  In this study we revisit the problem of computing steady Navier-Stokes flows
in two-dimensional unbounded domains. Precise quantitative characterization of
such flows in the high-Reynolds number limit remains an open problem of
theoretical fluid dynamics. Following a review of key mathematical properties
of such solutions related to the slow decay of the velocity field at large
distances from the obstacle, we develop and carefully validate a
spectrally-accurate computational approach which ensures the correct behavior
of the solution at infinity. In the proposed method the numerical solution is
defined on the entire unbounded domain without the need to truncate this domain
to a finite box with some artificial boundary conditions prescribed at its
boundaries. Since our approach relies on the streamfunction-vorticity
formulation, the main complication is the presence of a discontinuity in the
streamfunction field at infinity which is related to the slow decay of this
field. We demonstrate how this difficulty can be overcome by reformulating the
problem using a suitable background "skeleton" field expressed in terms of the
corresponding Oseen flow combined with spectral filtering. The method is
thoroughly validated for Reynolds numbers spanning two orders of magnitude with
the results comparing favourably against known theoretical predictions and the
data available in the literature.
