  A new fundamentally-based formulation of nonlocal effects in the rapid
pressure-strain correlation in turbulent flows has been obtained. The resulting
explicit form for the rapid pressure-strain correlation accounts for nonlocal
effects produced by spatial variations in the mean-flow velocity gradients, and
is derived through Taylor expansion of the mean velocity gradients appearing in
the exact integral relation for the rapid pressure-strain correlation. The
integrals in the resulting series expansion are solved for high- and
low-Reynolds number forms of the longitudinal correlation function $f(r)$, and
the resulting nonlocal rapid pressure-strain correlation is expressed as an
infinite series in terms of Laplacians of the mean strain rate tensor. The new
formulation is used to obtain a nonlocal transport equation for the turbulence
anisotropy that is expected to provide improved predictions of the anisotropy
in strongly inhomogeneous flows.
