Geir Kleivstul Pedersen

• Grue, John; Pedersen, Geir Kleivstul & Sætra, Øyvind (2022). Free Wave Effects in Meteotsunamis. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 127(2). doi: 10.1029/2021JC017669. Full text in Research Archive Show summary

  Free wave generation due to a ship or storm moving past a shallow, great depth change of the water, is measured on the shore (coast), modeled and compared. The free waves are generated at the depth change where the forced wave and velocity field attached to the moving pressure system adjust to the new depth. The wavenumber is a factor 1/12 smaller in the meteotsunami case compared to the ship case. The subcritical depth Froude numbers are similar in the two cases. The meteotsunami that occurred on the Norwegian Coast on 29–30 June 2019 was driven by a supercell thunderstorm moving at speed 110 km/hr. A localized, strong high pressure feature of width of 60 km and crest of 120 km obtained from weather forecast was used as input for a set of simulations of the water-level response including realistic bathymetry. At the transition between the North Sea and the Norwegian Trench, the storm generated a free depression wave. This arrived at the coast 24 min ahead of the depression attached to the storm. The calculation fits to a period of 23 min, of a series several oscillations of height of 0.3–0.4 m, as measured by the water-level gauge. An impulsive start-up generates an additional forerunning elevation wave. Short waves of period of 1/3 of the main ship-driven waves may originate from the steep gradients of the bow and stern. Similarly, short waves of period 6–7.5 min (0.002–0.003 Hz) are observed in the measured water-level on the coast.

• Pedersen, Geir Kleivstul (2021). Asymptotic, Convergent, and Exact Truncating Series Solutions of the Linear Shallow Water Equations for Channels with Power Law Geometry. SIAM Journal on Applied Mathematics. ISSN 0036-1399. 81(2), p. 285–303. doi: 10.1137/19M1305860. Full text in Research Archive Show summary

  The present study was originally motivated by some intriguing exact solutions for waves propagating in nonuniform media. In particular, for special depth profiles reflected waves did not appear and ray theory became exact. Herein, geometrical optics is employed to obtain asymptotic series for waves of general shapes in nonuniform narrow channels, within the framework of linear shallow water theory. While being kept simple, the series incorporate higher order contributions that may describe the evolution of waves with high accuracy. The higher orders also contain a secondary wave system. For selected classes of geometries and wave shapes explicit solutions are calculated and compared to numerical solutions. Apart from the vicinity of shorelines, say, higher order expansions generally may provide very accurate approximations to the full solutions. The asymptotic series are analyzed for different wave shapes and are found to be convergent for cases where the basic wave profiles have compact support (finite length). A number of new, closed form, exact solutions are also found. The asymptotic expansion is put into a context by employing it for the transmission of waves from a uniform channel section into a nonuniform one. Additional results and side topics are presented in a supplement.

• Zengaffinen, Thomas; Løvholt, Finn; Pedersen, Geir Kleivstul & Harbitz, Carl Bonnevie (2020). Effects of rotational submarine slump dynamics on tsunami genesis: new insight from idealized models and the 1929 Grand Banks event. Geological Society Special Publication. ISSN 0305-8719. doi: 10.1144/SP500-2019-201. Full text in Research Archive Show summary

  Sediment slumps are known to have generated important tsunamis such as the 1998 Papua New Guinea (PNG) and the 1929 Grand Banks events. Tsunami modellers commonly use solid blocks with short run-out distances to simulate these slumps. While such methods have the obvious advantage of being simple to use, they offer little or no insight into physical processes that drive the events. The importance of rotational slump motion to tsunamigenic potential is demonstrated in this study by employing a viscoplastic landslide model with Herschel-Bulkley rheology. A large number of simulations for different material properties and landslide configurations are carried out to link the slump's deformation, rheology, its translational and rotational kinematics, to its tsunami-genesis. The yield strength of the slump is shown to be the primary material property that determines the tsunami-genesis. This viscoplastic model is further employed to simulate the 1929 Grand Banks tsunami using updated geological source information. The results of this case study suggest that the viscoplastic model can be used to simulate complex slump induced tsunami. The simulations of the 1929 Grand Banks event also indicate that a pure slump mechanism is more tsunamigenic than a corresponding translational landslide mechanism.

