  Local and nonlocal contributions to the total strain rate tensor at any point
in a flow are formulated from an expansion of the vorticity field in a local
spherical neighborhood of radius R centered on x. The resulting exact
expression allows the nonlocal (background) strain rate tensor to be obtained
from the total strain rate tensor. In turbulent flows, where the vorticity
naturally concentrates into relatively compact structures, this allows the
local alignment of vorticity with the most extensional principal axis of the
background strain rate tensor to be evaluated. In the vicinity of any vortical
structure, the required radius R and corresponding order n to which the
expansion must be carried are determined by the viscous lengthscale. We
demonstrate the convergence to the background strain rate field with increasing
R and n for an equilibrium Burgers vortex, and show that this resolves the
anomalous alignment of vorticity with the intermediate eigenvector of the total
strain rate tensor. We then evaluate the background strain field in DNS of
homogeneous isotropic turbulence where, even for the limited R and n
corresponding to the truncated series expansion, the results show an increase
in the expected equilibrium alignment of vorticity with the most extensional
principal axis of the background strain rate tensor.
