Influence of variable Froude number on waves generated by ships in shallow water

Passage through the transcritical speed region of a moving disturbance in a shallow channel, is examined using numerical simulations based on a set of forced Boussinesq equations. The transition is accomplished either by accelerating the wave generating disturbance in a region of constant depth or by moving the disturbance with constant speed over a sloping bottom topography. A series of test cases are examined where the transcritical region is traversed both from subcritical to supercritical speed and vice versa. Results show that the generation of upstream solitary waves depends on the time required for the transition, with large waves being generated for long transition times. It is also apparent that the shape of the wave pattern, and the maximum amplitude of the waves, differ significantly depending on whether the Froude number increase or decrease during the transition of the transcritical region. However, the wave pattern is not determined simply in terms of the Froude number. The strength of the forcing term as well as the underlying process which cause the Froude number to vary, i.e., acceleration and depth variation, influence the wave pattern in different ways. The Froude number is none the less a useful indicator for the problem, as all cases with similar Froude number variations share some common characteristic features.