Session: 06-16-02 Wave Mechanics, Modeling and Wave Effects II

Paper Number: 79838

79838 - Evaluation of Nonlinear Fourier-Based Maximum Wave Height Predictors Under the Nonlinear Schrödinger Equation 

Traditionally, the analysis of free surface gravity waves  using the fast Fourier transform (FFT) assumes linear superposition of regular waves. This model is also commonly used in offshore engineering to predict extreme sea states for design and safety in construction. However, it looses accuracy when applied to nonlinear waves. Rogue waves are rare events with extreme amplitudes whose heights are larger than two times the significant wave height. The modulational instability and solitons on finite  backgrounds are two possible causes for large rogue waves that have been discussed in the literature. Both can only occur under nonlinear dynamics. The nonlinear Schrödinger (NLS) equation is simplest model for deep water ocean waves (i.e., kh>1.36 ) that incorporates these nonlinear effects. Using a suitable nonlinear Fourier transform (NFT), the NLS equation can be solved (Kotlyarov and Its, Dopov. Akad. Nauk. Ukr., 1976). Nonlinear phenomena such as the modulational instability and solitons can be clearly observed in the nonlinear Fourier domain due to their distinctive spectral portraits. See, e.g., Osborne (Springer, 2010). The nonlinear spectrum is furthermore invariant when the wave propagation is described by the NLS equation, which enables the identification of currently hidden structures in a time series.

Onorato et al. (Phys. Rev. Lett., 2001) generated random time series simulated from a JONSWAP spectrum and simulated their propagation both linearly and according to the NLS equation. They found that the average of the strength (which is maximum wave height over significant wave height) increases for the NLS simulations when the enhancement coefficient  is increased, while it stayed constant for the linear simulations. Islas and Schober (Phys. Fluids, 2005) considered a similar setup and found that under certain circumstances, a simple parameter that can be extracted from the nonlinear spectrum (the splitting distance) correlates with the strength of the observed (rogue) waves.

The objective of this study is to investigate several criteria for the prediction of rogue waves based on the work of Islas and Schober (Phys. Fluids, 2005) and Osborne (e.g. Ocean Dyn., 2019) that are computed in the nonlinear spectral domain. As already mentioned does the nonlinear spectrum stay invariant under the NLS equation, which is why such criteria might potentially reveal rogue waves that are not yet visible.  The setup will be similar to the works discussed above. We generate random time series from JONSWAP spectra, which represents various sea conditions including storm events. The time series are propagated using the narrow-band NLS equation. We then use use the open source software library FNFT by Wahls et al. (J. Open Source Softw., 2018; OMAE 2020) the compute the nonlinear spectra. Finally, we correlate the maximum rogue wave heights over time and space with several NFT-based criteria.

The novel aspects of this work are as follows. First, we will evaluate the splitting distance of Islas and Schober for longer and thus more complicated random time series. Second, we investigate the correlation for criteria based on the work of Osborne that have not been applied in such a setup before. Third, this is the first time that these criteria are compared against each other.

Presenting Author: Yu-Chen Lee Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering, Delft University of Technology

Authors:

Yu-Chen Lee Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering, Delft University of Technology
Sander Wahls Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering, Delft University of Technology
Markus Brühl Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering, Delft University of Technology