The study of nearshore wave-induced currents, which play a critical role in marine transport, has motivated numerous laboratory experiments, and yet, the understanding of cross-shore wave-induced currents under controlled laboratory conditions remains incomplete. For the first time, 3D Particle Tracking Velocimetry is applied in a laboratory flume to measure Lagrangian wave-induced currents in front of a slope under five different regular wave conditions. The wave-induced velocity profiles evolve over time, reaching a quasi-equilibrium after approximately one hour. In most cases, the observed profiles do not align with the theoretical Stokes or conduction solutions. The surface drift is consistently smaller than theoretically predicted, and in some cases even negative, indicating the presence of a strong Eulerian-mean return current in the upper portion of the water column. The observed patterns cannot be explained solely by the relative water depth kh and wave steepness ka, leading to the hypothesis that convection processes contribute to these discrepancies. Further investigation of visually observed coherent convective structures, such as vortex trains, will be undertaken.

We report experimental evidence of an Eulerian-mean flow, created by the interaction of surface waves and tailored ambient sub-surface turbulence, which partly cancels the Stokes drift, and present supporting theory. Water-side turbulent velocity fields and Eulerian-mean flows were measured with particle image velocimetry before vs after the passage of a wave group, and with vs without the presence of regular waves. We compare different wavelengths, steepnesses and turbulent intensities. In all cases, a significant change in the Eulerian-mean current is observed, strongly focused near the surface, where it opposes the Stokes drift. The observations support the picture that, when waves encounter ambient sub-surface turbulence, the flow undergoes a transition during which Eulerian-mean momentum is redistributed vertically (without changing the depth-integrated mass transport) until a new equilibrium state is reached, wherein the near-surface ratio between and approximately equals the ratio between the streamwise and vertical Reynolds normal stresses. This accords with a simple statistical theory derived here and holds regardless of the absolute turbulence level, whereas stronger turbulence means faster growth of the Eulerian-mean current. We present a model based on Rapid distortion theory which describes the generation of the Eulerian-mean flow as a consequence of the action of the Stokes drift on the background turbulence. Predictions are in qualitative, and reasonable quantitative, agreement with experiments on wave groups, where equilibrium has not yet been reached. Our results could have substantial consequences for predicting the transport of water-borne material in the oceans.

The large size of traditional drifters limits their ability to mimic the transport of buoyant objects at the ocean surface, which are subject to complex interactions among direct wind drag, fast-moving surface currents, and wave-induced transport. To better capture these dynamics, we track the trajectories of 12 novel, ultra-Thin surface drifters deployed in the southern North Sea over 68 d. We adopt a data-driven approach to model drifter velocity using hydrodynamic and atmospheric data, applying both a linear leeway parameterisation and two machine learning models: random forest and support vector regression. Machine learning model-Agnostic interpretation techniques reveal that tidal forcing predominantly drives zonal motion, whereas wind is the main driver in the meridional direction in this region. Notably, the wind exhibits a saturation effect, and its contribution to explaining the variance of the drifter velocity decreases at higher speeds. In trajectory prediction experiments, we find that machine learning models, particularly random forest, outperform linear models, with the latter achieving comparable accuracy only at short time scales. Using a hybrid approach and deriving a non-linear function of the wind from machine learning interpretable methods to include in the leeway parameterisation significantly improves the model prediction of the drifter trajectory. Finally, we test the generalisability of the North Sea-Trained models using an independent drifter dataset from the Tyrrhenian Sea. Despite the differences in ocean dynamics between the regions, the machine learning models reproduce the observed trajectories with comparable accuracy to state-of-The-Art studies, demonstrating robust explanatory skill and a low degree of overfitting in this instance.

