The drift associated with the motion of inviscid, irrotational water waves was first derived by Stokes in the mid 19^th century, and is today called Stokes drift. In deep water this takes the form u_s=a²kωe^2kz₀, where a is the wave amplitude, k the wavenumber, ω the radian frequency and z₀ the initial particle depth. This formally second-order quantity is derived from linear theory, and is implemented in a wide variety of wave models to calculate the motion of marine contaminants and other passive tracers.

Adhering to linear wave theory, superposition allows for the immediate generalisation of the Stokes drift from a single wave to a wave spectrum. However, once more than one Fourier mode is included in the lowest order solution, nonlinear effects occurring at second and third order - chief among them the appearance of bound modes - should be considered when calculating Stokes drift.

We introduce a new, analytical correction to the Stokes drift

u_s= ∑_j a_j²ω_jk_je^2k_jz₀+∑_ki>kjω_ia_i²a_j²(k_i-k_j)²(ω_i-ω_j)^-1e^{2(k_i-k_j)z₀}

under assumptions of unidirectional waves and deep water for analytical simplicity - and test this using direct numerical integration of particle paths [1]. Velocity fields for numerical work up to third order are obtained from the reduced Hamiltonian formulation of the water-wave problem due to Zakharov [2], and allow for the inclusion or exclusion of bound harmonics, amplitude evolution and dispersion correction to distinguish among competing effects. In particular, on the typical scale of particle motion the amplitude evolution can be neglected, allowing us to use an algebraic expression for the velocity field in terms of the (initial) Fourier amplitude spectrum [1]. Such an approach has also been successfully employed for deterministic forecasts of the ocean surface [3].

To summarise: we show how higher order contributions to the Stokes drift have an effect throughout the water column. At the surface this is connected to the critical role of high frequencies in the Stokes drift, where dispersion corrections are most influential, as well as contributions from sum-harmonic terms. At greater depths difference harmonics can come to dominate the flow-field and therefore the Stokes drift, as previously demonstrated for wave groups. All of this points to a need to reconsider the common formulation stemming from linear wave theory.

References:

[1] R. Stuhlmeier, Wave-induced drift in third-order deep-water theory, arXiv:2507.15688 (2025).

[2] R. Stuhlmeier, An introduction to the Zakharov equation for modelling deep water waves, D. Henry (ed.) Nonlinear Dispersive Waves (Springer Lecture Notes in Mathematical Fluid Mechanics), Springer (2024), pp. 99-131.

[3] M. Galvagno, D. Eeltink, and R. Stuhlmeier, Spatial deterministic wave forecasting for nonlinear sea-states, Physics of Fluids, (2021) 33 102116

How to cite: Stuhlmeier, R.: On the higher-order wave-induced drift in deep water, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-4780, https://doi.org/10.5194/egusphere-egu26-4780, 2026.

Semi-analytical studies have demonstrated that water compressibility, seabed elasticity, and gravitational potential modify tsunami phase speed and can explain systematic arrival-time deviations observed in farfield measurements [1]. However, operational and research tsunami models remain based on incompressible formulations, preventing explicit simulation of acoustic modes and limiting investigation of gravity–acoustic coupling in large-scale free-surface flows.

We present the derivation and numerical implementation of a compressible set of water-wave evolution equations compatible with the widely used finite-volume tsunami modelling frameworks. Starting from the compressible Euler equations, the formulation retains weak compressibility and acoustic propagation while preserving the long-wave structure required for basin scale simulations. Particular attention is given to the pressure closure, dispersion relation, and numerical consistency with existing solvers.

The equations are being implemented within an open-source solver and validated against analytical limits and controlled numerical benchmarks. Preliminary results demonstrate stable coexistence of surface-gravity and acoustic modes, recovery of expected dispersion behaviour, and improved consistency of wavefront propagation speed relative to incompressible formulations. Synthetic impulsive source experiments of landslides illustrate the generation and radiation of coupled hydroacoustic–surface wave fields and their sensitivity to compressibility effects.

