•Morphodynamics of alternate bars under unsteady discharge is investigated.•repeated specific hydrographs lead to an equilibrium of alternate bars.•This equilibrium state causes non-time dependent wavelength and migration periods.•Under this state, the migration period becomes identical to the hydrograph cycle.•Relation between hydrodynamics and bar growth controls this state. Discharge unsteadiness plays a key role in the dynamics of alternate bars, however, how migrating alternate bars determine their shape under unsteady discharge conditions, especially in the long-term, is still unclear. In this study, we numerically investigate long-term behaviors of migrating alternate bars subject to repeated hydrographs. For this, the same discharge variation but different hydrograph cycles were tested. The results show that even under unsteady flow conditions, specific combinations of hydrograph cycles and discharge variations result in an equilibrium state of migrating alternate bars (i.e., non-time dependent wavelength and migration period). This may be a unique feature of the alternate bar morphodynamics, since dynamic equilibrium state arising from steady discharge counterparts is time-dependent feature. Meanwhile, it is observed that when the discharge changes abruptly, the response of alternate bar morphodynamics changes along the time. Within a limited period, the response of alternate bars is not strong enough to destroy the original wavelength, suggesting that the hydrograph cycle that achieves this equilibrium state must be moderately long such that the timescale of the hydrograph is similar but slightly smaller than the bar growth.