  Whenever linear eigenmodes of open flows are computed on a numerical domain
that is truncated in the streamwise direction, artificial boundary conditions
may give rise to spurious pressure signals that are capable of providing
unwanted perturbation feedback to upstream locations. The manifestation of such
feedback in the eigenmode spectrum is analysed here for two simple
configurations. First, explicitly prescribed feedback in a Ginzburg-Landau
model is shown to produce a spurious eigenmode branch, named the 'arc branch',
that strongly resembles a characteristic family of eigenmodes typically present
in open shear flow calculations. Second, corresponding mode branches in the
global spectrum of an incompressible parallel jet in a truncated domain are
examined. It is demonstrated that these eigenmodes of the numerical model
depend on the presence of spurious forcing of a local k+ instability wave at
the inflow, caused by pressure signals that appear to be generated at the
outflow. Multiple local k+ branches result in multiple global eigenmode
branches. For the particular boundary treatment chosen here, the strength of
the pressure feedback from the outflow towards the inflow boundary is found to
decay with the cube of the numerical domain length. It is concluded that
arc-branch eigenmodes are artifacts of domain truncation, with limited value
for physical analysis. It is demonstrated, for the example of a non-parallel
jet, how spurious feedback may be reduced by an absorbing layer near the
outflow boundary.