The proposed framework provides a physically consistent pathway for extending dispersion based corrections into fully time-dependent numerical models, which enables systematic investigation of gravity–acoustic coupling, compressibility effects, and wave–acoustic energy partitioning in long-wave ocean dynamics. The formulation also establishes a foundation for coupling numerical wave physics with hydroacoustic observations in future integrated modelling studies.

Reference

[1] A. Abdolali, U. Kadri, & J. Kirby, 2019. Effect of Water Compressibility, Sea-floor Elasticity, and Field Gravitational Potential on Tsunami Phase Speed. Scientific Reports, 9 (1), 1-8. 

How to cite: Kadri, U., Hunt, M., Abolali, A., Kim, J., Omira, R., and Ramalho, R. S.: Compressible water-wave evolution equations for coupled gravity–acoustic modelling of long ocean waves, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-21071, https://doi.org/10.5194/egusphere-egu26-21071, 2026.

The nearshore region provides the link between the land and the ocean. Waves play a crucial part in many nearshore processes including sediment transport, coastal erosion, dispersion of pollutants, rip currents, and many more. It is also the region where most people interact with the ocean. Nevertheless, the nearshore is not well presented in operational wave forecasts.

Here we test the merit of resolving the nearshore region in a regional WAVEWATCH III ® setup. We test this for two contrasting wave climates: the swell-dominated west coast of British Columbia with tidal ranges up to 4m, and the fetch-limited, non-tidal western Baltic Sea with storm surges reaching +-1.5m. Both models are on unstructured grids, and we test the feasibility of zoomed-in regions of very high grid resolution. The effect of currents and water level are evaluated as additional forcing fields.

The models are validated against in-situ wave buoy observations including an array that tracks the wave evolution along two 2km shoaling paths. Gradual wave height reductions of >25% per km are observed, but little change in the spectral shape or directional characteristics.

 These observations are challenging to replicate in the model. We find that the inclusion of currents and water level yield the strongest improvement on significant wave heights and directional spreading, whereas increased grid resolution is beneficial for resolving small-scale bathymetric features.

How to cite: Gemmrich, J., Brooks, B., and Holtermann, P.: Modelling and monitoring waves in the nearshore region, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-8446, https://doi.org/10.5194/egusphere-egu26-8446, 2026.

Global information about ocean wind waves is crucial for understanding their role in the climate system, validating model outputs, and assessing risks for shipping and marine structures. Recent advances in marine radar technologies have enabled accurate, high-resolution measurements of surface wind waves and their spectral characteristics. Making these measurements available in real-time opens a wide new range of products for many user communities. Here we introduce SeaVision, a ship-based monitoring system that, once integrated into a standard shipborne X-band radar, considerably improves real-time observational networks along major shipping routes. SeaVision automatically measures significant wave height, peak period and directional wave spectra at temporal resolutions down to seconds. First developed for research purposes in 2020, SeaVision passed an extensive period of validation using Spotter wave buoys and satellite data. Validation onboard research vessels was conducted for a wide range of latitudes, from the Arctic to Antarctica. SeaVision is fully operational, cost‑effective, and capable of transmitting wave parameters continuously via satellite. Further developments of SeaVision allow for retrieving near surface wind speed, surface currents and ice parameters with the same resolution. Extensive installations of SeaVision (as well as similar systems) onboard commercial and research vessels allow for establishing a near-global observational network (as a part of GCOS and GOOS) largely exceeding capabilities of the present VOS network which over the last few decades are experiencing a dramatic decline and is also regionally complementing satellite missions. SeaVision will enhance coverage of the so far inadequately sampled global oceans.

How to cite: Gulev, S., Ezhova, E., Natalia, T., Gavrikov, A., Sharmar, V., Trofimov, B., Bargman, S., Koltermann, P., Grigorieva, V., and Suslov, A.: Real-time open ocean wind waves from navigation radars for a truly global wind wave operational observing system, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-7925, https://doi.org/10.5194/egusphere-egu26-7925, 2026.

