Titles and abstracts 

Titles and abstracts appear in the order of presenters in the full program.

Title: Particle Dynamics in Ocean Waves

Presenter: Henrik Kalisch, UiB

Abstract: In the analysis of ocean waves, it is often assumed that as a periodic wavetrain enters the coastal zone from deep water and approaches a beach, the waves start behaving in some sense as individual solitary waves. This is described for example in the review by Galvin [6] who states that “the wave on the beach can be treated as a solitary wave.” 

However, there is a complication with this point of view which is the positioning of the wave relative the mean surface elevation. A solitary wave has a large excess mass, while a periodic wavetrain is usually assumed to have zero mean. At the same time, there is a strong forward mass flux in solitary waves while the net mass flux in a periodic wavetrain is given only by the Stokes drift which is much smaller. In fact, depending on the mean level in a periodic wave, it may feature either a weak forward drift due to the well known Stokes drift (see Figure 2, left panels) or a strong
forward drift similar to a solitary wave (see Figure 2, right panels). A moment of thought shows that at least in theory, all intermediate states are also possible. The goals the work presented here are twofold. First, we report on a field campaign aimed at understanding wave-by-wave dynamics and Lagrangian properties of ocean swell in the surf
zone. Using a custom-built stereo imaging system, we are able to track individual particles as they are cycling through the wave field approaching the beach. It appears that the mean level of the wavefield varies in a wave-by-wave fashion, and that it is strongly correlated to the wave average taken over one period (in this case, zero-crossing period).
Secondly, we show that the wave and particle motion can be described to a satisfactory degree with simple mathematical models such as the Korteweg-de Vries (KdV) equation [2, 12] or Boussinesq-type systems [1, 11]. Indeed, using standard asymptotic analysis in combination with simple nonlinear model equations yields a description of the wave field and particle motion which is in line with the field data [3].

The motivation for the present study is partially given by a number of recent theoretical and experimental results concerning Lagrangian properties of fluid particles in the context of surface wave motion. For example, some recent works have cast doubt on the ubiquity of the well known Stokes drift. Indeed, in some studies, in particular in the presence of a background current in deep water, it has been observed that there is no Stokes drift either in the average, or even in the pointwise sense [9]. On the other hand, the experiments reported in [4] seem to confirm the essence of Stokes’s original work. Still other works highlight the importance of the boundary layer both at the bed and at the free surface [7, 8]. In essence, these works argue that the Stokes drift may take a very different form than what was originally found by Stokes. The present work is aiming to understand particle drift under field conditions.

Title: Breakers and bubble plumes observed from above and below

Presenter: Maria Bjørnestad, MET

Abstract: Field measurements of bubble plume evolution and wave dynamics were obtained using a submerged acoustic Doppler current profiler (ADCP) deployed within the field of view of a stereo camera system at Ekofisk in the central North Sea. By leveraging the ADCP's multi-beam geometry, we extended traditional single-beam bubble detection methods to achieve broader spatial coverage of bubble plume measurements. The combined wave and bubble observations reveal that deep bubble plumes often occur spatially offset from surface whitecaps, suggesting that Langmuir-type circulation plays an important role in the formation and persistence of deep bubble plumes through both vertical and horizontal advection.

Title: Validation of coastal wave forecasts and hindcasts for the Norwegian coast

Presenter: Jan-Victor Björkqvist, MET

Abstract: Accurate information about surface wave conditions along the coastline is vital for maritime safety, as well as fixed and floating constructions. Observations are the most accurate way of retaining information about the wave field, but they are often costly and available only for shorter time periods. In situ observations, such as wave buoys, might also represent only a small area, especially when the coastline is very complex, as it is in Norway. Remote sensing products can offer significantly better coverage in time and space, but their usability is somewhat limited very close to the shoreline. Therefore, there is a need to complement available measurements with numerical models. Nonetheless, there is no obvious best candidate for all applications. We compare four different wave products that can be used near the coast of Norway: NORA3, NORAC, WAM800, and BarentsWatch. NORA3 is a decades-long larger scale (3 km) hindcast, while NORAC is a new downscaling of NORA3 that is made with an unstructured grid (down to 250 m resolution) for 7 years and covers only a part of the coastline. WAM800 is a 800 m forecast produced by MET Norway and BartentsWatch is a high-resolution (up to 100 m) wave forecast produced by NORCE. Both forecasts cover the entire Norwegian coastline. The four wave products are validated against available wave measurements, which include satellite data, wave buoy data around the Sulafjorden area provided by Statens Vegvesen, and new – previously unused – observations from Frohavet provided by SalMar Akar Ocean AS. The validation reveals that, depending on the area, the products can either agree well or not. Although the over-all accuracy of the products differs, the most important conclusion is that one has to consider the application at hand when weighing the pros and cons of the different products.

