Bow wave patterns

Keller (1974) has developed a method of computing wave patterns from the dispersion relation for a small Froude number. In the considered problem, an infinitely long cylinder with the cross section of the symmetric Joukowsky foil is employed as the ship and its trailing edge is taken to be the bow. The dispersion relation is a first-order partial differential equation for the phase function s. The differential equation is solved by the method of characteristics. A stationary ship instead of a ship moving at constant speed is considered. The relation between the local stream speed and the phase speed of local waves in the present problem is called the dispersion relation. Approaches of ray theory are employed in the discussed investigation. When the ship form is blunt, all of the waves from the bow are found to be divergent.