Extreme wave events are recurring meteorological and oceanographic hazards that have a significant impact on coastal regions, leading to infrastructure damage, beach erosion, and adverse effects on fisheries and port operations, resulting in substantial economic losses in Chile. In recent decades, both the frequency and intensity of extreme wave events have increased, and this trend is projected to continue due to climate change, making Chile's extensive coastline particularly vulnerable. In this context, having access to accurate and high-resolution coastal wave forecasting is crucial for coastal users and stakeholders involved in assessing and managing the risks associated with extreme wave events. Here, we present a high-resolution coastal wave forecasting system, which is validated using in situ measurements in Valparaíso Bay. Additionally, an impact-based extreme wave intensity scale has been developed to improve risk communication, support the issuance of official early warnings, and enhance emergency response. A five-category scale, derived from a qualitative analysis of historical impacts on beaches and coastal infrastructure, is fully integrated into the forecasting system. Video cameras have been installed to provide real-time broadcasts of the coastline, facilitating continuous monitoring of wave conditions and their impacts during extreme wave events. Furthermore, the information is disseminated through a dedicated public website and various social media platforms to effectively communicate warnings and promote preventive actions. Key national public institutions responsible for issuing warnings and managing emergencies participate in the information flow, thereby strengthening risk governance and public decision-making, and increasing confidence in the reliability of the coastal wave intensity forecasts.

How to cite: Aguirre, C., Correa, S., Molina, M., and Bahamondez, S.: Impact‑based extreme‑wave intensity scale for high‑resolution coastal forecasting, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-19619, https://doi.org/10.5194/egusphere-egu26-19619, 2026.

Extreme swell events along the Peruvian coast pose recurrent risks to coastal communities, infrastructure, and maritime activities. These events originate far offshore, with their sources varying seasonally: during the austral winter they primarily develop in the South Pacific, while in summer they are typically generated in the western North Pacific. This study investigates the atmospheric circulation patterns associated with extreme wave events along the Peruvian coast generated in both hemispheres, with particular emphasis on the characteristics of the upper-level jet. Furthermore, the potential influence of climate change on the intensity of these events is assessed using an analogue-based methodology.

Events classified by the Peruvian Directorate of Hydrography and Navigation as very strong were selected for those originating in the Southern Hemisphere (SH), whereas strong events were selected for those originating in the Northern Hemisphere (NH). This difference is because events originating further away experience greater dissipation and therefore tend to be weaker. Using ERA5 reanalysis data, a composite analysis of atmospheric circulation revealed characteristic patterns in each hemisphere. SH events were associated with a dipolar cyclonic–anticyclonic pattern, producing strong pressure gradients, intense southwesterly surface winds, and an almost barotropic vertical structure. In contrast, events originating in the western North Pacific were linked to a deep cyclonic system, also exhibiting a barotropic structure. Complementing these results, analysis of the upper-level jet across multiple parameters indicates a more intense and latitudinally confined jet, generally exhibiting a positive tilt in both hemispheres. However, a key hemispheric difference emerges: in the SH, these features correspond to the polar front jet, whereas in the NH they reflect a strengthening of the subtropical jet.

Finally, to assess the anthropogenic influence on 10-m wind intensity between past and present periods, a flow-analogue approach was applied. In the SH, atmospheric circulation similar to those observed during the events is associated with stronger winds in the recent period. This intensification appears to be partly driven by the positive trend in the Southern Annular Mode, linked to anthropogenic ozone depletion and greenhouse gas forcing. In contrast, for events originating in the NH, the anthropogenic signal is less evident due to the pronounced interannual and interdecadal variability of the North Pacific, resulting in analogue-based reconstructions that show wind intensification in some events and weakening in others. Overall, these results highlight the distinct atmospheric dynamics governing swell generation in each hemisphere and provide insights that may inform early-warning systems, coastal risk assessments, and long-term adaptation strategies for Peru.

Acknowledgments: This work was supported by the SAFETE project, which has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 847635 (UNA4CAREER).