Title: Constructions and properties in the mathematical theory of water waves

Presenter: Mats Ehrnstrom, NTNU

Abstract: This talk glimpses into some different aspects of the mathematical theory for water waves, in particular travelling such, and how the setting and solution properties are linked, and influence the mathematical constructions and analysis.

As this is the first meeting of its kind, part of the talk will be a presentation of the dispersive group in Trondheim and the work we have carried out during the last ten years. The central topic will be travelling waves over finite-depth water. I describe some of the questions asked, and the method we use to solve them. Themes include the Euler equations with vorticity, nonlocal models, singular waves, and properties of solutions.

The talk is based on a number of projects together with students and collaborators.

Title: Statistical distributions of ocean wave crest heights

Presenter: Odin Gramstad, DNV

Abstract: Understanding the statistical properties of ocean surface waves, such as the distribution of wave heights and crest heights, is essential for various engineering applications, such as risk assessment, reliability analysis, and design of marine structures. For a realistic description of ocean wave crests, it is necessary to include nonlinear effects, and today the most common model for crest heights used in engineering is the Forristal (2000) distribution, which is based on an empirical fit to numerical simulations of second-order random waves.
Although more theoretically grounded crest distributions exist, their adoption has been limited, likely because the distribution parameters - the skewness and kurtosis of the sea surface – are not easily available from observations or spectral wave models. In a recent study (Gramstad & Lian, 2024), a numerical method for calculating the theoretical skewness and kurtosis for a given wave spectrum is developed. This method provides new and more accurate parameterizations of the theoretical crest distributions in terms of common sea state parameters. The improved parameterizations for skewness and kurtosis, which consider wave steepness, water depth, spectral bandwidth, and directional spreading, offer a practical way to incorporate these factors into higher-order distributions for crest heights, wave heights, and surface elevation. Some comparisons with phase-resolved numerical simulations and field observations from the North Sea, as discussed in a recent paper by Vanem et al. (2024), are also presented.

Title: Topography estimation from scattering of water waves

Presenter: Adrian Kirkeby, Simula

Abstract: Is it possible to reconstruct a variable water depth by observing the water waves that propagate over it?

In this talk, we will present some recent results on this question. We show that in the linear regime, this problem can be modelled as a classical inverse scattering problem, but since water waves are easier to observe, we can actually measure the full scattered wave field. We present a conditional stability results for the depth estimation and show some numerical examples using a simple reconstruction method based on the PDE model. 

Title: An Open-Source Framework for Multiscale Modeling of Waves and Hydrodynamics

Presenter: Hans Bihs, NTNU

Abstract: Most of the coastal and marine hydrodynamic phenomena are multi-scale problems. Before waves reach the coast, they often travel long distances. When the waves interact with structures in the coastal zone such as for example with offshore wind turbines, the wave propagation problem turns into wave-structure interaction. The complex hydrodynamics of the wave breaking impact on the structure occurs within a domain of interest of only several meters and a comparatively short duration of time. Considering this, REEF3D is an open-source hydrodynamics framework with a focus on applications within coastal and marine engineering. It contains several large-scale phase-resolved wave models. The potential flow model FNPF and the non-hydrostatic model NHFLOW are designed to be able to model the complex coastal bathymetry of the Norwegian coast, including strong diffraction and refraction effects. A high-resolution computational fluid dynamics (CFD) solver resolves complex free surface flows in a two-phase flow manner. The CFD model focusses on near-field hydrodynamics and wave structure interaction, such as for example breaking waves and slamming. All models benefit from the overall HPC approach of the framework and are all fully parallelized. The large scale wave models can be used stand-alone or can be coupled to the CFD model through the hydrodynamic coupling feature. The presentation gives an overview over the framework and highlights relevant applications in the coastal and ocean engineering fields.

