  We present two-dimensional hydrodynamical simulations of the tidal
interaction between a supermassive black hole binary with moderate mass ratio,
and the fossil gas disc where it is embedded. Our study extends previous
one-dimensional height-integrated disc models, which predicted that the density
of the gas disc between the primary and the secondary black holes should rise
significantly during the ultimate stages of the binary's hardening driven by
the gravitational radiation torque. This snow-plough mechanism, as we call it,
would lead to an increase in the bolometric luminosity of the system prior to
the binary merger, which could be detected in conjunction with the
gravitational wave signal. We argue here that the snow-plough mechanism is
unlikely to occur. In two-dimensions, when the binary's hardening timescale
driven by gravitational radiation becomes shorter than the disc's viscous drift
timescale, fluid elements in the inner disc get funneled to the outer disc
through horseshoe trajectories with respect to the secondary. Mass leakage
across the secondary's gap is thus found to be effective and, as a result, the
predicted accretion disc luminosity will remain at roughly the same level prior
to merger.
