The velocity shear and vorticity across redshifts and non-linear scales
  The evolution of the large scale distribution of matter in the universe is
often characterized by the density field. Here we take a complimentary approach
and characterize it using the cosmic velocity field, specifically the
deformation of the velocity field. The deformation tensor is decomposed into
its symmetric component (known as the "shear tensor") and its anti-symmetric
part (the "vorticity"). Using a high resolution cosmological simulation we
examine the relative orientations of the shear and the vorticity as a function
of spatial scale and redshift. The shear is found to be remarkable stable to
the choice of scale, while the vorticity is found to quickly decay with
increasing spatial scale or redshift. The vorticity emerges out of the linear
regime randomly oriented with respect to the shear eigenvectors. Non-linear
evolution drives the vorticity to lie within the plane defined by the
eigenvector of the fastest collapse. Within that plane the vorticity first gets
aligned with the middle eigenvector and then it moves to be preferentially
aligned with the third eigenvector, of slowest collapse. Finally a scale of
"non-linearity" to be used when calculating properties of the non-linear
deformation tensor at different redshifts is suggested.
