Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.

We observe the dispersive breaking of cosine-type long waves [Phys. Rev. Lett. 15, 240 (1965)] in shallow water, characterizing the highly nonlinear “multisoliton” fission over variable conditions. We provide new insight into the interpretation of the results by analyzing the data in terms of the periodic inverse scattering transform for the Korteweg–de Vries equation. In a wide range of dispersion and nonlinearity, the data compare favorably with our analytical estimate, based on a rigorous WKB approach, of the number of emerging solitons. We are also able to observe experimentally the universal Fermi-Pasta-Ulam recurrence in the regime of moderately weak dispersion.

The problem of existence of stable nonlinear groups of gravity waves in deep water is considered by means of laboratory and numerical simulations with the focus on strongly nonlinear waves. Wave groups with steepness up to A_crω_m²/g ≈ 0.30 are reproduced in laboratory experiments (A_cr is the wave crest amplitude, ω_m is the mean angular frequency, and g is the gravity acceleration). We show that the groups remain stable and exhibit neither noticeable radiation nor structural transformation for more than 60 wavelengths or about 15-30 group lengths. These solitary wave patterns differ from the conventional envelope solitons, as only a few individual waves are contained in the group. Very good agreement is obtained between the laboratory results and numerical simulations of the potential Euler equations. The envelope soliton solution of the nonlinear Schrödinger equation is shown to be a reasonable first approximation for specifying the wave-maker driving signal. The short intense envelope solitons possess vertical asymmetry similar to regular Stokes waves with the same frequency and crest amplitude. Nonlinearity is found to have remarkably stronger effect on the speed of envelope solitons in comparison to the nonlinear correction to the Stokes wave velocity.

This paper discusses the potential of deterministic wave prediction as one basic module for decision support of offshore operations. Therefore, methods of different complexity—the linear wave solution, the non-linear Schrödinger equation (NLSE) of two different orders and the high-order spectral method (HOSM)—are presented in terms of applicability and limitations of use. For this purpose, irregular sea states with varying parameters are addressed by numerical simulations as well as model tests in the controlled environment of a seakeeping basin. The irregular sea state investigations focuses on JONSWAP spectra with varying wave steepness and enhancement factor. In addition, the influence of the propagation distance as well as the forecast horizon is discussed. For the evaluation of the accuracy of the prediction, the surface similarity parameter is used, allowing an exact, quantitative validation of the results. Based on the results, the pros and cons of the different deterministic wave prediction methods are discussed. In conclusion, this paper shows that the classical NLSE is not applicable for deterministic wave prediction of arbitrary irregular sea states compared to the linear solution. However, the application of the exact linear dispersion operator within the linear dispersive part of the NLSE increased the accuracy of the prediction for small wave steepness significantly. In addition, it is shown that non-linear deterministic wave prediction based on second-order NLSE as well as HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance, with the HOSM providing a high accuracy over a wider range of applications.