Velocity vector evaluation at free surface using wave elevation data

A fully nonlinear solution for the velocity vector at the water wave free surface is derived using the homotopy analysis method, based on the dynamic and kinematic free surface boundary conditions. Experimental tests were performed to validate the effectiveness of the proposed method. The results indicate substantial theoretical discrepancies in the dynamic free surface boundary condition, which occur between the wave crest/trough and the zero-crossing, rather than at the moments of maximum vertical or horizontal velocity. Corrections to the dynamic boundary condition at the free surface are necessary, as they significantly influence the wave nonlinearity in the evaluation of the velocity field. The nonlinear terms that dominate the horizontal velocity are confirmed. The experimental results demonstrate that the velocity vector at the free surface can be accurately evaluated by the proposed method.