Title: Open-Source Tool for Metocean Analysis and Metocean Data

Presenter: Thea Josefine Ellevold, MET

Abstract: The Norwegian Meteorological Institute has a long experience in producing hindcast data sets (e.g., NORA10 and NORA3) and metocean data analysis. This has now developed into an open-source Python tool called metocean-stats, where input data can be extracted using metocean-api.

The metocean-stats is a tool for comprehensive statistics (seasonal, annual, extremes) and visualization of metocean data (wind, waves, ocean currents, tide levels, air and water temperature, sea ice, and more). The input data is conveniently provided within the tool as a Pandas DataFrame (time series of metocean variables) from a single position.

The tool is designed with cross-platform compatibility in mind. It can smoothly operate on various operating systems, including Linux, Windows, and MacOS. Moreover, its compatibility with WEkEO Jupyter Lab allows seamless integration and use.

Title: Low cost, small wave buoys: where are we, and what perspectives?

Presenter: Jean Rabault, MET

Abstract: Wave buoys have traditionally been large and expensive. However, small low cost buoys (either commercial as the Sofar Spotter, or open source and community driven as the OpenMetBuoy and the MicroSwift) are now disrupting the wave buoy segment, providing an order of magnitude cost reduction compared to traditional solutions. In this presentation, we will provide an overview of the small low cost wave buoys available, their principle of operation and total cost of ownership, and their strengths and weaknesses. Moreover, we will discuss perspectives opened by the development of low cost small wave buoys for gathering novel datasets that go beyond the wave spectra that are traditionally gathered, which opens for new scientific opportunities.

Title: A precise conformally mapped method for water waves in complex transient environments

Presenter: Andreas Holm Akselsen, Sintef

Abstract: A two-dimensional water wave model based on conformal mapping is presented.
The model is exact in the sense that it does not rely on truncated series expansions nor suffer any numerical diffusion.
Additionally, it is computationally highly efficient as it numerically evaluates only the surface line while using a fixed number of FFT operations per time step.
A double layered mapping enforces prescribed outer boundaries without iteration.
The model also supports transient boundaries, including walls.
Mapping models are presented that support smooth bathymetries and angled overhanging geometries.
Exact wavemaker representations demonstrates the method's potential as a numerical wave tank.
It is also well suited for representing natural bathymetries, rising tectonic shelves, tsunamis, and wave interactions with mechanical structures.

Title: WAVE-DRIVEN VORTEX PATTERNS AT AN OPEN BEACH

Presenter: Andreas Bondehagen Jacobsen, UiB

Abstract: TBA. 

Title: Coastal wave refraction over varying currents and arbitrary depths.

Presenter: Trygve Halsne, MET

Abstract: Wave refraction—the veering of surface gravity waves due to underlying current and depth gradients—is a predominant mechanism causing spatially inhomogeneous wave fields. However, the interplay between depth- and current-induced refraction remains poorly understood. We present a new approximate analytical solution for the wave ray curvature, which is valid under the weak current assumption and the geometric optics approximation. The ray curvature is the appropriate measure of refraction, and denotes how much a curve departs from a straight line. The solution extends previous works that have either focused on deep water or finite depth conditions, and thus provides a seamless framework for computing the wave ray curvature at arbitrary depths under non-zero currents. We discuss various aspects of the interplay between current- and depth-induced wave refraction, particularly emphasizing the role of the horizontal gradients in the respective ambient fields. These computations are carried out in an open-source ray tracing framework, and the wave refraction is highlighted using a few limiting cases. The approximate solution has the form of a superposition of a current- and depth-altered component, which enables analysis of their individual and combined contribution to the wave refraction. In particular, we show situations where the two either amplify or counteract each other, and in the extreme limit cancel each other; such situations cause zero refraction, but are very sensitive to small changes in the respective ambient fields. Our results are expected to be relevant for applications related to oceanographic remote sensing retrievals and coastal wave forecasting services.

