# Nonlinear Four-Wave Interactions and Freak Waves

@article{Janssen2003NonlinearFI, title={Nonlinear Four-Wave Interactions and Freak Waves}, author={Peter A. E. M. Janssen}, journal={Journal of Physical Oceanography}, year={2003}, volume={33}, pages={863-884} }

Four-wave interactions are shown to play an important role in the evolution of the spectrum of surface gravity waves. This fact follows from direct simulations of an ensemble of ocean waves using the Zakharov equation. The theory of homogeneous four-wave interactions, extended to include effects of nonresonant transfer, compares favorably with the ensemble-averaged results of the Monte Carlo simulations. In particular, there is good agreement regarding spectral shape. Also, the kurtosis of the…

## 664 Citations

### Hamiltonian Description of Ocean Waves and Freak Waves

- Mathematics
- 2016

Freak wave generation and decay is discussed in the context of the Hamiltonian description of ocean waves. In linear theory the probability distribution function (p.d.f.) of the surface elevation is…

### Nonlinear Wave Statistics in a Focal Zone

- Physics
- 2009

Abstract In this paper, the combined effects of refraction and nonlinearity on the evolution of ocean surface wave statistics are considered and possible implications for the likelihood of extreme…

### Comparison of linear and nonlinear extreme wave statistics

- PhysicsActa Oceanologica Sinica
- 2016

An extremely large (“freak”) wave is a typical though rare phenomenon observed in the sea. Special theories (for example, the modulation instability theory) were developed to explain mechanics and…

### Quasi-resonant interactions and non-gaussian statistics in long crested waves

- Physics
- 2004

We compare the statistical properties of long crested surface gravity waves recorded in a long wave tank with numerical results obtained from a modified kinetic equation derived from the Dysthe…

### Extreme waves and modulational instability: wave flume experiments on irregular waves

- Physics
- 2003

We discuss the formation of large amplitude waves for sea states characterized by JONSWAP spectra with random phases. In this context we discuss experimental results performed in one of the largest…

### Freak waves in crossing seas

- Physics, Mathematics
- 2010

Abstract.
We consider the modulational instability in crossing seas as a potential mechanism for the formation of freak waves. The problem is discussed in terms of a system of two coupled Nonlinear…

### Modulational instability in crossing sea states: a possible mechanism for the formation of freak waves.

- MathematicsPhysical review letters
- 2006

It is shown that the introduction of a second plane wave, propagating in a different direction, can result in an increase in the instability growth rates and enlargement of the instability region.

### Effects of coherent dynamics of stochastic deep-water waves.

- Environmental SciencePhysical review. E
- 2020

A method of windowed spatiotemporal spectral filtering is proposed to segregate different nonlinear wave components and to calculate the surface of free waves, showing able to contribute essentially to the abnormally large values of the surface displacement kurtosis.

## References

SHOWING 1-10 OF 60 REFERENCES

### 366 Nonlinear Four Wave Interactions and Freak Waves

- Physics, Environmental Science
- 2002

Four-wave interactions are shown to play an important role in the evolution of the spectrum of surface gravity waves. This follows from direct simulations of an ensemble of ocean waves using the…

### Extreme waves and modulational instability: wave flume experiments on irregular waves

- Physics
- 2003

We discuss the formation of large amplitude waves for sea states characterized by JONSWAP spectra with random phases. In this context we discuss experimental results performed in one of the largest…

### The propagation of a weak nonlinear wave

- Mathematics, PhysicsJournal of Fluid Mechanics
- 1972

We consider the propagation of a weak nonlinear wave whose energy is concentrated in a narrow band of wavenumbers in a fluid which is both dispersive and dissipative. We use the small amplitude…

### Nonlinear Modulation of Gravity Waves

- Mathematics, Physics
- 1972

Slow modulation of gravity waves on water layer with uniform depth is investigated by using singular perturbation methods. It is found, to the lowest order of perturbation, that the complicated…

### On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory

- PhysicsJournal of Fluid Mechanics
- 1962

The energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method. The fifth-order…

### 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 &…

### Propagation of Wave Packets and Space-time Self-focusing in a Nonlinear Medium

- Physics
- 1967

Specific features of the propagation of modulated waves in a transparent nonlinear dispersive medium are investigated. In particular, it is shown that a monochromatic wave can be unstable with…

### Note on a modification to the nonlinear Schrödinger equation for application to deep water waves

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1979

The ordinary nonlinear Schrödinger equation for deep water waves, found by perturbation analysis to O(∊3) in the wave-steepness ∊ ═ ka, is shown to compare rather unfavourably with the exact…