Wave blocking

Water waves meeting an adverse current of which the velocity increases in the upstream direction can meet a point where the local adverse current velocity equals the wave energy transport velocity relative to the water (the intrinsic wave group velocity), so that relative to the fixed bed the wave energy transport velocity vanishes. This is called wave blocking. It is an important phenomenon where sea waves interact with a strong ebb current and/or a river outflow. In the present study we investigate the phenomenon of wave blocking with the aims as follows: (i) to generate more insight into the processes underlying the phenomenon of wave blocking, including wave energy dissipation and wave reflection in (near) blocking situations; (ii) to provide (additional) quantitative data of wave blocking, including blockage of periodic and random waves, and partial and complete blocking of random waves; (iii) to develop realistic modelling of wave blocking. Experiments were performed at the Laboratory of Fluid Mechanics, Delft University of Technology, The Netherlands. A novel experimental arrangement was designed and built in a laboratory flume, in which the current discharge decreases gradually in the downstream direction along the measurement section with constant cross section. This is obtained by withdrawal of water through a perforated false bottom. Waves were generated in a still-water region downstream from the measurement section. With regard to the longitudinal and vertical variations of the turbulence-averaged longitudinal current velocity, the experimental arrangement has functioned to full satisfaction. However, the perforated false bottom also results in additional wave damping and an altered dispersion relation. In order to minimise these unwanted effects, the bulk of the experiments was performed with waves in relatively deep water. Experiments of wave blocking were performed, including blockage of periodic and random waves, and partial and (nominally) complete blocking of random waves. Observations of wave blocking have shown that the incident waves shorten and steepen in the direction towards the blocking point, consistent with the theoretical predictions. Sufficiently steep waves break on the adverse current. Observations have also been made of the intriguing reflected waves with phase velocity directed upstream but with energy transport velocity directed downstream. The reflected waves are only significant in the vicinity of the blocking point. They decay rapidly downstream from the blocking point. Observations have also shown that the blocking point oscillates spatially in the longitudinal direction even in the case of periodic incident waves. Separation of incident and reflected waves has shown that the wave field is everywhere dominated by the incident waves, as also observed visually. Analyses of periodic data have shown generation of side band components for the waves in the vicinity of the blocking point, which is ascribed to nonlinear processes. Analyses of random data have shown a shift of the spectral peak to lower frequencies in the (nominally) complete blocking experiments. This is not observed in partial blocking experiments. This frequency downshifting is ascribed to amplification at lower frequencies and blocking at higher frequencies, but nonlinear transfer of wave energy within the spectrum may also play a role. We have developed a linear model for the amplitude evolution of periodic gravity waves blocked by a collinear adverse current. The amplitude evolution is modelled with a wave action balance (linear ray-approximation) in the region where blocking does not play an important role (far field) and with a uniformly-valid approximation in the vicinity of the blocking point (near field). The basic idea behind the uniformly-valid approximation is that the wave amplitude calculated using this approximation is finite at the blocking point, in contrast to that calculated using the ray approximation. Wave energy dissipation is modelled both in the far field and near field approximations, including dissipation in the side wall boundary layers, dissipation due to the perforated false bottom and dissipation due to wave breaking. In addition, we have developed a spectral model for blockage of long-crested random waves in the steady state situation. The structure of the model is similar to that for blockage of periodic waves referred to the above. Additional concepts are introduced in connection with the random character of the wave field.