  In currently favoured hierarchical cosmologies, the formation of massive
black hole binaries (MBHBs) following galaxy mergers is unavoidable. Still, due
the complex physics governing the (hydro)dynamics of the post-merger dense
environment of stars and gas in galactic nuclei, the final fate of those MBHBs
is still unclear. In gas-rich environments, it is plausible that turbulence and
gravitational instabilities feed gas to the nucleus in the form of a series of
cold incoherent clumps, thus providing a way to exchange energy and angular
momentum between the MBHB and its surroundings. Within this context, we present
a suite of smoothed-particle-hydrodynamical models to study the evolution of a
sequence of near-radial turbulent gas clouds as they infall towards equal-mass,
circular MBHBs. We focus on the dynamical response of the binary orbit to
different levels of anisotropy of the incoherent accretion events. Compared to
a model extrapolated from a set of individual cloud-MBHB interactions, we find
that accretion increases considerably and the binary evolution is faster. This
occurs because the continuous infall of clouds drags inwards circumbinary gas
left behind by previous accretion events, thus promoting a more effective
exchange of angular momentum between the MBHB and the gas. These results
suggest that sub-parsec MBHBs efficiently evolve towards coalescence during the
interaction with a sequence of individual gas pockets.