How to cite: Agurto Barragan, G., Collazo, S., and García-Herrera, R.: Atmospheric and Climate Drivers of Extreme Swells Along the Peruvian Coast, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-1676, https://doi.org/10.5194/egusphere-egu26-1676, 2026.

Exchanges of momentum and energy across the sea surface microlayer (SML)  are controlled by turbulent dynamics within the first millimeters above/below the wavy water surface. Wind-generated waves, ubiquitous at the ocean surface, strongly influence turbulent processes in the air and water near the surface, especially as the waves grow and (microscale) break. Surface-active substances, commonly found in coastal waters, are known to dampen waves over a wide range of scales. However, the influence of these surfactants on the coupled air-water flow dynamics and associated fluxes remains unclear. Indeed, some of the phenomena involved take place at a sub-millimeter scale, which makes it challenging to investigate the complex mechanisms at stake.

A combination of two experimental techniques (PIV, particle image velocimetry, and LIF, Laser Induced Fluorescence) with a high resolution (33 µm/pixel for the PIV and 55 µm/pixel for the LIF) were used to determine flow motions on both sides of the SML. The complex set-up was installed at a fetch of 15.5m at the 24-m long, 1-m wide, 1-5m high wind wave tank of the University of Hamburg (Germany) which is specially designed for studies with surfactants (Oleyl Alcohol, OLA in this work). Here, we focus on conditions with a reference windspeed of 4.5m/s measured by an ultrasonic anemometer at 64 cm above the water surface.

The wide field of view (51cm) enables us to capture the evolution in time and space of turbulent shear stress above and below individual wind waves. As the waves move through the field of view, steepen and microbreak, high magnitude turbulent shear is produced in the airflow past the wave-crest and can sometimes spread over several wavelengths when intense air-flow separation events occur. A quadrant analysis shows that negative momentum flux (Q1 and Q3) events are usually encountered before wave-crests whereas positive momentum fluxes (Q2 and Q4) events are produced past them on average. In the water, positive turbulent shear stress mainly shows up below the windward side of the waves, while negative turbulent shear is present below their leeward sides. An estimation of the viscous and turbulent energy dissipation integrated over the first centimeter underneath the water surface shows that the production of bound capillary waves enhances the energy dissipation, which becomes more intense as the capillary train grows up.

When surfactants are present, a reduction of sweeps and ejections (Q2 and Q4) past the dampened wave crests is notable and can be associated with the reduced occurrence and intensity of air-flow separation events. In the water, the removal of most capillary waves leads to a reduction in energy dissipation, as well as in the (phase) averaged turbulent kinetic energy below crests.

How to cite: Tondu, C., Buckley, M., Gade, M., and Marcelo Morales Meabe, J.: Laboratory study of turbulent momentum and energy fluxes above/below microscale breaking wind waves, and influence of surfactants, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-14205, https://doi.org/10.5194/egusphere-egu26-14205, 2026.

Results from a suite of simulations with a version of the Norwegian Earth-System Model which includes an ocean surface-waves (OSW) component, WW3, are presented.
OSW are forced by surface winds in the control integration and may be additionally coupled to atmosphere, ocean and sea-ice components through several parametrisations dependent on wave-supported stress, wave significant height, Stokes drift, and wave radiant stress.
Significant effects on the simulated model climatology are found for each of such additional couplings.
However, for the processes considered, the effects of two-way coupling between atmosphere and OSWs, or between sea-ice and OSWs, are highly dependent on the model background climatology -- and therefore also on model systematic biases.
By contrast, additional mixing caused by Langmuir turbulence systematically causes the ocean mixed layer to deepen, with a robust impact on sea-surface temperatures (SSTs), viz mid-latitude cooling in the summer hemisphere, and mid-latitude warming in the winter hemisphere.
Replacing the dynamic OSW model, WW3, with an analytical scheme predicated on a local equilibrium sea-state (Li et al., 2017) to drive Langmuir mixing gives similar results, with a slight exaggeration of the deepening especially in the tropics likely due to missing wind-wave misalignment in the analytical formulation.

