  We present an asymptotic theory for analytical characterization of the
high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free
circular cylinder. The viscosity-induced modifications to this flow are
localized and except in the neighborhood of the rear stagnation point, behave
like a linear perturbation of the inviscid flow. Our theory gives a highly
accurate description of these modifications by including the contribution from
the most significant viscous term in a correctional perturbation expansion
about an inviscid base state. We derive the boundary layer equation for the
flow and deduce a similarity transformation that leads to a set of infinite,
shear-free-condition-incompatible, self-similar solutions. By suitably
combining members from this set, we construct an
all-boundary-condition-compatible solution to the boundary layer equation. We
derive the governing equation for vorticity transport through the narrow wake
region and determine its closed-form solution. The near and far field forms of
our wake solution are desirably consistent with the boundary layer solution and
the well-known, self-similar planar wake solution, respectively. We analyze the
flow in the rear stagnation region by formulating an elliptic partial
integro-differential equation for the distortion streamfunction that
specifically accounts for the fully nonlinear and inviscid dynamics of the
viscous correctional terms. The drag force and its atypical logarithmic
dependence on Reynolds number, deduced from our matched asymptotic analysis,
are in remarkable agreement with the high-resolution simulation results. The
logarithmic dependence gives rise to a critical Reynolds number below which the
viscous correction term, counterintuitively, reduces the net dissipation in the
flow field.