• Zengaffinen, Thomas; Løvholt, Finn; Pedersen, Geir Kleivstul & Muhari, Abdul (2020). Modelling 2018 Anak Krakatoa Flank Collapse and Tsunami: Effect of Landslide Failure Mechanism and Dynamics on Tsunami Generation. Pure and Applied Geophysics (PAGEOPH). ISSN 0033-4553. 177, p. 2493–2516. doi: 10.1007/s00024-020-02489-x. Full text in Research Archive Show summary

  The 2018 Anak Krakatoa volcano flank collapse generated a tsunami that impacted the Sunda Strait coastlines. In the absence of a tsunami early warning system, it caused several hundred fatalities. There are ongoing discussions to understand how the failure mechanism of this event affected landslide dynamics and tsunami generation. In this paper, the sensitivity to different failure scenarios on the tsunami generation is investigated through numerical modelling. To this end, the rate of mass release, the landslide volume, the material yield strength, and orientation of the landslide failure plane are varied to shed light on the failure mechanism, landslide evolution, and tsunami generation. We model the landslide dynamics using the depth-averaged viscoplastic flow model BingClaw, coupled with depth-averaged long wave and shallow water type models to simulated tsunami propagation. We are able to match fairly well the observed tsunami surface elevation amplitudes and inundation heights in selected area with the numerical simulations. However, as observed by other authors, discrepancies in simulated and observed arrival times for some of the offshore gauges are found, which raises questions related to the accuracy of the available bathymetry. For this purpose, further sensitivity studies changing the bathymetric depth near the source area are carried out. With this alteration we are also able to match better the arrival times of the waves.

• Verschaeve, Joris C. G.; Pedersen, Geir Kleivstul & Tropea, Cameron (2018). Non-modal stability analysis of the boundary layer under solitary waves. Journal of Fluid Mechanics. ISSN 0022-1120. 836, p. 740–772. doi: 10.1017/jfm.2017.825. Full text in Research Archive
• Smith, Lisa; Jensen, Atle & Pedersen, Geir Kleivstul (2017). Investigation of breaking and non-breaking solitary waves and measurements of swash zone dynamics on a 5° beach. Coastal Engineering. ISSN 0378-3839. 120, p. 38–46. doi: 10.1016/j.coastaleng.2016.11.004. Full text in Research Archive Show summary

  This study presents an experimental investigation of plunging breakers on a sloping beach with an inclination of 5.1°. The incident waves are solitary waves with various amplitudes from non-breaking waves to plunging breakers, and the area investigated is the swash zone. PIV (Particle Image Velocimetry) is performed on images captured at four different field of views (FOV). Shoreline position and maximum runup are measured, and are repeatable in both time and height, although cross-sectional variations of the shoreline shape are observed at maximum runup. For non-breaking waves the runup and fluid flow is computed by a boundary integral technique combined with a boundary layer model. Then, there is excellent agreement between the experimental and the computed velocity profiles at the lower region of the beach, while the boundary integral technique overpredicts the maximum runup height severely. For breaking waves the experiments indicate that the motion becomes more irregular as we move further up the beach. In addition, there are more irregularities present for waves with larger amplitude. Length and velocity of air bubbles entrapped by the plunging breakers are extracted from an image series captured with a large FOV. The images showed that a large air bubble remains intact for a time period during runup for the breaking waves.

• Kim, Jihwan; Pedersen, Geir Kleivstul; Løvholt, Finn & LeVeque, Randall J. (2017). A Boussinesq type extension of the GeoClaw model - a study of wave breaking phenomena applying dispersive long wave models. Coastal Engineering. ISSN 0378-3839. 122, p. 75–86. doi: 10.1016/j.coastaleng.2017.01.005. Full text in Research Archive Show summary

  The nonlinear shallow water model is widely used in the study of tsunami propagation, but an increasing number of studies are dedicated to the dispersion dynamics of tsunamis. If the wave dispersion becomes important, Boussinesq-type models are often used. In this work, a general purpose Boussinesq solver, BoussClaw, is introduced for modeling non-linear dispersive tsunami propagation, taking into account inundation. The BoussClaw model is an extension of the GeoClaw tsunami model. It employs a hybrid of finite volume and finite difference methods to solve Boussinesq equations from the literature, which are based on the depth-averaged velocity and include enhanced dispersion properties. On the other hand, in the selected formulation only some non-linearity is retained in the dispersion term. In order to validate BoussClaw, numerical results are compared to analytic solutions, solutions obtained by pre-existing models, and laboratory experiments. Even though the equations of BoussClaw are not fully nonlinear they perform far better than standard Boussinesq equations with only linear dispersion terms. Furthermore, the wave steepening and breaking are carefully scrutinized, and we demonstrate that the point of wave breaking may be wrongly identified in many of the commonly used Boussinesq models.

