Reflectionless Internal-Wave Propagation in a Channel with Variable Cross Section and Current

The propagation of linear long internal waves of arbitrary shape in a stationary flow under a rigid cover of a two-layer fluid in a channel with variable cross section is considered. Two kinds of flows are found and analyzed in which waves propagate without reflection. The results obtained are compared with those for channels without current studied earlier. In particular, it is shown that in the presence of a steady flow, there are no self-consistent channels in which waves can propagate without reflection over unlimited distances. The main reason for limiting the extent of reflectionless channels with current is that the flow velocity changes much faster than that of wave propagation, and there is necessarily a point at which they become equal.