Particle paths in Stokes’ edge wave

We treat the particle motion in Stokes’ linear edge wave along a uniformly sloping beach. By a rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach, and conclude that particles have a longshore drift in the direction of wave propagation which decreases with depth and distance from the shoreline. We discuss the application of this rotated coordinate frame to higher mode (Ursell) and weakly nonlinear (Whitham) edge waves, and show that the weakly nonlinear case is identical to that for two-dimensional deep-water Stokes waves.