On the initial values of kinematic and dynamic free-surface boundary conditions for water wave problems

The kinematic and dynamic boundary conditions on the free surface of a fluid should be posed for water wave problems.In the framework of potential theory for an inviscid and incompressible fluid with an irrotational motion,the combined boundary condition,which involves the velocity potential only,is often used by eliminating the elevation terms mathematically.Such a combination is correct for the solutions in the frequency domain,and is not feasible for an initial-boundary-value problem in the time domain since it leads to a totally different physical formulation.The correct initial conditions for pure gravity waves and hydroelastic waves are presented.