How to cite: Ali, A., Bentsen, M., Breivik, Ø., Carrasco, A., Debernard, J. B., Ellevold, T., Michel, C., and Toniazzo, T.: Including dynamic ocean surface waves in NorESM climate simulations, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-12764, https://doi.org/10.5194/egusphere-egu26-12764, 2026.

Accurate prediction of surface waves under tropical cyclones requires realistic representation of storm-induced ocean currents, which can strongly modulate wave growth and propagation. This study synthesizes results from a coupled modeling investigation and an observational analysis using drifting buoys deployed in four Gulf of Mexico hurricanes: Ian (2022), Idalia (2023), Helene (2024), and Milton (2024). The modeling system consists of the WAVEWATCH III wave model coupled to the Modular Ocean Model 6. The ocean model uses a mixing scheme that explicitly includes wave-induced Langmuir turbulence enhancement, resulting in reduced surface Eulerian currents that are more consistent with observations. The surface current introduced in the wave model combines the Eulerian current and the enhancement of the dominant wave group velocity arising from nonlinear interactions with coexisting waves. Idealized experiments show that omitting surface currents leads to systematic overestimation of maximum significant wave height by up to ~9%, with similar sensitivity to the specification of the upper-ocean mixing scheme. In real storms, drifter-based validation confirms that neglecting storm-induced currents results in consistent overestimation of significant wave height and peak period, particularly in regions of strong currents. These current-induced reductions in wave energy occur primarily because dominant wave packets propagate more rapidly and spend less time under intense winds. The effect is strongest in deep water but remains substantial in intermediate depths (20–70 m), where most observations were collected. Together, these results provide compelling evidence that storm-driven currents frequently reduce wave heights and periods under tropical cyclones. Incorporating realistic surface‐current effects into operational models is therefore essential for improving wave forecasts in tropical cyclones and enhancing coastal hazard assessments.

How to cite: Ginis, I., Papandreou, A., and Hara, T.: Wave Reduction by Storm-Driven Ocean Currents in Tropical Cyclones: Coupled Modeling and Drifting Buoy Observations , EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-4294, https://doi.org/10.5194/egusphere-egu26-4294, 2026.

This study investigates wave-driven Langmuir turbulence (LT) in an idealized, depth-varying coastal channel representative of an estuarine bay or tidal river. In the open ocean, LT is a key turbulent process in the surface boundary layer, controlling the transport and mixing of momentum and density. LT arises from wave-current interactions that generate wind-aligned vortices, often visible as surface windrows of aggregated buoyant material such as plankton, bubbles, oil, and microplastics. To examine how LT influences the wind-, tide-, and density-driven circulation in a coastal channel, we develop a turbulence-resolving large eddy simulation (LES) framework with terrain-following coordinates representing a deeper central channel flanked by shallower margins. LT is generated through the Craik-Leibovich (CL) vortex force, which incorporates Stokes drift from wind-driven surface gravity waves. The simulations show that LT substantially enhances turbulent mixing, reducing vertical stratification and shear. Faster tidal currents in the deeper channel differentially advect salt, producing tidally varying lateral salinity gradients. These gradients generate baroclinically driven lateral and vertical tidal currents, whose development is both accelerated and intensified by LT. Conversely, vertical stratification and vertical shear of lateral currents can inhibit LT. Additionally, lateral shear of along‑channel currents associated with the channel bathymetry produces channel‑wide pairs of vertical vorticity that are tilted by Stokes‑drift shear, forming strong and persistent lateral circulations. Overall, the results reveal complex two‑way interactions between LT and the mean circulation, demonstrating that LT significantly modifies both tidally resolved and tidally averaged channel dynamics.

How to cite: Kukulka, T., Thoman, T., and Sullivan, P.: Langmuir turbulence in a depth-varying coastal channel: Insights from large eddy simulations, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-3198, https://doi.org/10.5194/egusphere-egu26-3198, 2026.