• Jeschke, Anja; Pedersen, Geir Kleivstul; Vater, Stefan & Behrens, Jörn (2017). Depth-averaged non-hydrostatic extension for shallow water equations with quadratic vertical pressure profile: equivalence to Boussinesq-type equations. International Journal for Numerical Methods in Fluids. ISSN 0271-2091. 84(10), p. 569–583. doi: 10.1002/fld.4361. Full text in Research Archive
• Løvholt, Finn; Pedersen, Geir Kleivstul & Harbitz, Carl Bonnevie (2016). Tsunami-Genesis Due to Retrogressive Landslides on an Inclined Seabed. In Lamarche, Geoffrey; Mountjoy, Joshu; Bull, Suzanne & Hubble, Tom (Ed.), Submarine Mass Movements and their Consequences: 7th International Symposium. Springer Publishing Company. ISSN 9783319209791. p. 569–578. doi: 10.1007/978-3-319-20979-1_57. Full text in Research Archive Show summary

  Clay-rich landslides commonly involve retrogressive mass and momentum release mechanisms. Motivated by the retrogressive behaviour of major landslides offshore Norway, previous studies have demonstrated substantial effects of the release rate on the generation of the tsunami. However, the few existing models are limited to overly idealized conditions. In the present study, we explore further the wave generation due to a continuous retrogressive landslide model, quantifying the effects of the wave model, landslide configuration, and the continental slope. In the present examples, we find that the landslides involve large accelerations that may be crucial for tsunami-genesis. Tsunami footprints due to individual short blocks comprising the landslide are smeared out by dispersion. Keeping landslide material properties constant, we investigate mobilised landslide mass and maximum tsunami crest elevations for three different slopes: 1°, 1.5°, and 2° respectively. In the present examples, the smaller volume landslides are stronger tsunami generators than the larger ones because they are situated in shallower water, thereby clearly demonstrating the importance of the water depth on the tsunami generation.

• Pedersen, Geir Kleivstul (2016). Fully nonlinear Boussinesq equations for long wave propagation and run-up in sloping channels with parabolic cross sections. Natural Hazards. ISSN 0921-030X. 84, p. 599–619. doi: 10.1007/s11069-016-2448-0. Full text in Research Archive Show summary

  A general framework for derivation of long wave equations in narrow channels, and their transformation to Lagrangian coordinates is briefly established. Then, fully nonlinear Boussinesq equations are derived for channels of parabolic cross sections. The simplified version with normal nonlinearity is compared with corresponding models from the literature, and propagation properties are discussed. A Lagrangian run-up model is adapted to the fully nonlinear set. This model is tested by means of controlled residues and by a well-controlled comparison to exact analytic solutions from the literature. Then, runup of solitary waves in simple geometries is simulated and compared to a semi-analytic solution that is derived for propagation and run-up in a composite channel. The dispersive model retains the higher run-up height in a parabolic channels, as reported in the recent literature for NLSW solutions, as compared to a rectangular channel.

• Løvholt, Finn; Glimsdal, Sylfest; Lynett, P. & Pedersen, Geir Kleivstul (2015). Simulating tsunami propagation in fjords with long-wave models. Natural Hazards and Earth System Sciences. ISSN 1561-8633. 15(3), p. 657–669. doi: 10.5194/nhess-15-657-2015. Full text in Research Archive Show summary

  Tsunamis induced by rock slides constitute a severe hazard towards coastal fjord communities. Fjords are narrow and rugged with steep slopes, and modeling the short-frequency and high-amplitude tsunamis in this environment is demanding. In the present paper, our ability (and the lack thereof) to simulate tsunami propagation and run-up in fjords for typical wave characteristics of rock-slide-induced waves is demonstrated. The starting point is a 1 : 500 scale model of the topography and bathymetry of the southern part of Storfjorden fjord system in western Norway. Using measured wave data from the scale model as input to numerical simulations, we find that the leading wave is moderately influenced by nonlinearity and dispersion. For the trailing waves, dispersion and dissipation from the alongshore inundation on the traveling wave become more important. The tsunami inundation was simulated at the two locations of Hellesylt and Geiranger, providing a good match with the measurements in the former location. In Geiranger, the most demanding case of the two, discrepancies are larger. The discrepancies may be explained by a combinations of factors, such as the accumulated errors in the wave propagation along large stretches of the fjord, the coarse grid resolution needed to ensure model stability, and scale effects in the laboratory experiments.

• Løvholt, Finn; Pedersen, Geir Kleivstul; Harbitz, Carl Bonnevie; Glimsdal, Sylfest & Kim, Jihwan (2015). On the characteristics of landslide tsunamis. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. ISSN 1364-503X. 373(2053). doi: 10.1098/rsta.2014.0376. Full text in Research Archive Show summary

  This review presents modelling techniques and processes that govern landslide tsunami generation, with emphasis on tsunamis induced by fully submerged landslides. The analysis focuses on a set of representative examples in simplified geometries demonstrating the main kinematic landslide parameters influencing initial tsunami amplitudes and wavelengths. Scaling relations from laboratory experiments for subaerial landslide tsunamis are also briefly reviewed. It is found that the landslide acceleration determines the initial tsunami elevation for translational landslides, while the landslide velocity is more important for impulsive events such as rapid slumps and subaerial landslides. Retrogressive effects stretch the tsunami, and in certain cases produce enlarged amplitudes due to positive interference. In an example involving a deformable landslide, it is found that the landslide deformation has only a weak influence on tsunamigenesis. However, more research is needed to determine how landslide flow processes that involve strong deformation and long run-out determine tsunami generation.

