  Hyperaccretion flows with mass accretion rates far above the Eddington rate
have an N-shaped equilibrium curve on the $\Sigma$-$\dot{M}$ plane (with
$\Sigma$ and $\dot{M}$ being surface density and mass accretion rate,
respectively). The accretion flow on the lower $\Sigma$ branch of the N-shape
is optically thick, advection-dominated accretion flow (ADAF) while that on the
upper one is neutrino-dominated accretion flow (NDAF). The middle branch has a
negative slope on the $\Sigma$-$\dot{M}$ plane, meaning that the flow on this
branch is secularly unstable. To investigate how the instability affects the
flow structure and what observable signatures are produced, we study the time
evolution of the unstable hyperaccretion flow in response to variable mass
injection rates by solving the height-averaged equations for viscous accretion
flows. When a transition occurs from the lower branch to the upper branch (or
from the upper branch to the lower branch), the surface density rapidly
increases (decreases) around that transition region, which induces locally
enhanced mass flow (referred to as non-steady mass flow) into (out of) that
region. We confirm that the non-steady flow can create a kind of disturbance
and that it propagates over the whole disk. However, the non-steady mass flow
is not strong enough to induce coherent transition over the whole disk, unless
the mass injection rate varies with time. When the injection rate continuously
changes, the neutrino luminosity varies intermittently, thus producing
step-function-like light curves, as the radiation efficiency discontinuously
changes every time the local transition occurs. The effects of changing the
N-shape and possible observational consequences on the gamma-ray burst emission
are briefly discussed in relation to gamma-ray bursts.
