River deltas are built by cycles of lobe growth and abrupt channel shifts, or avulsions, that occur within the backwater zone of coastal rivers. Previous numerical models differ on the origin of backwater-scaled avulsion nodes and their consistency with experimental data. To unify previous work, we developed a numerical model of delta growth that includes backwater hydrodynamics, river mouth progradation, relative sea level rise, variable flow regimes, and cycles of lobe growth, abandonment, and reoccupation. For parameter space applicable to lowland deltas, we found that flow variability is the primary mechanism to cause persistent avulsion nodes by focusing aggradation within the backwater zone. Backwater-scaled avulsion nodes also occur under less likely scenarios of initially uniform bed slopes or during rapid relative sea level rise and marine transgression. Our findings suggest that flow variability is a fundamental control on long-term delta morphodynamics. ©2019. American Geophysical Union. All Rights Reserved.