Surface gravity waves induce a drift on objects floating on the water's surface. This study presents laboratory experiments investigating the drift of large two-dimensional floating objects on deep-water, unidirectional, regular waves, with wave steepness ranging from 0.04 to 0.31 (0.04 0.31, where is the wavenumber and the wave amplitude). The objects were carefully designed to have a rectangular cross-section with a constant aspect ratio; their size varied from 2.6 to 27 of the incident wavelength. We observed Lagrangian behaviour for small objects. Small and large objects exhibited fundamentally different drift behaviour at high compared with low wave steepness, with a regime shift observed at a certain size and wave steepness. The scaling of object drift with steepness depends on the relative size of the object. For small objects, drift scales with steepness squared, whereas drift becomes a linear function of steepness as the object size increases. For objects that are relatively large but smaller than 13-16% of a wavelength (low to high steepness), we provide experimental evidence supporting the mechanisms of drift enhancement recently identified by Xiao et al. (J. Fluid Mech., vol. 980, 2024, p. A27) and termed the 'diffraction-modified Stokes drift'. This enhanced drift behaviour, compared with the theoretical Stokes drift for infinitely small fluid parcels, is attributed to changes in the objects' oscillatory motion and local wave amplitude distribution (standing wave pattern) due to the presence of the object. In the case of larger objects, similar to Harms (J. Waterw. Port Coast. Ocean Eng., vol. 113(6), 1987, pp. 606-622), we relate the critical size at which drift is maximised to their vertical bobbing motion. We determine the domain of validity for both Stokes drift and the diffraction-modified Stokes drift model of Xiao et al. (J. Fluid Mech., vol. 980, 2024, A27) in terms of relative size and wave steepness and propose an empirical parametrisation based on our experimental data.

Waves transport particles in the direction of wave propagation with the Stokes drift. When the Earth’s rotation is accounted for, waves induce an additional (Eulerian-mean) current that reduces drift and is known as the anti-Stokes drift. This effect is often ignored in oceanic particle-tracking simulations, despite being important. Although different theoretical models exist, they have not been validated by experiments. We conduct laboratory experiments studying the surface drift induced by deep-water waves in a purpose-built rotating wave flume. With rotation, the Lagrangian-mean drift deflects to the right (counterclockwise rotation) and reduces in magnitude. Compared with two existing steady theoretical models, measured drift speed follows a similar trend with wave Ekman number but is larger. The difference is largely explained by unsteadiness on inertial time scales. Our results emphasise the importance of considering unsteadiness when predicting and analysing the transport of floating material by waves.

Laboratory experiments were performed to investigate the attenuation of progressive deep-water waves by a mono-layer of loose- and close-packed floating spheres. We measured the decay distance of waves having different incident wave frequency and steepness. The attenuation of waves was strong if the surface concentration of particles was close-packed, with the decay distance being shorter for incident waves with higher frequency and steepness. The amplitude of the highest-frequency (2.0 Hz) and largest amplitude incident waves (with steepness 0.25) decayed by half over a distance of approximately 3 wavelengths. Theoretical models used previously in the study of surface wave damping by sea ice do not capture correctly the physics of wave attenuation by floating spheres. We developed a new theory that estimates the influence upon wave attenuation of turbulent dissipation resulting from oscillatory flow under a close-packing of spheres. This theory predicts that the wave amplitude decays as a power law, and gives a correct order-of-magnitude estimate of the observed decay distance. We explore the potential implications of these findings for the attenuation of progressive waves by (pancake) sea ice and for the indirect detection of marine plastic pollution from space.

Correction to: Naturehttps://doi.org/10.1038/s41586-024-07886-z Published online 14 September 2024 In the version of the article initially published, there was a typographical error where in the Fig. 5 title, now reading “For 3D waves, breaking onset does not limit crest height,” the word “not” was missing. The error has been corrected in the HTML and PDF versions of the article.

Wave breaking is a multifaceted physical phenomenon that is not fully understood and remains challenging to model. An effective method for investigating wave breaking involves utilising the two-phase Reynolds-averaged Navier–Stokes (RANS) equations to directly simulate breaking waves. In this study, we apply a RANS model with an adaptively refined mesh to simulate breaking waves in deep water using the stabilised RANS model proposed by Larsen and Fuhrman. This approach enables a more efficient simulation of the physics of breaking waves compared to Direct Numerical Simulations, as it places less stringent demands on grid resolution. Our findings demonstrate that the RANS model compares well with deep water wave breaking experiments in terms of surface elevation. We also give estimates of the breaking strength parameter of our RANS simulations and compared them with the literature.

