American Society of Civil Engineers

Oblique Long Waves on Beach and Induced Longshore Current

by Jin E. Zhang, (Asst. Prof., c/o EF, City Univ. of Hong Kong, Tat Chee Ave., Kowloon, Hong Kong) and Theodore Y. Wu, (Prof. Emeritus, Engrg. Sci., California Inst. of Tech., Pasadena, CA 91125)

Journal of Engineering Mechanics, Vol. 125, No. 7, July 1999, pp. 812-826, (doi:

     Access full text
     Purchase Subscription
     Permissions for Reuse  

Document type: Journal Paper
Abstract: This study considers the 3D runup of long waves on a uniform beach of constant or variable downward slope that is connected to an open ocean of uniform depth. An inviscid linear long-wave theory is applied to obtain the fundamental solution for a uniform train of sinusoidal waves obliquely incident upon a uniform beach of variable downward slope without wave breaking. For waves at nearly grazing incidence, runup is significant only for the waves in a set of eigenmodes being trapped within the beach at resonance with the exterior ocean waves. Fourier synthesis is employed to analyze a solitary wave and a train of cnoidal waves obliquely incident upon a sloping beach, with the nonlinear and dispersive effects neglected at this stage. Comparison is made between the present theory and the ray theory to ascertain a criterion of validity. The wave-induced longshore current is evaluated by finding the Stokes drift of the fluid particles carried by the momentum of the waves obliquely incident upon a sloping beach. Currents of significant velocities are produced by waves at incidence angles about 45° and by grazing waves trapped on the beach. Also explored are the effects of the variable downward slope and curvature of a uniform beach on 3D runup and reflection of long waves.

ASCE Subject Headings:
Littoral currents
Long waves
Solitary waves
Wave reflection
Wave runup