Despite the recognized impact of tidal bores on estuarine ecosystems, the large scale mechanism of bore formation in convergent alluvial estuaries is still under investigation. So far, field data exist only for a small number of estuaries, while numerical simulations employ the shallow water equations mainly focusing on the small-scale and local processes. In this work, firstly we apply the fully nonlinear weakly dispersive Serre-Green–Naghdi equations to simulate the tide propagation in a convergent estuary of idealized form, verifying that the local dispersion effects, responsible for the appearance of the secondary waves, do not influence the tidal bore onset, which only results from the large scale processes of amplification/damping and distortion of the incoming wave. In a second part, we numerically investigate (225 runs) the estuarine parameter space in order to identify the physical conditions that lead to tidal bore generation. In this parameter space, we determine a critical curve which divides estuaries according to tidal bore occurrence. As a result of this investigation we have shown that bore formation is controlled by the competition between two physical processes: (a) the knee-shaped distortion of the tidal wave, with flood dominance and eventually bore inception; (b) the dissipation of the tidal wave, which is unfavorable to bore formation. We also provide evidence that amplification due to topographic convergence is not a necessary condition for tidal bore generation and that there exist estuaries which display both wave damping and bore development. Finally, the validity of the results has been also assessed in the presence of freshwater river discharge, showing that for low river discharge, its effect on estuarine dynamics can be neglected.