• Harbitz, Carl Bonnevie; Glimsdal, Sylfest; Løvholt, Finn; Kveldsvik, Vidar; Pedersen, Geir Kleivstul & Jensen, Atle (2014). Rockslide tsunamis in complex fjords: From an unstable rock slope at Åkerneset to tsunami risk in western Norway. Coastal Engineering. ISSN 0378-3839. 88, p. 101–122. doi: 10.1016/j.coastaleng.2014.02.003. Full text in Research Archive Show summary

  An unstable rock volumeof more than 50 millionm3 has been detected in the Åkerneset rock slope in the narrow fjord, Storfjorden, Møre & Romsdal County, Western Norway. If large portions of the volume are released as a whole, the rockslide will generate a tsunami that may be devastating to several settlements and numerous visiting tourists along the fjord. The threat is analysed by amultidisciplinary approach spanning fromrock-slope stability via rockslide and wave mechanics to hazard zoning and risk assessment. The rockslide tsunami hazard and the tsunami early-warning system related to the two unstable rock slopes at Åkerneset and Hegguraksla in the complex fjord systemare managed by Åknes/Tafjord Beredskap IKS (previously the Åknes/Tafjord project). The present paper focuses on the tsunami analyses performed for this company to better understand the effects of rockslide-generated tsunamis fromÅkerneset and Hegguraksla. Two- and threedimensional site-specific laboratory experiments are conducted to study the generation, propagation, and run-up of thewave for several potential rockslide scenarios fromÅkerneset. Furthermore, the two models GloBouss and DpWaves are applied for numerical simulations of the generation/propagation phase and a third model MOST is applied for numerical simulations of the near-shore propagation and inundation of the wave in selected locations. Strong emphasis is put on verification, validation, and sensitivity of the numerical models. The best match between the numerical simulations and the laboratory experiments is found for the larger scenarios with the linear dispersive solution for the propagation phase; the corresponding calculated run-up values are remarkably similar to the ones observed during the laboratory experiments. During the risk assessment it was found that the rockslide tsunami hazard (probability of impact) is higher than accepted by the Norwegian Planning and Building Act. This should at that time prevent any further development in all the exposed areas of the entire fjord system. The Act is today altered to open for specified further development in the various hazard zones. The results of the tsunami analyses are applied in risk management in terms of hazard map production and land-use planning. Two failure scenarios for each of the two unstable rock slopes are designed for the hazard zoning. The larger and less probable scenarios (1 in 5000 years) are applied for evacuation zones and routes, while the smaller and more probable scenarios (larger than 1 in 1000 years) are applied for location and design of less critical facilities accepted in the inundation zone.

• Verschaeve, Joris C. G. & Pedersen, Geir Kleivstul (2014). Linear stability of boundary layers under solitary waves. Journal of Fluid Mechanics. ISSN 0022-1120. 761, p. 62–104. doi: 10.1017/jfm.2014.617. Full text in Research Archive
• Lindstrøm, Erika Kristina; Pedersen, Geir Kleivstul; Jensen, Atle & Glimsdal, Sylfest (2014). Experiments on slide generated waves in a 1:500 scale fjord model. Coastal Engineering. ISSN 0378-3839. 92, p. 12–23. doi: 10.1016/j.coastaleng.2014.06.010. Full text in Research Archive Show summary

  An unstable rock-slope is detected in Åkerneset, located in Storfjorden, Western Norway. In the future this rockslope will produce a slide and a subsequent tsunami. In accordance to this future event, experiments in a 1:500 scale model of the inner part of Storfjorden are performed,where themodel geometry is made after the real fjord bathymetry, while the slide is an idealized slide of block-type. The slide motion is monitored and the generated waves are measured at a number of wave gauges in the model. At selected locations local details of the flow, velocities and inundation are measured by digital image techniques and acoustic probes. Features of the wave system and the inundation are elaborately discussed with a view to the future event as well as to the application of models.

• Park, Yong Sung; Verschaeve, Joris C. G.; Pedersen, Geir Kleivstul & Liu, Phil Lin-Fan (2014). Boundary-layer flow and bed shear stress under a solitary wave: revision. Journal of Fluid Mechanics. ISSN 0022-1120. 753, p. 554–559. doi: 10.1017/jfm.2014.52. Full text in Research Archive Show summary

  We address two shortcomings in the article by Liu, Park & Cowen (J. Fluid Mech., vol. 574, 2007, pp. 449–463), which gave a theoretical and experimental treatise of the bottom boundary-layer under a solitary wave.