Title: Anti-Stokes flow induced by waves and turbulence

Presenter: Simen Ådnøy Ellingsen, NTNU

Abstract: In order to predict the motion of, e.g., microplastics, nutrients, pollutants and oil spills in the oceans, the role of waves must be taken into account. The mean motion due to Stokes drift could be essential, yet several experiments and field studies have observed that an opposite Eulerian-mean current tends to cancel this drift, causing small or no wave-induced surface motion. These surprising observations have bwwn unexplained for well over a decade. With experiment as well as theory we show that when waves encounter a turbulent current, the flow goes through a period of transition before a new, combined “equilibrium” state is reached where an Eulerian-mean “anti-Stokes” current has been created near the surface. Turbulence is invariably present in natural flows, making wave-turbulence interaction a candidate explanation for the puzzling observations. The induced flow modification changes sign with depth, and does not contribute to net mass transport, but could have important consequences for the motion of floating matter. The results come from three experiments at the large water channel facility at NTNU trondheim where waves were propagated against a current with different, tailored, turbulence properties, which investigate both the transient “transition” phase and the final “equilibrium” state. Theory is also presented for both of these stages which show clearly that the effect we observe can be ascribed to wave-turbulence interaction.

Title: Experimental evidence of transversal modulation and frequency down-shift of uniform waves in a long tank

Presenter: Karsten Trulsen

Abstract: It is well known that Stokes waves propagating in a long tank can develop sideband instability, known as Benjamin–Feir instability, by which the originally uniform wavesdevelop into a heavily modulated wave train. It is also  well-known that after a stage of heavy modulations, the wave train can come back to a state of uniform waves, known as Fermi–Pasta–Ulam recurrence. However, sometimes the recurrence is to uniform waves of a lower frequency, known as frequency downshift (Lake et al., 1977). We report experiments in a long tank showing that transversal Benjamin–Feir instability of Stokes waves can lead to a significant energy transfer into oscillations across the

tank. We observe frequency downshift in the long distance evolution of Stokes waves essentially only when significant interactions with unstable narrow-banded transversal modes are involved. With insufficient resolution of measurements across the tank, the energy transferred to transversal modes could be misinterpreted as dissipation. Our experiments suggest that the frequency downshift depends as much on narrow-banded unstable transversal modulations of type I as it does on damping or wave breaking. Broad-banded unstable modulations of type II and horseshoe modulation patterns do not imply downshift. Left two photos show examples of transversal modulations in an experiment that led to downshift. Right photo shows broad-banded type II horseshoe modulation in an experiment

that did not lead to downshift.

References: Lake, B. M., Yuen, H. C., Rungaldier, H. & Ferguson, W. E. 1977 Nonlinear deep-water waves: theory and experiment. Part 2: Evolution of a continuous wave train.

Title: GPUs and waves

Presenter: André Brodtkorp, OsloMet

Abstract: GPUs were once upon a time a curious accelerator meant to compute three dimensional graphics. I remember buying a computer from Komplett.no with the advanced 3dfx Vodoo2 graphics card, and the even more powerful ATI Radeon 9700 a few years later. I played Counter Strike beta, and attended “The Gathering” during one easter for a week filled with computer screens. Today, my use of GPUs has changed. I still use them actively, but today I use them for scientific computing. This talk will go through the development of GPU simulators starting with an OpenGL-powered simulation engine up to a Python-powered GPU simulator for clusters. The take-home message from this talk will not be new mathematics or physics (though a lot of the works has included that as well). It will be on
how we can use the hardware we have available in the most efficient way to simulate real-world phenomena. Videos will be shown.

Title: Extreme statistics of wave forces on a horizontal cylinder behind a shoal

Presenter: Karen Samseth, UiO

Abstract: We present the laboratory experiments reported in Samseth and Trulsen [2025], of long-crested irregular water surface waves propagating over a shoal, with attention to the region over the down-slope behind the shoal (see figure below). We measure the surface elevation field, the horizontal velocity field in the water, and the resulting forces on a horizontal submerged cylinder placed over the down-slope of the shoal. In addition, we calculate the horizontal acceleration field. From this, we find that the presence of the shoal can modify the wave field such that the resulting forces on the submerged cylinder can be enhanced with thicker extreme tails and increased values of skewness and kurtosis depending on the location of the cylinder. The spatial dependence of the statistics of forces is different from the spatial dependence of the statistics of horizontal velocity, horizontal acceleration and surface elevation. 

