Stokes waves revisited: exact solutions in the asymptotic limit

Megan Davies, Amit K. Chattopadhyay

Research output: Contribution to journalArticle

Abstract

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations
in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.
Original languageEnglish
Article number69
Number of pages5
JournalEuropean Physical Journal
Volume131
Issue number3
Early online date28 Mar 2016
DOIs
Publication statusE-pub ahead of print - 28 Mar 2016

Fingerprint

Surface waves
secular variations
Gravity waves
gravity waves
engineers
surface waves
estimating
velocity distribution
engineering
Engineers
expansion
propagation
estimates

Bibliographical note

The final publication is available at Springer via http://dx.doi.org/10.1140/epjp/i2016-16069-7

Cite this

@article{3740c14daf384edfb739eae87c8435d5,
title = "Stokes waves revisited: exact solutions in the asymptotic limit",
abstract = "The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximationsin the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.",
author = "Megan Davies and Chattopadhyay, {Amit K.}",
note = "The final publication is available at Springer via http://dx.doi.org/10.1140/epjp/i2016-16069-7",
year = "2016",
month = "3",
day = "28",
doi = "10.1140/epjp/i2016-16069-7",
language = "English",
volume = "131",
journal = "European Physical Journal",
issn = "1951-6355",
publisher = "Springer",
number = "3",

}

Stokes waves revisited : exact solutions in the asymptotic limit. / Davies, Megan; Chattopadhyay, Amit K.

In: European Physical Journal, Vol. 131, No. 3, 69, 28.03.2016.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stokes waves revisited

T2 - exact solutions in the asymptotic limit

AU - Davies, Megan

AU - Chattopadhyay, Amit K.

N1 - The final publication is available at Springer via http://dx.doi.org/10.1140/epjp/i2016-16069-7

PY - 2016/3/28

Y1 - 2016/3/28

N2 - The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximationsin the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

AB - The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximationsin the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

UR - http://link.springer.com/article/10.1007/s11187-016-9810-1

UR - http://www.scopus.com/inward/record.url?scp=85007268724&partnerID=8YFLogxK

U2 - 10.1140/epjp/i2016-16069-7

DO - 10.1140/epjp/i2016-16069-7

M3 - Article

AN - SCOPUS:85007268724

VL - 131

JO - European Physical Journal

JF - European Physical Journal

SN - 1951-6355

IS - 3

M1 - 69

ER -