CIRCULATION KINEMATICS IN NONLINEAR LABORATORY WAVES

A weakly nonlinear solution is presented for the two-dimensional wave kinematics forced by a generic wavemaker of variable-draft. The solution is valid for both piston and hinged wavemakers of variable draft that may be double articulated. The second-order propagating waves generated by a planar wave board are composed of two components; viz., a Stokes second-order wave and a second-harmonic wave forced by the wavemaker which travels at a different speed. A previously neglected time-independent solution that is required to satisfy a kinematic boundary condition on the wavemaker as well as a mixed boundary condition on the free surface is included for the first time. A component of the time-independent solution is found to accurately estimate the mean return current (correct to second-order) in a closed wave flume. This mean return current is usually estimated from kinematic considerations by a conservation of mass principle.