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.

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.

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.

Marine pollution is a major global environmental problem. The transport and dispersion of marine pollution is driven by a wide range of hydrodynamic processes, including wave-induced currents (e.g., Stokes drift) that are generated by free-surface and internal gravity waves in density-stratified fluids. While the (Lagrangian-mean) Stokes drift is known to fundamentally change transport patterns, wave-induced Eulerian-mean currents, such as those generated in the presence of the Coriolis force due to the Earth's rotation, are generally less well understood. To address this, the Delta Transport Processes Laboratory (DTP-Lab), a multi-purpose lab with novel facilities and state-of-the-art equipment, is being constructed in the Hydraulic Engineering Laboratory at TU Delft. The DTP-Lab combines multiple components: a 4.40-m diameter turntable, which can support a (removable) 5-m long flume; a 12.7-m long stainless steel flume; a piston-type, wet-back, force-controlled surface wave generator; a pumping system to create any type of density stratification; and a 3D Particle Tracking Velocimetry (PTV) system. The design and construction of these components along with technical validation and performance tests are presented in this technical note. A scaling analysis demonstrates the suitability of the laboratory to investigate wave-induced current under rotation. The DTP-Lab will pioneer the combined experimental study of surface waves, density stratification and Coriolis forces. The DTP-Lab is presented here with the objective of giving practical information to future users and to describe its novelty and range of applications.

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.

Numerical simulations of marine surface particle dispersal are a crucial tool for addressing many outstanding issues in physical oceanography of societal relevance, such as marine plastic pollution. However, the quality of these Lagrangian simulations depends on the ability of the underlying numerical model to represent prevailing ocean circulation features. Here, we investigate how simulated marine surface particle dispersal changes if the – often omitted or only approximated – impact of wind-generated surface waves on upper-ocean circulation is considered. We use velocity fields from a high-resolution coupled ocean–wave model simulation and a complementary stand-alone ocean model simulation for the Mediterranean Sea to answer the following questions: (1) how does the explicit representation of waves impact simulated surface particle dispersal, and what is the relative impact of Stokes drift and wave-driven Eulerian currents? (2) How accurately can the wave impact be approximated by the commonly applied approach of advecting particles with non-wave-driven Eulerian currents and Stokes drift from stand-alone ocean and wave models? We find that the representation of surface waves tends to increase the simulated mean Lagrangian surface drift speed in winter through the dominant impact of Stokes drift and tends to decrease the mean Lagrangian surface drift speed in summer through the dominant impact of wave-driven Eulerian currents. Furthermore, simulations that approximate the surface wave impact by including Stokes drift (but ignoring wave-driven Eulerian currents) do not necessarily yield better estimates of surface particle dispersal patterns with explicit wave impact representation than simulations that do not include any surface wave impact. Our results imply that – whenever possible – velocity fields from a coupled ocean–wave model should be used for surface particle dispersal simulations.

We present a mathematical model to investigate heat transfer and mass transport dynamics in the wave-driven free-surface boundary layer of the ocean under the influence of long-crested progressive surface gravity waves. The continuity, momentum and convection–diffusion equations for fluid temperature are solved within a Lagrangian framework. We assume that eddy viscosity and thermometric conductivity are dependent on Lagrangian coordinates, and derive a new form of the second-order Lagrangian mass transport velocity, applicable across the entire finite water depth. We then analyse the convective heat dynamics influenced by the free-surface boundary layer. Rectangular distributions of free-surface temperature (i.e. a Dirichlet boundary condition) are considered, and analytical solutions for thermal boundary layer temperature fields are provided to offer insights into free-surface heat transfer mechanisms affected by ocean waves. Our results suggest the need to improve existing models that neglect the effects of free-surface waves and the free-surface boundary layer on ocean mass transport and heat transfer.

Under the influence of surface gravity waves, a floating object experiences a drift in addition to its oscillatory motion. Due to its inertia, both the object's oscillatory motion and its drift will experience a deviation from that of a fluid particle, with the drift of the object typically exceeding the Stokes drift of a fluid particle. This study uses two-dimensional numerical simulations to examine the drift of floating objects in unidirectional, regular, deep-water waves. We investigate the effects of vorticity and turbulence induced by different object shapes. We consider two corner shapes: sharp and round. We investigate object sizes ranging from 1% to 10% of the wavelength. Three types of (two-dimensional) numerical simulations are performed to explore the roles played by viscosity and turbulence: simulations based on the Reynolds-Averaged Navier–Stokes equations (RANS), viscid simulations using the Navier–Stokes equations, and inviscid simulations solving the Euler equations. Objects smaller than 4% of the wavelength are predicted to have a drift equal to the Stokes drift for both corner shapes. As size increases, objects with sharp corners exhibit greater drift enhancement compared to round-cornered objects of equivalent size (compared to the Stokes drift, we report a 454% increase for a sharp-cornered box and a 134% increase for a round-cornered box, both with an object size of 10% of the wavelength). In addition to differences in diffraction patterns and phase differences in the linear motion between objects with two different shapes, a new mechanism for drift enhancement, which is caused by the vorticity generated by the sharp corners, has been identified. The vorticity that arises due to the sharp corners is asymmetrically distributed between the two sides of the object, leading to a non-symmetric dynamic pressure field and, thereby, mean horizontal forces in the direction of wave propagation. The influence of viscosity and turbulence on drift is explored. Viscosity is found to play a dual role. On the one hand, it induces a phase difference in the linear motion and thus increases the drift. On the other hand, viscosity reduces vorticity and thereby decreases the drift enhancement. Finally, we define an unsteadiness ratio of object drift to examine the effect of non-zero acceleration, revealing a correlation between unsteadiness and drift enhancement.

