Improved explicit approximation of linear dispersion relationship for gravity waves

S. Beji

doi:10.1016/j.coastaleng.2012.10.002

Improved explicit approximation of linear dispersion relationship for gravity waves

S. Beji^*

^*Corresponding author for this work

Department of Shipbuilding and Ocean Engineering

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

29 Citations (Scopus)

Abstract

For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given.

Original language	English
Pages (from-to)	11-12
Number of pages	2
Journal	Coastal Engineering
Volume	73
DOIs	https://doi.org/10.1016/j.coastaleng.2012.10.002
Publication status	Published - Mar 2013

Keywords

Accurate empirical water wave dispersion formula
Water wave dispersion relationship

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10.1016/j.coastaleng.2012.10.002

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title = "Improved explicit approximation of linear dispersion relationship for gravity waves",

abstract = "For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5\%, the improved relationship has a maximum relative error of less than 0.05\%. A simpler form of the relationship with 0.2\% accuracy is also given.",

keywords = "Accurate empirical water wave dispersion formula, Water wave dispersion relationship",

author = "S. Beji",

year = "2013",

month = mar,

doi = "10.1016/j.coastaleng.2012.10.002",

language = "English",

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pages = "11--12",

journal = "Coastal Engineering",

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publisher = "Elsevier B.V.",

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AU - Beji, S.

PY - 2013/3

Y1 - 2013/3

N2 - For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given.

AB - For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given.

KW - Accurate empirical water wave dispersion formula

KW - Water wave dispersion relationship

UR - https://www.scopus.com/pages/publications/84868479017

U2 - 10.1016/j.coastaleng.2012.10.002

DO - 10.1016/j.coastaleng.2012.10.002

M3 - Article

AN - SCOPUS:84868479017

SN - 0378-3839

VL - 73

SP - 11

EP - 12

JO - Coastal Engineering

JF - Coastal Engineering

ER -

Improved explicit approximation of linear dispersion relationship for gravity waves

Abstract

Keywords

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