  Time evolution of advection-dominated accretion flow (ADAF) around a rotating
compact object is presented. The equations of time-dependent of fluid including
the Coriolis force along with the centrifugal and pressure gradient forces are
derived. In this research, it is assumed that angular momentum transport is due
to viscous turbulence and the {\alpha}-prescription is used for the kinematic
coefficient of viscosity. Moreover, the general relativistic effects are
neglected. In order to solve the equations, we have used a self-similar
solution. The solutions show that the behaviour of the physical quantities in a
dynamical ADAF is different from that for a steady accretion flow. Our results
indicate that the physical quantities are dependent of rotation parameter which
is defined as the ratio of the intrinsic angular velocity of the central body
to the angular velocity of disc. Also, the effect of rotation parameter on
these quantities is different for co and counter-rotating flows. The solution
shows that by increasing the rotation parameter a, inflow-outflow region
approaches the central object for co-rotating flow and moves outward for
counter-rotating flow. We find that when flow is fully advection dominated (f !
1), the entire gas has positive Bernoulli function. Also, we suggest that the
Bernoulli function becomes more positive when the effect of rotation on the
structure of disc decreases.
