MS Thesis R. Hager - Hawaii National Marine Renewable Energy ...

U , (1)where Φ denotes the real part of the complex velocity potential, denotes the spatial partof the complex potential, and denotes the spatial part of the real part of the complexpotential 1 . i te i te The total potential per unit wave amplitude is:T it DIjje (2)jfor j=1,3,5where Ddenotes the diffraction potential, Idenotes the incident potential, and jdenotesthe radiation potential in the j th direction. These will be further defined in sections 3.3.2 and3.3.3.Combining the continuity equation and Eq. (1) results in the governing equation, namelyLaplace’s equation:2 22 2 2xz 0(3)in the fluid domainLaplace’s equation must be satisfied by all potentials listed in Eq. (2).Kinematic Free-Surface Boundary Condition (k.f.s.b.c.)The k.f.s.b.c. states that the normal velocities of the fluid particles and the boundary surfaceare equal at the free-surface. The k.f.s.b.c. is derived from the material derivative:Let1 denotes the real part of the equation36