Solitary Waves Incident on a Submerged Horizontal Plate

Abstract

Wave scattering of a solitary wave traveling over a submerged horizontal plate was studied. Experiments for normal incidence were conducted in a wave flume, with a horizontal plate suspended at two different depths in the middle of the flume. Gauge pressures above and underneath the plate, surface elevations on and near the plate, and flow velocities at three representative fields of view were measured. The flow underneath the plate was found to behave almost like a plug flow, driven by the time-dependent, spatially uniform pressure gradient between the two openings. Complex vortices formed near the two edges of the plate as the plate acted like a flow divider. A numerical model based on two-dimensional Navier-Stokes equations was used to confirm the main features captured by the experimental measurements. Analytical solutions based on the linear long wave theory, which admits a soliton-like impulse wave solution, were also derived. The linear theory was applicable for obliquely incident impulse waves. When the analytical solutions were applied to the wave conditions used in the experiments, it was found that the theory described pressure and surface elevation satisfactorily when the nonlinearity was insignificant. Based on the pressure distribution above and beneath the plate, the total vertical force and moment exerted on the plate were calculated. As the wave passed over the plate, the plate first experienced a lift, followed by a force in the downward direction, and then a lift again. As a result, a nonzero time-varying moment existed. The analytical solution was also utilized to examine the effects of relative plate width on the transmitted and reflected waves. The effects of the angle of incidence are also discussed briefly.