Energy Transfer From Wind to Wave Groups: Theory and Experiment

Shahrdad G. Sajjadi; Andrei Ludu

doi:10.17654/DM020010021

Energy Transfer From Wind to Wave Groups: Theory and Experiment

Shahrdad G. Sajjadi, Andrei Ludu

Mathematics

Embry-Riddle Aeronautical University

Research output: Contribution to journal › Article › peer-review

Abstract

<div class="line" id="line-23"> Three major unresolved problems that remain in oceanography are studied in depth, namely (a) unsteady waves, where waves are allowed to grow or decay in time and space; (b) sharp-crested waves (also known as fully nonlinear Stoke waves), which are note characteristic in oceans; and (c) group of waves, which can often become sharp-crested as they propagate  downstream, as demonstrated here experimentally in a wave tank. The ultimate aim of such investigation is to improve the parameterization of the energy input from wind to waves. In this paper, we (i) present results on the simplest approximation to wave groups which result to a fully nonlinear Stokes waves (those having a sharp-crest); (ii) impose the boundary condition at the surface wave, rather than at the mean surface; (iii) assume the wave phase velocity is complex which consequently allows the wave amplitude to vary according to  <img src="http://www.pphmj.com.ezproxy.libproxy.db.erau.edu/admin/tinymce_uploads/2apr26three_2.gif"/>   where  <img src="http://www.pphmj.com.ezproxy.libproxy.db.erau.edu/admin/tinymce_uploads/2apr27three_3.gif"/>   is the initial constant amplitude,  k  is the wave number, and  <img src="http://www.pphmj.com.ezproxy.libproxy.db.erau.edu/admin/tinymce_uploads/2apr28three_4.gif"/>   is the wave complex phase speed; and, (iv) include the dominant viscous term in the perturbation equations. It is shown that: (i) yields an energy-transfer coefficient that is larger than that previously calculated for monochromatic waves and agree well with experimental data; (ii) has no major effect on the end-results; (iii) shows the variation of dimensionless energy-transfer parameter  b  with the wave age for unsteady waves; (iv) the vertical component of perturbation velocity is not singular at the critical point. </div>

Original language	American English
Journal	Advances and Applications in Fluid Mechanics
Volume	21
DOIs	https://doi.org/10.17654/DM020010021
State	Published - Jan 2017

Keywords

nonlinear waves
air-sea interaction
sharp-crested Stokes waves
wave tank experiment
wave groups

Disciplines

Oceanography and Atmospheric Sciences and Meteorology
Fluid Dynamics
Statistical, Nonlinear, and Soft Matter Physics

Access to Document

10.17654/DM020010021License: Unspecified

Cite this

@article{1775a8170d244614bbcc09f6253a8a74,

title = "Energy Transfer From Wind to Wave Groups: Theory and Experiment",

abstract = " Three major unresolved problems that remain in oceanography are studied in depth, namely (a) unsteady waves, where waves are allowed to grow or decay in time and space; (b) sharp-crested waves (also known as fully nonlinear Stoke waves), which are note characteristic in oceans; and (c) group of waves, which can often become sharp-crested as they propagate  downstream, as demonstrated here experimentally in a wave tank. The ultimate aim of such investigation is to improve the parameterization of the energy input from wind to waves. In this paper, we (i) present results on the simplest approximation to wave groups which result to a fully nonlinear Stokes waves (those having a sharp-crest); (ii) impose the boundary condition at the surface wave, rather than at the mean surface; (iii) assume the wave phase velocity is complex which consequently allows the wave amplitude to vary according to    where    is the initial constant amplitude,  k  is the wave number, and    is the wave complex phase speed; and, (iv) include the dominant viscous term in the perturbation equations. It is shown that: (i) yields an energy-transfer coefficient that is larger than that previously calculated for monochromatic waves and agree well with experimental data; (ii) has no major effect on the end-results; (iii) shows the variation of dimensionless energy-transfer parameter  b  with the wave age for unsteady waves; (iv) the vertical component of perturbation velocity is not singular at the critical point. ",

keywords = "nonlinear waves, air-sea interaction, sharp-crested Stokes waves, wave tank experiment, wave groups",

author = "Sajjadi, {Shahrdad G.} and Andrei Ludu",

year = "2017",

month = jan,

doi = "10.17654/DM020010021",

language = "American English",

volume = "21",

journal = "Advances and Applications in Fluid Mechanics",

}

TY - JOUR

T1 - Energy Transfer From Wind to Wave Groups: Theory and Experiment

AU - Sajjadi, Shahrdad G.

AU - Ludu, Andrei

PY - 2017/1

Y1 - 2017/1

N2 - Three major unresolved problems that remain in oceanography are studied in depth, namely (a) unsteady waves, where waves are allowed to grow or decay in time and space; (b) sharp-crested waves (also known as fully nonlinear Stoke waves), which are note characteristic in oceans; and (c) group of waves, which can often become sharp-crested as they propagate  downstream, as demonstrated here experimentally in a wave tank. The ultimate aim of such investigation is to improve the parameterization of the energy input from wind to waves. In this paper, we (i) present results on the simplest approximation to wave groups which result to a fully nonlinear Stokes waves (those having a sharp-crest); (ii) impose the boundary condition at the surface wave, rather than at the mean surface; (iii) assume the wave phase velocity is complex which consequently allows the wave amplitude to vary according to    where    is the initial constant amplitude,  k  is the wave number, and    is the wave complex phase speed; and, (iv) include the dominant viscous term in the perturbation equations. It is shown that: (i) yields an energy-transfer coefficient that is larger than that previously calculated for monochromatic waves and agree well with experimental data; (ii) has no major effect on the end-results; (iii) shows the variation of dimensionless energy-transfer parameter  b  with the wave age for unsteady waves; (iv) the vertical component of perturbation velocity is not singular at the critical point.

AB - Three major unresolved problems that remain in oceanography are studied in depth, namely (a) unsteady waves, where waves are allowed to grow or decay in time and space; (b) sharp-crested waves (also known as fully nonlinear Stoke waves), which are note characteristic in oceans; and (c) group of waves, which can often become sharp-crested as they propagate  downstream, as demonstrated here experimentally in a wave tank. The ultimate aim of such investigation is to improve the parameterization of the energy input from wind to waves. In this paper, we (i) present results on the simplest approximation to wave groups which result to a fully nonlinear Stokes waves (those having a sharp-crest); (ii) impose the boundary condition at the surface wave, rather than at the mean surface; (iii) assume the wave phase velocity is complex which consequently allows the wave amplitude to vary according to    where    is the initial constant amplitude,  k  is the wave number, and    is the wave complex phase speed; and, (iv) include the dominant viscous term in the perturbation equations. It is shown that: (i) yields an energy-transfer coefficient that is larger than that previously calculated for monochromatic waves and agree well with experimental data; (ii) has no major effect on the end-results; (iii) shows the variation of dimensionless energy-transfer parameter  b  with the wave age for unsteady waves; (iv) the vertical component of perturbation velocity is not singular at the critical point.

KW - nonlinear waves

KW - air-sea interaction

KW - sharp-crested Stokes waves

KW - wave tank experiment

KW - wave groups

U2 - 10.17654/DM020010021

DO - 10.17654/DM020010021

M3 - Article

VL - 21

JO - Advances and Applications in Fluid Mechanics

JF - Advances and Applications in Fluid Mechanics

ER -