Capillary-gravity ship wave patterns

Ship wave pattern is a fascinating research topic in the fields of marine hydrodynamics and water waves. Within the pure-gravity wave theory, the ship wave pattern composed of transverse waves and divergent waves appearing on the downstream is confined within a sector symmetrical about the ship track with a half-angle . However, when the surface tension is accounted for, the wave pattern is greatly modified especially at a low translating speed. Besides the minimum speed of capillary waves c_min = 0.23 m/s below which waves cannot be generated, there is another critical speed c_div = 0.45 m/s associated with the disappearance of divergent waves. In the present paper, the wave patterns created by a steadily translating source are studied, and they are examined with the crestlines obtained from the asymptotic analysis.