Marine plastic debris floating on the ocean surface is a major environmental problem. However, its distribution in the ocean is poorly mapped, and most of the plastic waste estimated to have entered the ocean from land is unaccounted for. Better understanding of how plastic debris is transported from coastal and marine sources is crucial to quantify and close the global inventory of marine plastics, which in turn represents critical information for mitigation or policy strategies. At the same time, plastic is a unique tracer that provides an opportunity to learn more about the physics and dynamics of our ocean across multiple scales, from the Ekman convergence in basin-scale gyres to individual waves in the surfzone. In this review, we comprehensively discuss what is known about the different processes that govern the transport of floating marine plastic debris in both the open ocean and the coastal zones, based on the published literature and referring to insights from neighbouring fields such as oil spill dispersion, marine safety recovery, plankton connectivity, and others. We discuss how measurements of marine plastics (both in situ and in the laboratory), remote sensing, and numerical simulations can elucidate these processes and their interactions across spatio-temporal scales. Environ. Res. Lett. 15 (2020) 023003 E van Sebille et al Environ. Res. Lett. 15 (2020) 023003 E van Sebille et al References Acha E M, Mianzan H W, Iribarne O, Gagliardini D A, Lasta C and Daleo P 2003 The role of the Rı́o de la Plata bottom salinity front in accumulating debris Mar. Pollut. Bull. 46 197-202 Acha E M, Piola A, Iribarne O and Mianzan H 2015 Ecological Processes at Marine Fronts: Oases in the Ocean (Berlin: Springer) Aliani S and Molcard A 2003 Hitch-hiking on floating marine debris: macrobenthic species in the Western Mediterranean Sea Hydrobiologia 503 59-67 Allen J 1985 Principles of Physical Sedimentology (Berlin: Springer) Alpers W 1985 Theory of radar imaging of internal waves Nature 314 245-7 Alsina J M and Cáceres I 2011 Sediment suspension events in the inner surf and swash zone. Measurements in large-scale and high-energy wave conditions Coast. Eng. 58

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 , 441-455). 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. 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. 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. 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. 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. We also discuss remote sensing of the Stokes drift from high-frequency radar. 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. 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. 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.This article is part of the theme issue 'Nonlinear water waves'.

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