Stokes drift in two-dimensional wave flumes

Abstract

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.

Second-order theory for coupling 2D numerical and physical wave tanks: Derivation, evaluation and experimental validation

“…Before presenting the results, the correctness of the computer code is verified numerically by reproducing some numerical results described by Hudspeth and Sulisz (1991) and Sulisz and Hudspeth (1993). Fig.…”

“…Ottesen-Hansen et al (1980), Sand (1982) and Sand and Donslund (1985) discussed the second-order long wave generation in the laboratory. Hudspeth and Sulisz (1991) derived the complete second-order Eulerian theory for waves generated by a monochromatic wave paddle motion with special emphasis on Stokes drift and return flow in wave flumes. In addition, Flick and Guza (1980) and Sulisz and Hudspeth (1993) addressed the effects of spurious super-harmonic waves.…”

A study of flow structure of bichromatic waves through PIV analysis

“…Research on wave-making tests in wave basins has brought many methods for analyzing topics of linear and nonlinear irregular waves. Hudspeth and Sulisz (1991) carried out wave-making tests of monochromatic waves, considering 2nd order Stokes waves. Moubayed and Williams (1994), and Schäffer (1996) carried out experiments on bichromatic waves.…”

Second-Order Waves in a Three-Dimensional Wave Basin With Perfectly Reflecting Sidewalls

“…Sand & Mansard (1986) extended the approach and presented a technique necessary to produce the correct higher harmonics in an irregular sea state. Hudspeth & Sulisz (1991) and Sulisz & Hudspeth (1993a, b) presented a complete second-order frequency-domain solution for the wave "elds produced by the monochromatic oscillations of both #ap-and piston-type wave makers by an eigenfunction expansion approach. Their solution has been extended to deal with bichromatic wave-maker motions by Moubayed & Williams (1994) and, more recently, by Scha!er (1996).…”

“…The solutions to the boundary-value problems at "rst and second order are obtained by the method of eigenfunction expansions and are correct to second order in wave-maker stroke (wave amplitude). The solution is validated by comparison with two limiting cases, namely the "rst-order three-dimensional solution of Williams & Crull (1996) and the second-order two-dimensional solution of Hudspeth & Sulisz (1991). Then, numerical results are presented that illustrate the in#uence of the various wave maker and basin parameters on the generated wave "eld, in particular the in#uence of wave angle and basin width is investigated.…”