Although other types of waves can display Stokes drift, such as vertically confined internal wave modes, oceanic Kelvin and Rossby waves or acoustic waves, the focus of this review is on surface gravity waves. As a result of these two effects, the particle experiences a net forward drift, which is proportional to the square of the steepness of the waves. A fluid particle, which oscillates backwards and forwards due to the linear wave motion, spends more time in the forward-moving region underneath the crest than in the backward-moving region underneath the trough and undergoes its forward motion at greater height, where the velocities are larger. The linearized trajectories of Lagrangian particles underneath linear unidirectional surface gravity waves are formed by closed ellipses, tending to circles in the limit when the water depth is large relative to the wavelength, as is illustrated in figure 1. Following the motion of particles underneath a wave, ‘in addition to the motion of oscillation the particles are transferred forwards, that is, in the direction of propagation, with a constant velocity’, p. This article is part of the theme issue ‘Nonlinear water waves’.Īlthough their leading-order motion is periodic-in other words backwards and forwards-surface gravity waves induce a net drift in the direction of wave propagation known as the Stokes drift. Together with the advent of new space-borne instruments that can measure surface Stokes drift, such models hold the promise of quantifying the impact of wave effects on the global atmosphere–ocean system and hopefully contribute to improved climate projections. Future climate models will probably involve full coupling of ocean and atmosphere systems, in which the wave model provides consistent forcing on the ocean surface boundary layer. Finally, the paper discusses the three main areas of application of the Stokes drift: in the coastal zone, in Eulerian models of the upper ocean layer and in the modelling of tracer transport, such as oil and plastic pollution. We also discuss remote sensing of the Stokes drift from high-frequency radar. In the field, rapid advances are expected due to increasingly small and cheap sensors and transmitters, making widespread use of small surface-following drifters possible. Despite more than a century of experimental studies, laboratory studies of the mean circulation set up by waves in a laboratory flume remain somewhat contentious. After briefly reviewing the fundamental physical processes, most of which have been established for decades, the review addresses progress in laboratory and field observations of the Stokes drift. This paper reviews progress in fundamental and applied research on the induced mean flow associated with surface gravity waves since the first description of the Stokes drift, now 170 years ago. More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel and the average Eulerian flow velocity of the fluid. During its periodic motion, a particle floating at the free surface of a water wave experiences a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes 1847 Trans.
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