  We study hydrodynamic models of astrophysical wormholes when water waves can
be amplified in the course of propagation between two critical points where
wave and current speeds coincide. Such models can be realised in shallow
laboratory ducts with variable width and depths. In this paper, we derive the
basic set of equations for shallow water waves on the spatially variable flow
in the duct of a variable cross-section and present the asymptotic analysis of
solutions in the neighbourhood of the critical points. The critical points
mimic either the black hole (BH) horizon if the flow transits from the
subcritical to the supercritical regime, or the white hole (WH) horizon if the
flow transits from the supercritical to the subcritical regime. We study then,
the wave propagation in the flow with two horizons when the flow transits first
the BH horizon and then the WH one. The region between the horizons mimics a
wormhole in general relativity. For the sake of completeness, we also study the
successive transition through WH and BH horizons. The theoretical results are
illustrated by numerical calculations of wave propagation in both these
arrangements. It is shown that the wave amplification after passing the active
zone between the horizons takes place in BH{WH arrangements only and can occur
for different relationships between the subcritical and supercritical flow
velocities. The frequency dependence of the amplification factor is obtained
and quantified in terms of the velocity ratio within and outside the \wormhole
domain". In the next paper, we plan to present exact solutions for the specific
velocity profile.
