Hydrodynamic Forces on Ships in Dredged Channels

The problem to be treated here is that of steady longitudinal motion of a ship in a dredged channel, with specific attention to the prediction of sinkage and trim, and wave resistance. The dredged channel is idealized to be of rectangular cross section, and linearized shallow-water solutions are developed for the dredged or deep section, and for the two shallow regions alongside the channel. The ship is assumed slender, moving along the centerline of the channel, and is replaced by an equivalent source distribution, as in the earlier theories of Tuck for shallow water of constant depth. At the channel boundaries a matching of solutions is carried out, between the deep and shallow regions, and it is shown that the effects of the shallow regions can be replaced by a mixed boundary condition on the solution for the channel region. Calculations of the sinkage and trim and of the wave resistance are presented and discussed, for the cases where the channel region is subcritical and where the shallow regions are either subcritical or supercritical.