• Løvholt, Finn; Harbitz, Carl Bonnevie; Vanneste, Maarten; Blasio, Fabio V De; Urgeles, Roger & Iglesias, Olaia [Show all 10 contributors for this article] (2014). Modeling Potential Tsunami Generation by the BIG’95 Landslide. In Krastel, S.; Behrmann, J.H.; Völker, D.; Stipp, Michael; Berndt, C.; Urgeles, R.; Chaytor, J.; Huhn, K.; Strasser, M. & Harbitz, Carl Bonnevie (Ed.), Submarine Mass Movements and Their Consequences: 6th International Symposium. Springer. ISSN 9783319009711. p. 507–515. doi: 10.1007/978-3-319-00972-8_45. Full text in Research Archive
• Wroniszewski, Pawel A.; Verschaeve, Joris C. G. & Pedersen, Geir Kleivstul (2014). Benchmarking of Navier–Stokes codes for free surface simulations by means of a solitary wave. Coastal Engineering. ISSN 0378-3839. 91, p. 1–17. doi: 10.1016/j.coastaleng.2014.04.012. Full text in Research Archive Show summary

  The paper presents a benchmark of four freely available solvers for Navier–Stokes equations: Gerris, OpenFOAM, Thétis and Truchas. These models are selected because they have been reported to deal successfully with oceanographic and coastal engineering applications. The benchmark includes two free surface problems: propagation of a solitary wave and runup of a solitary wave on a plane beach. The fluids are inviscid, which allows a detailed study of energy conservation and comparison of the results with a reference solution given by a boundary integral solver. The Navier–Stokes solvers use the finite volume discretization and free surface capturing techniques based on the volume-of-fluid (VOF) method. In the first benchmark test, we investigate the influence of numerical dissipation and other spurious effects on the energy balance of thewave. In the second problem,we focus on the runup heights and compare themwith the reference solution. The beach in the runup problemis represented with a solid body immersed in the Cartesian mesh. The solid boundaries are describedwith a VOF type approach or a staircase representation, depending on the features of the solver. In addition to the immersed boundary description a couple of body fitted meshes are tested for the runup case.

• Glimsdal, Sylfest; L'Heureux, Jean-Sébastien; Harbitz, Carl Bonnevie & Pedersen, Geir Kleivstul (2013). Modelling of the 1888 landslide tsunami, Trondheim, Norway. In Margottini, Claudio; Canuti, Paolo & Sassa, Kyoji (Ed.), Landslide Science and Practice, Volume 5: Complex Environment. Springer. ISSN 9783642314261. p. 73–79. doi: 10.1007/978-3-642-31427-8_9. Full text in Research Archive
• Løvholt, Finn; Lynett, P. & Pedersen, Geir Kleivstul (2013). Simulating run-up on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities. Nonlinear processes in geophysics. ISSN 1023-5809. 20(3), p. 379–395. doi: 10.5194/npg-20-379-2013. Full text in Research Archive Show summary

  Tsunamis induced by rock slides plunging into fjords constitute a severe threat to local coastal communities. The rock slide impact may give rise to highly non-linear waves in the near field, and because the wave lengths are relatively short, frequency dispersion comes into play. Fjord systems are rugged with steep slopes, and modeling non-linear dispersive waves in this environment with simultaneous run-up is demanding. We have run an operational Boussinesq-type TVD (total variation diminishing) model using different run-up formulations. Two different tests are considered, inundation on steep slopes and propagation in a trapezoidal channel. In addition, a set of Lagrangian models serves as reference models. Demanding test cases with solitary waves with amplitudes ranging from 0.1 to 0.5 were applied, and slopes were ranging from 10 to 50°. Different run-up formulations yielded clearly different accuracy and stability, and only some provided similar accuracy as the reference models. The test cases revealed that the model was prone to instabilities for large non-linearity and fine resolution. Some of the instabilities were linked with false breaking during the first positive inundation, which was not observed for the reference models. None of the models were able to handle the bore forming during drawdown, however. The instabilities are linked to short-crested undulations on the grid scale, and appear on fine resolution during inundation. As a consequence, convergence was not always obtained. It is reason to believe that the instability may be a general problem for Boussinesq models in fjords.

• Glimsdal, Sylfest; Pedersen, Geir Kleivstul; Harbitz, Carl Bonnevie & Løvholt, Finn (2013). Dispersion of tsunamis: does it really matter? Natural Hazards and Earth System Sciences. ISSN 1561-8633. 13(6), p. 1507–1526. doi: 10.5194/nhess-13-1507-2013. Full text in Research Archive Show summary

