Nonlinear Behaviour of Sea Surface Waves Based on Low-Gradient Phase-Only Scattering Effects

Jonathan Blackledge; Eugene Coyle; Derek Kearney

doi:10.21427/d7rg0v

Nonlinear Behaviour of Sea Surface Waves Based on Low-Gradient Phase-Only Scattering Effects

Jonathan Blackledge, Eugene Coyle, Derek Kearney

Research output: Contribution to conference › Paper › peer-review

Abstract

Nonlinear sea waves generated by the wind, including freak waves, are considered to be phenomena that can be modelled using the nonlinear (cubic) Schrodinger equation, for example. However, there is a problem with this approach which is that sea surface waves, driven by wind speeds of varying strength, must be considered to be composed of two distinct types, namely, linear waves and nonlinear waves. In this paper, we consider a different approach to modelling ‘nonlinear’ waves that is based on a solution to the linear wave equation under a low-gradient, phase-only condition. This approach is entirely compatible with the fluid equations of motion (the Navier-Stokes equations) and is thereby not based on a phenomenological model such as the nonlinear Schr¨odinger equation.

Original language	English
DOIs	https://doi.org/10.21427/d7rg0v
Publication status	Published - 2011
Event	International Conference on Environment and Electrical Engineering - Rome, Italy Duration: 1 Jan 2011 → 31 Dec 2011

Conference

Conference	International Conference on Environment and Electrical Engineering
Country/Territory	Italy
City	Rome
Period	1/01/11 → 31/12/11

Keywords

Nonlinear sea waves
wind
freak waves
nonlinear Schrodinger equation
linear waves
nonlinear waves
low-gradient
phase-only condition
Navier-Stokes equations

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10.21427/d7rg0vLicence: CC BY-NC-SA

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title = "Nonlinear Behaviour of Sea Surface Waves Based on Low-Gradient Phase-Only Scattering Effects",

abstract = "Nonlinear sea waves generated by the wind, including freak waves, are considered to be phenomena that can be modelled using the nonlinear (cubic) Schrodinger equation, for example. However, there is a problem with this approach which is that sea surface waves, driven by wind speeds of varying strength, must be considered to be composed of two distinct types, namely, linear waves and nonlinear waves. In this paper, we consider a different approach to modelling {\textquoteleft}nonlinear{\textquoteright} waves that is based on a solution to the linear wave equation under a low-gradient, phase-only condition. This approach is entirely compatible with the fluid equations of motion (the Navier-Stokes equations) and is thereby not based on a phenomenological model such as the nonlinear Schr¨odinger equation.",

keywords = "Nonlinear sea waves, wind, freak waves, nonlinear Schrodinger equation, linear waves, nonlinear waves, low-gradient, phase-only condition, Navier-Stokes equations",

author = "Jonathan Blackledge and Eugene Coyle and Derek Kearney",

year = "2011",

doi = "10.21427/d7rg0v",

language = "English",

note = "International Conference on Environment and Electrical Engineering ; Conference date: 01-01-2011 Through 31-12-2011",

}

TY - CONF

T1 - Nonlinear Behaviour of Sea Surface Waves Based on Low-Gradient Phase-Only Scattering Effects

AU - Blackledge, Jonathan

AU - Coyle, Eugene

AU - Kearney, Derek

PY - 2011

Y1 - 2011

N2 - Nonlinear sea waves generated by the wind, including freak waves, are considered to be phenomena that can be modelled using the nonlinear (cubic) Schrodinger equation, for example. However, there is a problem with this approach which is that sea surface waves, driven by wind speeds of varying strength, must be considered to be composed of two distinct types, namely, linear waves and nonlinear waves. In this paper, we consider a different approach to modelling ‘nonlinear’ waves that is based on a solution to the linear wave equation under a low-gradient, phase-only condition. This approach is entirely compatible with the fluid equations of motion (the Navier-Stokes equations) and is thereby not based on a phenomenological model such as the nonlinear Schr¨odinger equation.

AB - Nonlinear sea waves generated by the wind, including freak waves, are considered to be phenomena that can be modelled using the nonlinear (cubic) Schrodinger equation, for example. However, there is a problem with this approach which is that sea surface waves, driven by wind speeds of varying strength, must be considered to be composed of two distinct types, namely, linear waves and nonlinear waves. In this paper, we consider a different approach to modelling ‘nonlinear’ waves that is based on a solution to the linear wave equation under a low-gradient, phase-only condition. This approach is entirely compatible with the fluid equations of motion (the Navier-Stokes equations) and is thereby not based on a phenomenological model such as the nonlinear Schr¨odinger equation.

KW - Nonlinear sea waves

KW - wind

KW - freak waves

KW - nonlinear Schrodinger equation

KW - linear waves

KW - nonlinear waves

KW - low-gradient

KW - phase-only condition

KW - Navier-Stokes equations

U2 - 10.21427/d7rg0v

DO - 10.21427/d7rg0v

M3 - Paper

T2 - International Conference on Environment and Electrical Engineering

Y2 - 1 January 2011 through 31 December 2011

ER -

Nonlinear Behaviour of Sea Surface Waves Based on Low-Gradient Phase-Only Scattering Effects

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