Title:  Inertial particle dynamics induced by Nonlinear shallow-water surface gravity waves

Presenter: Rosa Maria Vargas Magana, UiB

Abstract: The motion of inertial particles driven by surface gravity waves plays a crucial role in coastal processes such as sediment transport, pollutant dispersion, and the accumulation of impurities in the ocean. While significant progress has been made in deep-water settings under monochromatic waves, this study extends the analysis to shallow-water regimes, where nonlinear wave phenomena—such as cnoidal and solitary waves—create distinct trajectories for finite-sized particles. We also investigate the influence of mean water level variation (set-up and set-down) on the trajectories of positively buoyant particles under both linear and nonlinear gravity waves in deep and shallow waters. Additionally, the horizontal drift of buoyant and neutrally buoyant particles initially located near the wave crest of a solitary wave is examined. This work provides new insights into inertial particle transport under highly nonlinear wave conditions, emphasizing the complex interplay between particle inertia and surface wave conditions. This work was done in collaboration with F. Desquines and H. Kalisch

Title: Oscillating wave-induced boundary layer

Presenter: Lars Erik Holmedal, NTNU

Abstract: The turbulent wave-induced boundary layer flow for waves propagating along a vertical wall is investigated by direct numerical simulations. The Reynolds averaged mean velocity within this boundary layer is examined and compared to the velocity within the unidirectional Stokes boundary layer. The turbulence budget for these two oscillating boundary layers has been applied to explain the differences.

Title: Wave-turbulence interaction and their decomposition

Presenter: Olav Rømcke, NTNU

Abstract: Study of wave-turbulence interaction and their effect on the natural processes is of paramount importance with regards to mixing processes in the upper part of the ocean. This includes transport of dissolved gasses, nutrients and pollutants, and the flux of heat and gas between ocean and atmosphere.

In order to study how the waves affect the turbulent motion, it is necessary to decompose the flow into its wave and turbulent contributions. The first part of our talk will discuss different techniques for achieving this separation of motion from Particle Image Velocitmetry measurements. Our focus is modal decomposition techniques such as Proper Orthogonal Decomposition, Dynamic Mode Decomposition and Empirical Mode Decomposition while compare them with traditional techniques such as Phase Condition Averaging and Syncro-Squeeze Wavelets. We report the effect on turbulence metrics such as turbulent kinetic energy, integral length scales and structure functions.
The second part of our talk presents an ongoing experimental campaign in the Water Channel facility at NTNU Trondheim, including some early results. Our objective is to study the triple interaction between waves, turbulence and a shear current, and how near-surface mixing and transport are affected. When waves encounter a turbulent flow with wave-following vertical shear, the ambient turbulent structures grow and become Langmuir turbulence, according to the theory of Craik and Leibovich. In the ocean the wind creates both shear, waves and turbulence, while in our lab we create all three components individually in a controlled manner. The flow profile and turbulent conditions are tailored using an active grid at the inlet, with waves propagating upstream, giving the maximum interaction time between waves and flow. We simultaneously measure velocity fields (stereoscopic PIV), mixing of a passive scalar (Laser-induced fluorescence) and visualize the surface turbulence using an infrared camera. With this unique combination of simultaneous measurements we aim at quantifying vertical mixing in the upper part of the ocean.

Title: Asymmetric Travelling Capillary-Gravity Waves

Presenter: Karl Johan Douglas Svensson Seth, NTNU

Abstract: Periodic travelling waves that solve the capillary-gravity Whitham equation have been fully characterised in the case of small and even waves. This characterisation is complemented by the work presented in this talk dealing with small asymmetric periodic travelling waves. Such asymmetric waves are far more scarce than the even ones and can only be constructed in certain cases for weak surface tension. The method also generalizes in a straightforward way to a class of similar equations for which we either can prove the existence of or non-existence of asymmetric solutions. However, the proof relies on some technical calculations that are different for each equation. We discuss how this can be done for the Babenko equation, which is equivalent to the full water wave problem, to determine the existence of small amplitude Capillary-Gravity Waves.

