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.