Nonlinear Deepwater Extreme Wave Height and Modulation Wave Length Relation

Prediction of extreme wave heights has always been a challenge in both the naval and energy industries. The survivability and safe operation and design of marine vehicles and devices are highly dependent on the probability distribution of the wave heights of extreme waves. In traditional linear approaches, researchers use various probability distribution functions mostly generated from field measurements and are usually modified with some statistical methods to account for the distribution of wave heights. These approaches do not take into account nonlinearity and instability in wave train behavior and solely relies on linear wave theory assumptions and perhaps some second order effects in more advanced probability models. This study emphasizes the application of modulation wavelengths and periods, resulting from modulational instability analysis of the nonlinear Schrödinger equation (NLS). In this study, state-of-the-art nonlinear Fourier analysis (NLFA) based on NLS is employed to calculate the unstable wave components. The resulting rise time and travel distance for such unstable modes and their maximum possible growth amplitudes are used to derive a range of probable occurrences. Numerical simulation results from CFD computations are used to examine the capability of such an approach in predicting the magnitude and location of extreme wave occurrence. It is shown that application of the proposed NLS-based analytical procedure enables a more accurate prediction of the extreme wave field.