A time-dependent nonlinear mild-slope equation for water waves

Beji, S; Nadaoka, K

doi:10.1098/rspa.1997.0018

A time-dependent nonlinear mild-slope equation for water waves

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, cilt.453, sa.1957, ss.319-332, 1997 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 453 Sayı: 1957
Basım Tarihi: 1997
Doi Numarası: 10.1098/rspa.1997.0018
Dergi Adı: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.319-332
İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

A weakly nonlinear and dispersive water wave equation, which in linearized form yields a new version of the time-dependent mild-slope equation of Smith & Sprinks (1975), is derived. The applicable spectral width of the new wave equation for random waves is found to be more satisfactory than that of Smith and Sprinks (1975). For very shallow depths the equation reduces to the combined form of Airy's nonlinear non-dispersive wave equations; if the lowest-order dispersion is retained it produces the combined form of Boussinesq's equations. In the deep-water limit the equation admits the second-order Stokes waves as analytical solutions. Furthermore, by introducing a right-moving coordinate transformation, the equation is recast into a unidirectional form, rendering the KdV equation in one limit while reproducing the second-order Stokes waves in the other.