# Reduced-order precursors of rare events in unidirectional nonlinear water waves

@article{Cousins2016ReducedorderPO, title={Reduced-order precursors of rare events in unidirectional nonlinear water waves}, author={William T. Cousins and Themistoklis P. Sapsis}, journal={Journal of Fluid Mechanics}, year={2016}, volume={790}, pages={368 - 388} }

We consider the problem of short-term prediction of rare, extreme water waves in irregular unidirectional fields, a critical topic for ocean structures and naval operations. One possible mechanism for the occurrence of such rare, unusually intense waves is nonlinear wave focusing. Recent results have demonstrated that random localizations of energy, induced by the linear dispersive mixing of different harmonics, can grow significantly due to modulation instability. Here we show how the…

## 80 Citations

Reduced-order prediction of rogue waves in two-dimensional deep-water waves

- MathematicsJ. Comput. Phys.
- 2017

Predicting ocean rogue waves from point measurements: An experimental study for unidirectional waves.

- PhysicsPhysical review. E
- 2019

The prediction potentials of a comprehensive rogue-wave reduced-order precursor tool that has been recently developed to predict extreme events due to spatially localized modulation instability are experimentally quantified.

Rogue waves and large deviations in deep sea

- Environmental ScienceProceedings of the National Academy of Sciences
- 2018

The results indicate that rogue waves occur when the system hits unlikely pockets of wave configurations that trigger large disturbances of the surface height, and the rogue wave precursors in these pockets are wave patterns of regular height, but with a very specific shape that is identified explicitly, thereby allowing for early detection.

Probabilistic analysis of the dynamical mechanisms responsible for rare events in 2D waves

- Physics
- 2021

Extreme rare events in ocean waves, the so-called rogue waves, is a well-documented phenomenon with potential for catastrophic consequences. There have been two main lines of thought for the…

Wave group focusing in the ocean: estimations using crest velocities and a Gaussian linear model

- PhysicsNatural Hazards
- 2020

Wave group focusing gives rise to the formation of large gravity waves at the surface of the ocean, some of which are called rogue waves and represent a natural hazard for ships and offshore…

Soliton groups as the reason for extreme statistics of unidirectional sea waves

- Physics
- 2017

The results of the probabilistic analysis of the direct numerical simulations of irregular unidirectional deep water waves are discussed. It is shown that an occurrence of large-amplitude…

Extreme wave formation in unidirectional sea due to stochastic wave phase dynamics

- PhysicsPhysics Letters A
- 2018

Rapid phase-resolved prediction of nonlinear dispersive waves using machine learning

- PhysicsApplied Ocean Research
- 2021

DYNAMICALLY ORTHOGONAL REDUCED-ORDER MODELING OF STOCHASTIC NONLINEAR WATER WAVES

- Mathematics
- 2015

In this thesis, we implement a reduced-order framework for the stochastic evolution of nonlinear water waves governed by the nonlinear Schrördinger (NLS) equation and subject to random initial…

Strong solutions for the Alber equation and stability of unidirectional wave spectra

- MathematicsKinetic & Related Models
- 2020

The Alber equation is a moment equation for the nonlinear Schrodinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea states in terms of…

## References

SHOWING 1-10 OF 74 REFERENCES

Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract We study the occurrence and dynamics of rogue waves in three-dimensional deep water using phase-resolved numerical simulations based on a high-order spectral (HOS) method. We obtain a large…

A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation

- PhysicsJournal of Fluid Mechanics
- 1985

In existing experiments it is known that the slow evolution of nonlinear deep-water waves exhibits certain asymmetric features. For example, an initially symmetric wave packet of sufficiently large…

Unsteady evolution of localized unidirectional deep-water wave groups.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

This work analytically quantify the role of spatial localization in the evolution of localized wave groups in unidirectional water wave envelope equations, and introduces a technique to reduce the underlying partial differential equation dynamics to a simple ordinary differential equation for the wave packet amplitude.

The nonlinear evolution and approximate scaling of directionally spread wave groups on deep water

- GeologyProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2012

The evolution of steep waves in the open ocean is nonlinear. In narrow-banded but directionally spread seas, this nonlinearity does not produce significant extra elevation but does lead to a large…

The effects of randomness on the stability of two-dimensional surface wavetrains

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1978

A simplified nonlinear spectral transport equation, for narrowband Gaussian random surface wavetrains, slowly varying in space and time, is derived fron the weakly nonlinear equations of Davey &…

Modulational instability and non-Gaussian statistics in experimental random water-wave trains

- Physics
- 2005

We study random, long-crested surface gravity waves in the laboratory environment. Starting with wave spectra characterized by random phases we consider the development of the modulational…

The disintegration of wave trains on deep water Part 1. Theory

- MathematicsJournal of Fluid Mechanics
- 1967

The phenomenon in question arises when a periodic progressive wave train with fundamental frequency ω is formed on deep water—say by radiation from an oscillating paddle—and there are also present…

A chronology of freaque wave encounters

- Environmental Science
- 2007

Freaque waves is a newly coined term that combines the two common synonymously used terms of rogue and freak waves. Long before the recent sweeping recognition of the existence of freaque waves,…

Extreme wave events in directional, random oceanic sea states

- Mathematics
- 2001

We discuss the effect of the directional spreading on the occurrence of extreme wave events. We numerically integrate the envelope equation recently proposed by Trulsen et al. [Phys. Fluids 12, 2432…