  Gravitational instability plays an important role in driving gas accretion in
massive protostellar discs. Particularly strong is the global gravitational
instability, which arises when the disc mass is of order 0.1 of the mass of the
central star and has a characteristic spatial scale much greater than the
disc's vertical scale-height. In this paper we use three-dimensional numerical
hydrodynamics to study the development of gravitational instabilities in a disc
which is embedded in a dense, gaseous envelope. We find that global
gravitational instabilities are the dominant mode of angular momentum transport
in the disc with infall, in contrast to otherwise identical isolated discs. The
accretion torques created by low-order, global modes of the gravitational
instability in a disc subject to infall are larger by a factor of several than
an isolated disc of the same mass. We show that this global gravitational
instability is driven by the strong vertical shear at the interface between the
disc and the envelope, and suggest that this process may be an important means
of driving accretion on to young stars.