  This article focuses on the effect of dispersion in the field of tsunami modeling. Frequency dispersion in the linear long-wave limit is first briefly discussed from a theoretical point of view. A single parameter, denoted as "dispersion time", for the integrated effect of frequency dispersion is identified. This parameter depends on the wavelength, the water depth during propagation, and the propagation distance or time. Also the role of long-time asymptotes is discussed in this context. The wave generation by the two main tsunami sources, namely earthquakes and landslides, are briefly discussed with formulas for the surface response to the bottom sources. Dispersive effects are then exemplified through a semi-idealized study of a moderate-strength inverse thrust fault. Emphasis is put on the directivity, the role of the "dispersion time", the significance of the Boussinesq model employed (dispersive effect), and the effects of the transfer from bottom sources to initial surface elevation. Finally, the experience from a series of case studies, including earthquake- and landslide-generated tsunamis, is presented. The examples are taken from both historical (e.g. the 2011 Japan tsunami and the 2004 Indian Ocean tsunami) and potential tsunamis (e.g. the tsunami after the potential La Palma volcanic flank collapse). Attention is mainly given to the role of dispersion during propagation in the deep ocean and the way the accumulation of this effect relates to the "dispersion time". It turns out that this parameter is useful as a first indication as to when frequency dispersion is important, even though ambiguity with respect to the definition of the wavelength may be a problem for complex cases. Tsunamis from most landslides and moderate earthquakes tend to display dispersive behavior, at least in some directions. On the other hand, for the mega events of the last decade dispersion during deep water propagation is mostly noticeable for transoceanic propagation.

• Gramstad, Odin; Zeng, Huiming; Trulsen, Karsten & Pedersen, Geir Kleivstul (2013). Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water. Physics of Fluids. ISSN 1070-6631. 25(12). doi: 10.1063/1.4847035. Full text in Research Archive
• Pedersen, Geir Kleivstul; Lindstrøm, Erika Kristina; Bertelsen, Arnold F; Jensen, Atle; Laskovski, Daniela & Sælevik, Gunnstein (2013). Runup and boundary layers on sloping beaches. Physics of Fluids. ISSN 1070-6631. 25(1). doi: 10.1063/1.4773327. Full text in Research Archive
• Sælevik, Gunnstein; Jensen, Atle & Pedersen, Geir Kleivstul (2013). Runup of solitary waves on a straight and a composite beach. Coastal Engineering. ISSN 0378-3839. 77, p. 40–48. doi: 10.1016/j.coastaleng.2013.02.007. Full text in Research Archive
• Løvholt, Finn; Pedersen, Geir Kleivstul; Bazin, Sara; Kühn, Daniela; Bredesen, Rolv Erlend & Harbitz, Carl Bonnevie (2012). Stochastic analysis of tsunami runup due to heterogeneous coseismic slip and dispersion. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 117. doi: 10.1029/2011JC007616. Full text in Research Archive Show summary

  Most tsunami models apply dislocation models that assume uniform slip over the entire fault plane, followed by standard analytical models based on Volterra's theory of elastic dislocations for the seabed deformation. In contrast, we quantify tsunami runup variability for an earthquake with fixed magnitude but with heterogeneous rupture distribution assuming plane wave propagation (i.e., an infinitely long rupture). A simple stochastic analysis of 500 slip realizations illustrates the expected variability in coseismic slip along a fault plane and the subsequent runup that occurs along a coastline in the near field. Because of the need for systematically analyzing different fault geometries, grid resolutions, and hydrodynamic models, several hundred thousand model runs are required. Thus, simple but efficient linear models for the tsunami generation, propagation, and runup estimation are used. The mean value and variability of the maximum runup is identified for a given coastal slope configuration and is analyzed for different dip angles. On the basis of the ensemble runs, nonhydrostatic effects are discussed with respect to their impact on generation, nearshore propagation, and runup. We conclude that for the geometry and magnitude investigated, nonhydrostatic effects reduce the variability of the runup; that is, hydrostatic models will produce an artificially high variability.

• Løvholt, Finn; Kaiser, Gunilla; Glimsdal, Sylfest; Scheele, Lasse; Harbitz, Carl Bonnevie & Pedersen, Geir Kleivstul (2012). Modeling propagation and inundation of the 11 March 2011 Tohoku tsunami. Natural Hazards and Earth System Sciences. ISSN 1561-8633. 12(4), p. 1017–1028. doi: 10.5194/nhess-12-1017-2012. Full text in Research Archive Show summary

  On 11 March 2011 the Tohoku tsunami devastated the east coast of Japan, claiming thousands of casualties and destroying coastal settlements and infrastructure. In this paper tsunami generation, propagation, and inundation are modeled to hindcast the event. Earthquake source models with heterogeneous slips are developed in order to match tsunami observations, including a best fit initial sea surface elevation with water levels up to 8 m. Tsunami simulations were compared to buoys in the Pacific, showing good agreement. In the far field the frequency dispersion provided a significant reduction even for the leading wave. Furthermore, inundation simulations were performed for ten different study areas. The results compared well with run-up measurements available and trim lines derived from satellite images, but with some overestimation of the modeled surface elevation in the northern part of the Sanriku coast. For inundation modeling this work aimed at using freely available, medium-resolution data for topography, bottom friction, and bathymetry, which are easily accessible in the framework of a rapid assessment. Although these data come along with some inaccuracies, the results of the tsunami simulations suggest that their use is feasible for application in rapid tsunami hazard assessments. A heterogeneous source model is essential to simulate the observed distribution of the run-up correctly, though.

