  The analytical study of long wave scattering in a canal with a rapidly
varying cross-section is presented. It is assumed that waves propagate on a
stationary current with a given flow rate. Due to the fixed flow rate, the
current speed is different in the different sections of the canal, upstream and
downstream. The scattering coefficients (the transmission and reflection
coefficients) are calculated for all possible orientations of incident wave
with respect to the background current (downstream and upstream propagation)
and for all possible regimes of current (subcritical, transcritical, and
supercritical). It is shown that in some cases negative energy waves can appear
in the process of waves scattering. The conditions are found when the
overreflection and over-transmission phenomena occur. In particular, it is
shown that a spontaneous wave generation can arise in a trans-critical
accelerating flow, when the background current enhances due to the canal
narrowing. This resembles a spontaneous wave generation on the horizon of an
evaporating black hole due to the Hawking effect.
