A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (Benjamin–Feir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrodinger equation, the Davey–Stewartson system, the Korteweg–de Vries equation, the Kadomtsev–Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon.

/pdf/physical-mechanisms-of-the-rogue-wave-phenomenon-iao5kemdkh.pdf

Physical Mechanisms of the Rogue Wave Phenomenon

http://personalpages.to.infn.it/~onorato/publications_files/2013_Onorato_etal_PhysRep.pdf

Rogue waves and their generating mechanisms in different physical contexts

Curious wave phenomena that occur in optical fibres due to the interplay of instability and nonlinear effects are reviewed.

/pdf/instabilities-breathers-and-rogue-waves-in-optics-252ilwzt4i.pdf

Instabilities, breathers and rogue waves in optics

The nonlinear Schrodinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

/pdf/observation-of-kuznetsov-ma-soliton-dynamics-in-optical-df7wim9dhb.pdf

Observation of Kuznetsov-Ma soliton dynamics in optical fibre

Loads for use in the design of ships and offshore structures

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrodinger 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.

https://ueaeprints.uea.ac.uk/41940/1/journal.pone.0054629.pdf

Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

Sophisticated routing of ships is increasingly recognised as an important contribution to safe, reliable and economical ship operation. The more reliable the weather forecasts and the performance simulation of ships in a seaway become, the better they serve to identify the best possible route in terms of criteria like estimated time of arrival (ETA), fuel consumption (FUEL), safety (of ship, crew, passengers and cargo) and comfort. This establishes a multi-objective, non-linear and constrained optimisation problem in which a suitable compromise has to be found between opposing targets. For its solution, a new optimisation approach to select the most advantageous route on the basis of hydrodynamic simulations and sophisticated weather forecasts is posed. Transfer functions are employed to assess the operating behaviour of a ship in waves. Probabilistic ensemble forecasts are applied to account for the stochastic behaviour of weather. A multi-objective genetic algorithm turns out to be a suitable optimisati...

Robust Pareto-optimum routing of ships utilising deterministic and ensemble weather forecasts

Gaussian wave packets — a new approach to seakeeping testsof ocean structures*

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 Acrωm2/g ≈ 0.30 are reproduced in laboratory experiments (Acr is the wave crest amplitude, ωm 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 Schrodinger equation is shown to be a reasonable first approximation for specifying the wave-maker driving signal. The short intense envelope solitons possess ver...

https://mt.dms.tu-berlin.de/publikationen/2013/_ojpstmp_stampPdf_d_28T11_18_PHFLE6_25_6_067105_1.pdf

Simulations and experiments of short intense envelope solitons of surface water waves

The problem of existence of stable nonlinear groups of gravity waves in deep water is revised by means of laboratory and numerical simulations with the focus on intense waves. Wave groups with steepness up to $A_{cr} \omega_m^2 /g \approx 0.30$ are reproduced in laboratory experiments ($A_{cr}$ is the wave crest amplitude, $\omega_m$ 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 wave lengths 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 strongly nonlinear numerical simulations of the potential Euler equations. The envelope soliton solution of the nonlinear Schr\"odinger equation is shown to be a reasonable first approximation for specifying the wavemaker 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.

Günther F. Clauss

Papers

Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

Robust Pareto-optimum routing of ships utilising deterministic and ensemble weather forecasts

Gaussian wave packets — a new approach to seakeeping testsof ocean structures*

Simulations and experiments of short intense envelope solitons of surface water waves

Simulations and experiments of short intense envelope solitons of surface water waves