Lagrangian Measurements Of Surface Water Waves: Relation Between Drift Velocities And Set-Down

Abstract

Since the work of Stokes on steady progressive surface waves (Stokes, 1847), there has been interest in fluid particle trajectories and associated mass flux. The original result obtained by Stokes was based on linear theory, and implied that there is a net forward drift in the fluid beneath a propagating surface wave. In the non-dimensional case, the drift velocity for a sinusoidal wave on a fluid of depth h is given by

Recent works suggest that in many cases, particularly in waves propagating over a shear flow, a net Eulerian flow may develop, which is opposed to the Stokes drift. Monismith et al. (2007) suggested that in a deep-water setting, the net Eulerian backflow may cancel the Lagrangian Stokes drift on a pointwise basis. Further, Grue & Kolaas (2017) found good agreement with the theoretical findings of Longuet-Higgins (1953), except near the bottom and near the free surface, where boundary layers have a discernable impact on the induced flow.

In recent field measurements, it was observed that the drift velocity correlates positively with the local average fluid depth (Bjørnestad et al., 2021). In other words, a wave with a set-up features a large forward drift, while a wave with a set-down features a negative net drift. The present work aims at investigating what observed in the field by means of laboratory experiments carried out in a wave flume, where monochromatic and bichromatic waves of different characteristics have been run.