A Ray Theory for Nonlinear Ship Waves and Wave Resistance

摘要

Analytical and numerical methods for application of ray theory in computing ship waves are investigated. The potentially important role of ray theory in analyses of nonlinear waves and wave resistance is demonstrated. The reflection of ship waves from the hull boundary is analyzed here for the first time. When a wave crest touches the ship surface, the ray exactly follows the ship surface. When the wave crest is nearly perpendicular to the ship surface the ray is reflected many times as it propagates along the ship surface. Many rays of reflected elementary waves intersect each other. The envelope to the first reflected rays forms a line like a shock front which borders the area of large waves or breaking waves near the ship. For the Wigley hull, ray paths, wave phases, and directions of elementary waves are computed by the ray theory and a method of computing wave resistance is developed. The wave phase is compared with that of linear theory as a function of ship-beam length ratio to identify the advancement of the bow wave phase which influences the design of bow bulbs. The wave resistance of the Wigley hull is computed using the amplitude function from Michell's then ship theory and compared with values of Michell's wave resistance. The total wave resistance has the phase of hump and hollow shifted considerably. (Author)