  The physical mechanism of angular momentum transport in poorly ionized
regions of protoplanetary discs, the dead zones (DZs), is not understood. The
presence of a DZ naturally leads to conditions susceptible to the Rossby wave
instability (RWI), which produces vortices and spiral density waves that may
revive the DZ and be responsible for observed large-scale disc structures. We
present a series of two-dimensional hydrodynamic simulations to investigate the
role of the RWI in DZs, including its impact on the long-term evolution of the
disc and its morphology. The nonlinear RWI can generate Reynolds stresses
(effective $\alpha$ parameter) as large as $0.01 - 0.05$ in the DZ, helping to
sustain quasi-steady accretion throughout the disc. It also produces novel disc
morphologies, including azimuthal asymmetries with $m = 1, 2$, and atypical
vortex shapes. The angular momentum transport strength and morphology are most
sensitive to two parameters: the radial extent of the DZ and the disc
viscosity. The largest Reynolds stresses are produced when the radial extent of
the DZ is less than its distance to the central star. Such narrow DZs lead to a
single vortex or two coherent antipodal vortices in the quasi-steady state. The
edges of wider DZs evolve separately, resulting in two independent vortices and
reduced angular momentum transport efficiency. In either case, we find that,
because of the Reynolds stresses generated by the nonlinear RWI, gravitational
instability is unlikely to play a role in angular momentum transport across the
DZ, unless the accretion rate is sufficiently high.
