On particle trajectories for Stokes’ edge waves

Abstract: The matter of particle motion beneath water waves is one of the most natural of questions; it is immediately clear from observations that water particles do not generally travel with the speed of the waveform, but the exact character of their motion in different types of waves has been the matter of much investigation. We treat the particle motion in Stokes’ linear edge wave, which propagates along a uniformly sloping beach: a three-dimensional wave with variation in the cross-shore and long-shore directions. Using analogies between the exact, rotational solution developed by Gerstner and linear water wave theory, and an appropriate rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach. Some applications to weakly nonlinear edge waves, as well as modern results by Constantin, Ehrnström, and Villari on particle paths will also be discussed.

This seminar is suitable for undergraduates as well as interested staff.