Diffraction by a slender ship: uniform theory for head and oblique seas

Abstract

The diffraction problem for a slender ship held fixed in short regular incident waves is solved by a matched-asymptotic-expansion method which is uniform with respect to all incident wave directions including head seas. Special inner solutions are employed which satisfy the Helmholtz equation in cross-sectional planes of the ship and are non-singular in head seas. The inner expansion of the outer solution is derived directly for all wave directions rather than as a composite. The case of a ship with a long parallel middle body is studied by means of a mixed numerical and analytical solution which explicitly exhibits the transition between the distinctive behaviours of head and oblique seas and distinguishes effects generated at the bow from those of the parallel middle body. Calculations of the pressure distributions and wave elevations along a ship are reported and compared with experimental measurements. The agreement between theory and experiment is generally good, especially at the upwave end of the ship and along the upwave side.