation
exponent, which measures how local averages tend to cancel out as the averaging
scale increases, in space or time. Past experimental work suggests that the
exponents in turbulence depend on whether one considers quantities in full
three-dimensional space or uses their one- or two-dimensional cuts. We compute
cancellation exponents of vorticity and longitudinal as well as transverse
velocity gradients in isotropic turbulence at Taylor-scale Reynolds number up
to 1300 on $8192^3$ grids. The 2D cuts yield the same exponents as those for
full 3D, while the 1D cuts yield smaller numbers, suggesting that the results
in higher dimensions are more reliable. We make the case that the presence of
vortical filaments in isotropic turbulence leads to this conclusion. This
effect is particularly conspicuous in magnetohydrodynamic turbulence, where an
increased degree of spatial coherence develops along the imposed magnetic
field.
