We analyze two time-dependent cluster cooling flow models in spherical symmetry. The first assumes that the intracluster gas resides in a static external potential, and includes the effects of optically thin radiative cooling and mass deposition. This corresponds to previous steady-state cooling flow models calculated by White & Sarazin (1987). Detailed agreement is found between steady-state models and time-dependent models at fixed times in the simulations. The mass accretion rate is found either to increase or remain nearly constant once flows reach a steady state. The time rate of change of the accretion rate is strongly sensitive to the value of the mass deposition parameter q, but only mildly sensitive to the ratio beta of gravitational binding energy to gas temperature. We show that previous scaling arguments presented by Bertschinger (1988) and White (1988) are valid only for mature cooling flows with weak mass deposition (q ~< 1). The second set of models includes the effects of a secularly deepening cluster potential and secondary infall of gas from the Hubble flow. We find that such heating effects do not prevent the flows from reaching a steady state within an initial central cooling time.

Comment: 22 pages (AASTeX) with 16 EPS figures; accepted for publication in The Astrophysical Journal