  The paper considers a two-dimensional flow in a channel, which consists of
straight inlet and outlet branches and a circularly 90-degree curved bend. An
incompressible viscous fluid flows through the elbow under the action of a
constant pressure gradient between the inlet and outlet. Navier-Stokes
equations were solved numerically using a high-fidelity spectral/hp element
method. In a range of Reynolds numbers, an adaptive selective frequency dumping
method was used to get a steady-state flow. It was found that three separation
bubbles and vortex shedding can exist in the bend. The modal stability of two-
and three-dimensional perturbations was investigated. Critical Reynolds number
of the two-dimensional disturbances was found as extrapolation by lower
Reynolds number results. It is much greater than three-dimensional one, but the
two-dimensional flow could subcritically unstable with respect to the imposed
small-amplitude white noise. For three-dimensional perturbations, the
dependence of the critical Reynolds numbers on the bending radius is obtained.
For a case of a moderate bending radius the neutral curve is provided and
eigenfunctions are studied in detail: three-dimensional instability can be
caused by periodic or monotonically growing mode, these unstable modes regard
to the recirculation bubbles that occur after the bend.
