  The paper considers a two-dimensional flow in a channel, which consists of
straight inlet and outlet branches and a circularly 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 separation
bubbles and vortex shedding can exist in the bend. The instability of the
three-dimensional linear perturbations is investigated. It was found that the
critical numbers of the two-dimensional disturbances according to the linear
approach are much greater than those of three-dimensional ones, but the
two-dimensional flow is unstable with respect to the perturbations of finite
amplitude. White noise can be amplified by two-dimensional nonlinear mechanisms
at relatively small Reynolds numbers, and a nonlinear instability scenario is
realized that competes with the linear instability of three-dimensional
perturbations. This way of instability development is characterized by the
formation of a two-dimensional vortices sequence, where the amplitude varies
along the channel in a quasi-periodic manner.
