Computation of Short-Crested Deepwater Waves

Abstract

Short-crested waves are three-dimensional waves that may be generated through a reflection of a two-dimensional Stokes wave on a seawall. Thus, they are more likely to be observed near ports or any consequent marine structure. Two numerical methods are used to compute three-dimensional surface gravity short-crested waves on deepwater. The first method is an asymptotic procedure and the second computes a direct numerical solution. One of the main properties is the four-wave resonance. Such resonance introduces nonu- niqueness with several solution branches connected through a turning point. We show that both computational methods are reliable for nonresonant waves, but that the direct numerical method converges faster. For resonant waves, the direct method is more appropriate because all solution branches can be obtained. The asymptotic method computes only one branch of solutions for any given parameter values, and is uncertain around and past any turning point. Stability analysis of the branches shows that, although sporadic, an instability associated with harmonic resonance is more likely to appear for one branch in the vicinity of the turning point. Consequently this could amplify the unstable resonant mode. The nonuniqueness of the solution requires careful attention in every study on the impact of surface waves on marine structures. It is shown here that the wave force exerted on a seawall may change drastically from one branch of solution to another.