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.

The presence of marine pollutants such as marine plastics has increased significantly over the last decades and poses a major environmental problem, in both the coastal and offshore area. Marine pollutants are transported, mixed and diffused in the ocean, which means the understanding and modelling of marine transport is key for mitigation purposes (Moulton et al., 2022). Additional to large scale and planetary currents that play a major role in marine transport, free surface waves, internal gravity waves in density stratified fluids and the Coriolis force due to the rotation of the Earth are also fundamental drivers of transport that need to be accounted for. The fundamental fluid mechanics processes associated with these are often not resolved in large-scale models, but are instead included in a parametrised form. However, some fundamental processes associated with wave-induced currents (e.g., Stokes drift) in rotating, density-stratified fluids with a free surface remain unclear and untested. In addition, parametrisation for different environments, forcings and time scales must be developed and tested before being implemented into models for them to reliably predict transport, accumulation and storage of marine pollutants. For this purpose, the Delta Transport Processes Laboratory (DTPLab) is being developed at TUDelft Hydraulic Engineering Laboratory. This laboratory pioneers the combined experimental study of surface waves, density stratification and Coriolis forces in a single laboratory. The DTPLab was designed with a multi- users and purposes vision, with interchangeable facilities and state-of-the-art measurement devices. This paper presents the DTPLab facilities (under construction) and equipment that make this laboratory unique in the world, and describes, as an example of what is feasible, a novel experiment that will be performed in this lab.</jats:p>

Floating objects will drift due to the action of surface gravity waves. This drift will depart from that of a perfect Lagrangian tracer due to both viscous effects (non-potential flow) and wave–body interaction (potential flow). We examine the drift of freely floating objects in regular (non-breaking) deep-water wave fields for object sizes that are large enough to cause significant diffraction. Systematic numerical simulations are performed using a hybrid numerical solver, qaleFOAM, which deals with both viscosity and wave–body interaction. For very small objects, the model predicts a wave-induced drift equal to the Stokes drift. For larger objects, the drift is generally greater and increases with object size (we examine object sizes up to 10% of the wavelength). The effects of different shapes, sizes and submergence depths and steepnesses are examined. Furthermore, we derive a ‘diffraction-modified Stokes drift’ akin to Stokes (Trans. Camb. Phil. Soc., vol. 8, 1847, pp. 411–455), but based on the combination of incident, diffracted and radiated wave fields, which are based on potential-flow theory and obtained using the boundary element method. This diffraction-modified Stokes drift explains both qualitatively and quantitatively the increase in drift. Generally, round objects do not diffract the wave field significantly and do not experience a significant drift enhancement as a result. For box-shape objects, drift enhancement is greater for larger objects with greater submergence depths (we report an increase of 92% for simulations without viscosity and 113% with viscosity for a round-cornered box whose size is 10% of the wavelength). We identify the specific standing wave pattern that arises near the object because of diffraction as the main cause of the enhanced drift. Viscosity plays a small positive role in the enhanced drift behaviour of large objects, increasing the drift further by approximately 20%.

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.

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.

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.

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.

Although a ubiquitous natural phenomenon, the onset and subsequent process of surface wave breaking are not fully understood. Breaking affects how steep waves become and drives air–sea exchanges1. Most seminal and state-of-the-art research on breaking is underpinned by the assumption of two-dimensionality, although ocean waves are three dimensional. We present experimental results that assess how three-dimensionality affects breaking, without putting limits on the direction of travel of the waves. We show that the breaking-onset steepness of the most directionally spread case is double that of its unidirectional counterpart. We identify three breaking regimes. As directional spreading increases, horizontally overturning ‘travelling-wave breaking’ (I), which forms the basis of two-dimensional breaking, is replaced by vertically jetting ‘standing-wave breaking’ (II). In between, ‘travelling-standing-wave breaking’ (III) is characterized by the formation of vertical jets along a fast-moving crest. The mechanisms in each regime determine how breaking limits steepness and affects subsequent air–sea exchanges. Unlike in two dimensions, three-dimensional wave-breaking onset does not limit how steep waves may become, and we produce directionally spread waves 80% steeper than at breaking onset and four times steeper than equivalent two-dimensional waves at their breaking onset. Our observations challenge the validity of state-of-the-art methods used to calculate energy dissipation and to design offshore structures in highly directionally spread seas.

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.

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.