Stokes drift in two-dimensional wave flumes

A complete second-order solution is presented for the two-dimensional wave motion forced by a generic planar wavemaker. The wavemaker is doubly articulated and includes both piston and hinged wavemakers of variable draught. It is shown that the first-order evanescent eigenseries cannot be neglected when computing the amplitude of the second-order free wave. A previously neglected, time-independent solution that is required to satisfy an inhomogeneous kinematic boundary condition on the wavemaker as well as an mhomogeneous Neumann boundary condition on the free surface is examined in detail for the first time. This time-independent solution is found to accurately estimate the mean return flow in a closed wave flume computed by the Eulerian method. This mean return current due to Stokes drift is usually estimated using the principle of kinematic conservation of mass flux. Even though the first-order eigenseries will converge for any geometry of a generic planar wavemaker, the second-order solutions obtained from Stokes perturbation expansions will not converge for all planar wavemaker geometries.