Task-Related Rogue Waves Embedded in Extreme Seas

Abstract

This paper describes a new technique for the generation of tailored design wave sequences in extreme seas which are simulated under laboratory conditions. The wave field is fitted to predetermined global and local target characteristics defined in terms of significant wave height, peak period as well as wave height, crest height, and period of individual waves. The generation procedure is based on two steps: Firstly, a linear approximation of the desired wave train is computed by a Sequential Quadratic Programming (SQP) method which optimises an initially random phase spectrum for a given variance spectrum. The wave board motion derived from this initial guess serves as starting point for directly fitting the physical wave train to the target parameters. The subplex method developed by Rowan (1990) is applied to improve systematically a certain time frame of the wave board motion which is responsible for the evolution of the design wave sequence. The discrete wavelet transformation is introduced to reduce significantly the number of free variables to be considered in the fitting problem. Wavelet analysis allows to localise efficiently the relevant information of the electrical control signal of the wave maker in time and frequency scale. Nonlinear free surface effects, even wave breaking are included in the fitting process since the simulation of the physical wave evolution under laboratory conditions is an integral part of the new technique. This feature is especially important for simulating experimentally wave/structure interactions in rogue waves and critical wave groups. As an illustration of this technique the Draupner “New Year Wave” is simulated and generated in a physical model wave tank. Also a “Three Sisters” wave sequence with succeeding wave heights Hs … 2Hs … Hs, embedded in an extreme sea, is synthesised.