Criteria of wave breaking onset and its variability in irregular wave trains

Abstract

Wave breaking is a random process that causes extreme hydrodynamic loads on offshore structures which lead to structural degradation and destruction. The majority of studies in literature analysed single wave breaking events in (quasi-)monochromatic wave trains and focused on energy dissipation and slamming forces on structures. Due to the random nature of wave breaking, its parameters vary widely and cannot be predicted with an exact value at a future instant of time, but instead must be described with probabilistic statements and statistical averages. This thesis analyses the variability of wave breaking onset, in order to gain deeper knowledge of the frequency and likelihood of occurrence of wave breaking, providing many applications to a more economic design and safety of offshore structures. Breaking onset is de fined as an instantaneous state of wave dynamics where a wave has not started to break but cannot return to a stable state either. Present investigations focus on the evolution of wave trains towards and at breaking onset to describe the stochastic process of breaking onset, to find precursors and indicators of breaking onset, and to determine the optimal sample size of test runs to get a reliable result of the parameters of breaking onset. By this means, insights on the variability of breaking onset and its distribution function are achieved, which have not been available beforehand. In this context, investigations on breaking onset in irregular wave trains (JONSWAP sea spectrum) in intermediate water depth are carried out using laboratory and hydronumerical model tests. The physical model tests are carried out in the wave flume of the Ludwig-Franzius-Institute in a length scale of 1:40. In parallel, hydronumerical model tests using a numerical wave fl ume developed by Sriram (2008) and Sriram et al. (2006; 2007; 2010), based on the fully non-linear potential flow theory (semi-arbitrary Lagrangian-Eulerian Finite Element Method (SALE-FEM, structured version)), are conducted in the same length scale to complement the laboratory investigations and to increase the possible test run length and number. As design database the wave measurements of research platform FINO1 in the North Sea for the time period 2004-2011 are used and JONSWAP spectra are selected in such a way that daily and storm events are covered. By means of the random phase angle distribution, every considered spectrum is transformed multiple times to artificial, but physically-sound time series of water surface elevations. The cause-effect relationship between input wave train and breaking onset is investigated with a dimensional analysis (Buckingham Pi theorem) and an analysis of the uni- and bivariate (copula) distribution functions. The optimal sample size of test runs is derived by means of a convergence analysis. Indicators of breaking onset are detected by analysing the surface elevation (over time and over flume length) and applying the threshold method which assumes that breaking onset happens when a parameter exceeds a certain threshold value. A novel detection indicator based on the Hilbert transform is introduced. Precursors of breaking onset are presented with Markov chains of the geometrical and instantaneous parameters, which describe the conditions that had to be met stochastically for wave instability to occur.