Improved explicit approximation of linear dispersion relationship for gravity waves

Beji S.

COASTAL ENGINEERING, vol.73, pp.11-12, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73
  • Publication Date: 2013
  • Doi Number: 10.1016/j.coastaleng.2012.10.002
  • Title of Journal : COASTAL ENGINEERING
  • Page Numbers: pp.11-12


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. (C) 2012 Elsevier B.V. All rights reserved.