Numerical and analytical study of undular bores governed by the full water wave equations and bidirectional Whitham–Boussinesq equations

Undular bores, also termed dispersive shock waves, generated by an initial discontinuity in height as governed two forms of the Boussinesq system weakly nonlinear shallow water wave theory, standard formulation and a Hamiltonian formulation, related Whitham–Boussinesq equations, full equations for gravity surface waves are studied compared. It is found that systems give solutions excellent agreement with numerical positions leading trailing edges bore up until onset on modulational instability. The systems, which far simpler than can then be used to accurately model undular bores. Finally, comparisons show slightly lower threshold instability terms step generating bore.