  We study sign changes and scaling laws in the Cartesian components of the
velocity and vorticity of rotating turbulence, in the helicity, and in the
components of vertically-averaged fields. Data for the analysis is provided by
high-resolution direct numerical simulations of rotating turbulence with
different forcing functions, with up to 1536^3 grid points, with Reynolds
numbers between ~1100 and ~5100, and with moderate Rossby numbers between ~0.06
and ~8. When rotation is negligible, all Cartesian components of the velocity
show similar scaling, in agreement with the expected isotropy of the flow.
However, in the presence of rotation only the vertical components of the fields
show clear scaling laws, with evidence of possible sign singularity in the
limit of infinite Reynolds number. Horizontal components of the velocity are
smooth and do not display rapid fluctuations for arbitrarily small scales. The
vertical velocity and vorticity, as well as the vertically-averaged vertical
velocity and vorticity, show the same scaling within error bars, in agreement
with theories that predict that these quantities have the same dynamical
equation for very strong rotation.