Title: Remote sensing of surface currents in a large hydrodynamic laboratory

Presenter: Benjamin Smeltzer, Sintef

Abstract: Optical-based remote sensing of surface currents in the SINTEF Ocean Basin Laboratory is presented. Video recordings acquired from a camera viewing an area of the free surface contain information concerning the propagation of short surface waves, which in turn may be used to infer the background current atop which the waves propagate. Dividing the field of regard of the camera and recording duration into subwindows, the spatial and temporal variability of the currents may be characterized. Preliminary results for different current speeds are presented, where the remotely-sensed currents are compared against measurements from in situ sensors. Applications, along with limitations, error sources and uncertainties are discussed.

Title: On the MET Pan-Arctic wave model

Presenter: Ana Carrasco

Abstract: The purpose of this talk is to present the Pan-Arctic wave forecast and hindcast (NORA3) produced at the Norwegian Meteorological Institute (MET). These products are part of the ARC-MFC Copernicus project. Both are run in the same geographic domain using the same code: WAM_Cycle 4.7.

Title: Multi-scale wave modeling framework and wave forecasting assisted with machine learning

Presenter: Widar Weizhi Wang, NTNU

Abstract: The ocean wave fields become very inhomogeneous and nonlinear as they propagate over complex coastal topo-bathymetry towards the shoreline. The nonlinear coastal wave transformations challenge the assumptions of homogeneous and ergodic sea states in the offshore area and there is rarely an analytical wave spectrum for a specific coastal area. Phase-averaged wave models are often used for offshore areas but are insufficient to resolve many nonlinear wave transformations in the coastal region, especially diffraction, leading to the underestimation of waves in shore-ward waters after diffraction. Phase-resolving models are needed for a more accurate representation of the complex coastal wave fields. In order to achieve time-efficient predictions, offshore hindcast data, spectral wave models for offshore wave spectra development and phase-resolving model for coastal wave transformation are combined in a down-scale approach. With the specific application in Norway, we have developed the NORA-SARAH (NORA-SWANREEF3D-ALE-HDC) down-scale procedure, where NORA represents the open-access hindcast databases NORA3 and NORA10-EI provided by the Norwegian Meteorological Institute, SWAN is the widely used open-source spectral wave model, REEF3D is the open-source hydrodynamics suite developed at NTNU consisting of a few different phase-resolving wave models, ALE (Arbitrary Lagrangian-Eulerian) represents the fast run-time force calculation method inside REEF3D and HDC is the inertial hydrodynamic coupling procedure among the REEF3D models, for example between the potential flow based model and full Navier-Stokes CFD solver. As the hindcast data accumulate, machine learning techniques such as neural networks can be employed for offshore wave forecast. The NORA-SARAH down-scale approach is used to generate synthetic training data for coastal waves and establish a correlation between the offshore and the coastal wave fields in the area of interest. Combining the predictions of offshore waves based on the hind-cast data and the offshore-coastal wave correlations based on NORA-SARAH, a potential coastal wave prediction procedure with the assistance of machine learning techniques can be established. In a case study, the long-short-term memory (LSTM) algorithm is used for offshore wave time sequence forecast based on the open-access hindcast database NORA in Norway. A feed-forwards neural network (FNN) is used to correlate the offshore waves and nearshore waves using the phase-resolving wave models. The workflow is illustrated in Fig. 1. The neural network algorithm requires an initial batch of simulations of different sea-states but can potentially predict future events near-instantly once established.

Title: Efficiency and Accuracy of Numerical Schemes for the Shallow Water Equations

Presenter: Aadi Bhure, NGI

Abstract: Shallow water equations are popular in natural hazard prevention like tsunami, dam break, and flood modeling. Although numerical schemes for shallow water equations have parallel implementations, the precise improvement for each is not clear. In this talk, we will compare the accuracy and computational efficiency of numerical schemes for the shallow water equations. The end goal is time-to-result of a given solution accuracy, and it is not given which numerical scheme yields the best results with this metric. The selected schemes include Lax-Friedrichs (LxF), FORCE, Harten-Lax-van Leer (HLL), Kurganov-Petrova (KP07), and Weighted Average Flux (WAF). We then compute peak performance and rates of convergence as well as the absolute error for each scheme. Using these metrics we are able to judge how efficiently a scheme uses performance to provide accuracy.