Bernoulli waves in deep and shallow water at low speed

Free-surface waves generated by a tanker, a container ship and a catamaran in deep and shallow water are investigated at low speed. In particular the effect of the Bernoulli wave in shallow water is discussed. The free-surface waves are computed using a non-linear potential-flow method of the Rankine-source type and the Bernoulli wave can easily be computed from a zero Froude number solution using a Rankine source panel method.Computations are carried out at 12 knots, which means that the three ships are operating in the length Froude number range 0.124 - 0.22. The three vessels are investigated for deep water and for shallow water in the depth Froude number range 0.13 - 0.73. The influence of different bottom profiles on the Bernoulli wave is also investigated for the tanker.The investigation shows that the Bernoulli wave contributes significantly to the total wave pattern, in particular close to the ship, but also further away from the ship in shallow water. It is also noted that the depth at the position of the ship is important for the Bernoulli wave in shallow areas aside of the ship.It is demonstrated that the blockage effect and the draught/depth ratio is important for the Bernoulli wave in shallow water while the far-field wave pattern is almost unchanged if the depth Froude number is small. Even though the Bernoulli wave height is relatively small, a large volume of water is moved in a short period of time when the ship passes a shallow area. This may result in high local velocities and erosion in shallow areas close to the shore.