Floating marine litter is transported by several mechanisms, including surface waves. In studies of marine litter transport, the wave-induced drift is set to be equal to the Stokes drift, corresponding to the Lagrangian-mean wave-induced drift of an infinitesimally small tracer. Large-scale experiments are used to show how the wave-induced drift of objects of finite size depends on their size, density, and shape. We observe increases in drift of 95% compared to Stokes drift for discs with diameters of 13% of the wavelength, up to 23% for spheres with diameters of 3% of the wavelength, whereas drift is reduced for objects that become submerged such as nets. We investigate what these findings may imply for the transport of plastic pollution in realistic wave conditions and we predict an increase in wave-induced drift for (very) large plastic pollution objects. The different extrapolation techniques we explore to make this prediction exhibit a large range of uncertainty.

Understanding the effect of wind forcing on steep unidirectional waves is important for the study of wind-wave interaction. In this paper, unidirectional random wave experiments are carried out in a large-scale wave tank in which waves interacted with turbulent wind generated by wind fans. The properties and evolution of deep-water gravity waves subject to following wind forcing are investigated through parametric laboratory experiments. The effect of wind forcing on the significant wave height varies with the initial wave steepness. Wind forcing increases the growth of waves of small initial steepness but attenuates large, steep waves as a result of the vertical angle of the wind to the free surface in our experiments. The energy input by wind forcing increases the high-frequency tail of the wave spectra, and this effect increases with fetch. The mean frequency increases under wind forcing. The effect of wind forcing on the probability of extreme events is investigated. Wind forcing enhances wave steepness, resulting in a deviation of the exceedance probability from first-order and second-order theoretical distributions and an increased value of kurtosis but not skewness.

Wave breaking is a complex physical process about which open questions remain. For some applications, it is critical to include breaking effects in phase-resolved envelope-based wave models such as the non-linear Schrödinger. A promising approach is to use machine learning to capture breaking effects. In the present paper we develop the machine learning architecture to model breaking developed by Eeltink et al. (2022) further, potentially enabling more detailed breaking physics to be captured. We show that this model can be trained on focused wave groups but can also capture breaking in random waves and modulated plane waves. Analysis of the model suggests that the machine learning has broken the problem into two—one part which detects whether the wave is breaking and another which captures the subsequent behaviour, consistent with the way human scientists routinely understand the breaking problem.

The statistical treatment of random weakly nonlinear interactions between waves, called wave turbulence (WT), is fundamental to understanding the development of the ocean surface. For gravity waves, wave turbulence predicts a dual (direct and inverse) cascade of energy and wave action, which yield power-law solutions for the energy spectrum. While energy cascades were predicted more than 50 years ago, observing them in the laboratory with mechanical forcing remains a challenge. Here, we present experiments in which we attempted to reproduce both direct and inverse cascades in a large circular wave tank. The geometry of the wave tank allows for the creation of isotropically spread surface waves, which is an assumption that underlies WT theory. Although we did see evidence of a direct cascade of energy, we did not observe an inverse cascade of wave action. We discuss the competing effects of dissipation and intermittency, which may dominate or obscure the weakly nonlinear dynamics.

Remote sensing technologies have the potential to support monitoring of floating plastic litter in aquatic environments. An experimental campaign was carried out in a large-scale hydrodynamic test facility to explore the detectability of floating plastics in ocean waves, comparing and contrasting different microwave and optical remote sensing technologies. The extensive experiments revealed that detection of plastics was feasible with microwave measurement techniques using X and Ku-bands with VV polarization at a plastic threshold concentration of 1 item/m² or 1–10 g/m². The optical measurements further revealed that spectral and polarization properties in the visible and infrared spectrum had diagnostic information unique to the floating plastics. This assessment presents a crucial step towards enabling the detection of aquatic plastics using advanced remote sensing technologies. We demonstrate that remote sensing has the potential for global targeting of plastic litter hotspots, which is needed for supporting effective clean-up efforts and scientific evidence-based policy making.