Oblique long waves on beach and induced longshore current

This study considers the 3D runup of long waves on a uniform beach of const ant or variable downward slope that is connected to an open ocean of unifor m depth. An inviscid linear long-wave theory is applied to obtain the funda mental 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. Comparis on is made between the present theory and the ray theory to ascertain a cri terion of validity. The wave induced longshore current is evaluated by find ing the Stokes drift of the fluid particles carried by the momentum of the waves obliquely incident upon a sloping beach. Currents of significant velo cities are produced by waves at incidence angels about 45 degrees and by gr azing waves trapped on the beach. Also explored are the effects of the vari able downward slope and curvature of a uniform beach on 3D runup and reflec tion of long waves.