• Pedersen, Geir Kleivstul (2011). Oblique runup of non-breaking solitary waves on an inclined plane. Journal of Fluid Mechanics. ISSN 0022-1120. 668, p. 582–606. doi: 10.1017/S0022112010005343. Full text in Research Archive
• Glimsdal, S.; Pedersen, Geir Kleivstul; Langtangen, Hans Petter; Shuvalov, Valery & Dypvik, Henning (2010). The Mjølnir tsunami. In Dypvik, Henning; Tsikalas, Filippos & Smelror, Morten (Ed.), The Mjølnir impact event and its consequences. Geology and geophysics of a Late Jurassic/Early Cretaceous marine impact event. Springer. ISSN 9783540882596. p. 257–271. Full text in Research Archive
• Løvholt, Finn; Pedersen, Geir Kleivstul & Glimsdal, Sylfest (2010). Coupling of dispersive tsunami propagation and shallow water coastal response. The Open Oceanography Journal. 4, p. 71–82. doi: 10.2174/1874252101004010071. Full text in Research Archive Show summary

  The key issue of this article is the concept of combining a model dedicated to dispersive large scale propagation of tsunamis with ComMIT, developed and made freely available by NOAA, that is a state of the art tool for tsunami impact studies. First, the main motivation for this approach, namely the need for efficient computation of runup of tsunamis from submarine/subaerial slides and certain types of earthquake, is discussed. Then the models involved are presented. We describe in some detail the dispersive model component which is a Boussinesq type model that is recently developed for tsunami propagation purposes. Finally, the performance and flexibility of the joint model approach is illustrated by two case studies including inundation computations at selected cites. The potentially disastrous, but small probability, flank-collapse event at the La Palma Island is used as an example of slide generated tsunamis where dispersion plays an important role. The second example is a tsunami from a potential inverse thrust fault at the Lesser Antilles. In this case dispersion during propagation is important for some regions, but not for others.

• Løvholt, Finn & Pedersen, Geir Kleivstul (2009). Instabilities of Boussinesq models in non-uniform depth. International Journal for Numerical Methods in Fluids. ISSN 0271-2091. 61(6), p. 606–637. doi: 10.1002/fld.1968. Full text in Research Archive
• Sælevik, Gunnstein; Jensen, Atle & Pedersen, Geir Kleivstul (2009). Experimental investigation of impact generated tsunami; related to a potential rock slide, Western Norway. Coastal Engineering. ISSN 0378-3839. 56(9), p. 897–906. doi: 10.1016/j.coastaleng.2009.04.007. Full text in Research Archive
• Handegard, Nils Olav; Pedersen, Geir & Brix, Ole (2009). Estimating tail-beat frequency using split-beam echosounders. ICES Journal of Marine Science. ISSN 1054-3139. 66(6), p. 1252–1258. doi: 10.1093/icesjms/fsp003. Full text in Research Archive Show summary

  Data from a standard split-beam echosounder are used to estimate tail-beat frequency within a dense herring (Clupea harengus L.) layer. The data were collected by lowering a horizontally projecting 38 kHz split-beam transducer into a herring layer at 245-m depth. Individual targets were concatenated into tracks, and a fast Fourier transform was used to estimate the periodogram of the backscattering strengths along each track. A simple model, assumed accurate under certain conditions, was used to relate the periodogram to tail-beat frequency. The requisite conditions are discussed. Examples of accurate tail-beat estimates from single high-quality tracks, which are consistent with statistics on all tracks in the test dataset, are presented. In addition, the cross periodogram between closely spaced individuals was calculated on selected tracks to estimate the relative phase between the adjacent tracks within the school. Finally, the potential use of this method to resolve schooling behaviour, improve target-strength estimates, and even estimate fish condition, is discussed.

