TIME-DOMAIN SIMULATION OF THE GENERATION AND PROPAGATION OF SECOND-ORDER STOKES WAVES IN A TWO-DIMENSIONAL WAVE FLUME. PART I: MONOCHROMATIC WAVEMAKER MOTIONS

A time-domain simulation of the generation and propagation of second-order Stokes waves in a semi-infinite, narrow channel of uniform depth is presented. The wave motion is generated by the small-amplitude, oscillatory motion of a generic planar wavemaker. A novel second-order radiation boundary condition is applied at the far-field boundary. The suitability of this condition is verified by considering the forms of the computed second-order wave profiles for various locations of the radiation boundary. The accuracy of the solution is studied by monitoring the difference between the energy flux at the boundaries of the computational domain and the rate of change of kinetic energy of the fluid. Free-surface elevations predicted by the present approach exhibit good agreement with experimental results in a laboratory wavetank, and with those obtained from a second-order frequency-domain solution. In order to test the solution methodology further, the problem of wave propagation in a channel containing a rectangular step of infinite extent is also considered. The numerical results for this case indicate that the step may have a significant influence on the second-order wave field. It is concluded that the present approach provides an accurate and efficient technique to simulate the generation and propagation of nonlinear Stokes waves in a two-dimensional wavetank.