  This paper concerns the large Reynold number limits and asymptotic behaviors
of solutions to the 2D steady Navier-Stokes equations in an infinitely long
convergent channel. It is shown that for a general convergent infinitely long
nozzle whose boundary curves satisfy curvature-decreasing and any given finite
negative mass flux, the Prandtl's viscous boundary layer theory holds in the
sense that there exists a Navier-Stokes flow with no-slip boundary condition
for small viscosity, which is approximated uniformly by the superposition of an
Euler flow and a Prandtl flow. Moreover, the singular asymptotic behaviors of
the solution to the Navier-Stokes equations near the vertex of the nozzle and
at infinity are determined by the given mass flux, which is also important for
the constructions of the Prandtl approximation solution due to the possible
singularities at the vertex and non-compactness of the nozzle. One of the key
ingredients in our analysis is that the curvature-decreasing condition on
boundary curves of the convergent nozzle ensures that the limiting inviscid
flow is pressure favourable and plays crucial roles in both the Prandtl
expansion and the stability analysis.
