Existing avulsion models are decoupled from nearshore processes. Here, I explore quantitatively how the interplay of wave energy with fluvial input of sediment and water controls the aggradation rate and avulsion timescale of a single distributary channel. My approach rigorously couples a diffusive, moving-boundary theory of fluvial morphodynamics with a diffusive treatment of shoreface morphodynamics. I use this deterministic model to quantify the time required for channel-belt superelevation, normalized with channel depth, to attain a threshold value for nodal avulsion at a specified channel location. Increasing the long-term wave energy relative to fluvial input by an order of magnitude increases longshore sediment dispersal, thereby reducing the rate of channel-belt aggradation and associated seaward extension and increasing the avulsion timescale by a factor of approximately 50. Far-field processes eventually limit the ability of wave energy to suppress avulsion.