To better understand the physical mechanisms behind particle engulfment dynamics under fluctuating solidification velocities, transient simulations are performed for a SiC particle in a silicon solidification system with oscillating growth rates using a rigorous finite-element model developed previously. Simulations reveal complicated behaviors that require a re-examination of the classical notion of a steady-state, critical growth velocity, vc, for particle engulfment. Under sinusoidal growth variations at a frequency representative of turbulent fluctuations in a large-scale melt, stable pushing states featuring nonlinear particle-growth front oscillations can arise, even when the maximum growth velocity slightly exceeds vc. However, higher-amplitude growth oscillations at the same frequency are shown to result in particle engulfment. Significantly, engulfment under such dynamic conditions can occur at average solidification rates far below the steady-state critical velocity, a behavior consistent with many experimental observations.