Breaking of ship bores in a Boussinesq-type ship-wake model

A numerical study of ship-induced bores is carried out with a focus on soliton generation in different supercritical regimes, and the transition from breaking solitons to a pure bore measured in Gourlay's (2001) laboratory experiments. The fully nonlinear Boussinesq model, FUNWAVE-TVD, with appropriate dissipation schemes, is able to simulate ship-induced broken bores with amplitudes and periods consistent with the measured data. Two breaking dissipation schemes with different breaking criteria (a viscosity dissipation scheme with the surface slope breaking criterion, and a shock-capturing dissipation scheme with the wave height or surface elevation breaking criteria) are examined in a series of numerical experiments. It is found that both models predict soliton generation and the general trend of the transition from breaking solitons at lower Froude numbers to a pure bore at higher Froude numbers. Some differences are identified between the two different breaking schemes, including breaking locations, soliton propagation speed, amplitudes of wakes behind the ship, and the critical Froude number for the transition from a broken undular bore to a pure bore. In general, the viscosity-type breaker with the surface slope criterion performs more consistently with the laboratory observation compared with the shallow water equation-based shock-capturing breaker.