• Torsvik, Tomas; Pedersen, Geir Kleivstul; Pedersen, Geir & Dysthe, Kristian (2009). Waves Generated by a Pressure Disturbance Moving in a Channel with a Variable Cross-Sectional Topography. Journal of waterway, port, coastal, and ocean engineering. ISSN 0733-950X. 135(3), p. 120–123. doi: 10.1061/3(120. Full text in Research Archive
• Løvholt, Finn; Pedersen, Geir Kleivstul & Gisler, Galen Ross (2008). Oceanic propagation of a potential tsunami from the La Palma Island. Journal of Geophysical Research (JGR). ISSN 0148-0227. 113. doi: 10.1029/2007JC004603. Full text in Research Archive
• Pedersen, Geir Kleivstul (2008). Modeling run-up with depth integrated equation models. In Liu, Philip L-F; Yeh, Harry & Synolakis, Costas (Ed.), ADVANCED NUMERICAL MODELS FOR SIMULATING TSUNAMI WAVES AND RUNUP. World Scientific. ISSN 9789812700124. p. 3–41. Full text in Research Archive
• Pedersen, Geir Kleivstul (2008). A Lagrangian Model Applied to Runup Problems. In Liu, Philip L-F; Yeh, Harry & Synolakis, Costas (Ed.), ADVANCED NUMERICAL MODELS FOR SIMULATING TSUNAMI WAVES AND RUNUP. World Scientific. ISSN 9789812700124. p. 311–315. Full text in Research Archive
• Glimsdal, Sylfest; Pedersen, Geir Kleivstul; Langtangen, Hans Petter; Shuvalov, Valery & Dypvik, Henning (2007). Tsunami generation and propagation from the Mjølnir asteroid impact. Meteoritics and Planetary Science. ISSN 1086-9379. 42(9), p. 1473–1493. Full text in Research Archive
• Bredesen, Rolv Erlend; Langtangen, Hans Petter & Pedersen, Geir Kleivstul (2007). Benchmark of a Tsunami Run-Up Code. In Skallerud, B & Andersson, H. I. (Ed.), MekIT'07. Tapir Akademisk Forlag. ISSN 9788251922357. p. 127–134. Full text in Research Archive
• Cai, Xing; Pedersen, Geir Kleivstul; Langtangen, Hans Petter & Glimsdal, Sylfest (2006). Parallel Simulation of Tsunamis Using a Hybrid Software Approach. In Joubert, G. R.; Peters, F. J.; Tirado, P; Nagel, W. E.; Plata, O. & Zapata, E. (Ed.), Parallel Computing: Current and Future Issues of Highe End Computing. John von Neumann Institute for Computing. ISSN 9783000173523. p. 383–390. Full text in Research Archive Show summary

  Parallel Simulation of Tsunamis Using a Hybrid Software Approach

• Birknes, Jørn & Pedersen, Geir Kleivstul (2006). A particle finite element method applied to long wave run-up. International Journal for Numerical Methods in Fluids. ISSN 0271-2091. 52(3), p. 237–261. doi: 10.1002/fld.1172. Full text in Research Archive Show summary

  This paper presents a Lagrangian-Eulerian finite element formulation for solving fluid dynamics problems with moving boundaries and employs the method to long wave run-up. The method is based on a set of Lagrangian particles which serve as moving nodes for the finite element mesh. Nodes at the moving shoreline are identified by the alpha shape concept which utilizes the distance from neighboring nodes in different directions. An efficient triangulation technique is then used for the mesh generation at each time step. In order to validate the numerical method the code has been compared with analytical solutions and a preexisting finite difference model. The main focus of our investigation is to assess the numerical method through simulations of three-dimensional dam break and long wave run-up on curved beaches. Particularly the method is put to test for cases where different shoreline segments connect and produce a computational domain surrounding dry regions.

• Masson, D. g.; Harbitz, Carl Bonnevie; Wynn, R. B.; Pedersen, Geir Kleivstul & Løvholt, Finn (2006). Submarine landslides: processes, triggers and hazard prediction. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. ISSN 1364-503X. 364, p. 2009–2039. Full text in Research Archive
• Lovholt, F.; Bungum, H.; Harbitz, Carl Bonnevie; Glimsdal, S.; Lindholm, C. D. & Pedersen, Geir Kleivstul (2006). Earthquake related tsunami hazard along the western coast of Thailand. Natural Hazards and Earth System Sciences. ISSN 1561-8633. 6, p. 979–997. Full text in Research Archive
• Tomas, Torsvik; Dysthe, Kristian & Pedersen, Geir (2006). Influence of variable Froude number on waves generated by ships in shallow water. Physics of Fluids. ISSN 1070-6631. 18. Full text in Research Archive
• Harbitz, Carl Bonnevie; Løvholt, Finn; Pedersen, Geir Kleivstul; Glimsdal, Sylfest & Masson, D. g. (2006). Mechanisms of tsunami generation by submarine gravity mass flows. Norsk Geologisk Tidsskrift. ISSN 0029-196X. 86, p. 255–264. Full text in Research Archive
• Cai, Xing; Pedersen, Geir Kleivstul & Langtangen, Hans Petter (2005). A parallel multi-subdomain strategy for solving Boussinesq water wave equations. Advances in Water Resources. ISSN 0309-1708. 28(3), p. 215–233. Full text in Research Archive
• Glimsdal, Sylfest; Pedersen, Geir Kleivstul & Langtangen, Hans Petter (2005). An Investigation of Domain Decomposition Methods for One-Dimensional Dispersive Long Wave Equations. Advances in Water Resources. ISSN 0309-1708. 27(11), p. 1111–1133. Full text in Research Archive
• Jensen, Atle; Mayer, Stefan & Pedersen, Geir Kleivstul (2005). Experiments and computation of onshore breaking solitary waves. Measurement Science and Technology. ISSN 0957-0233. 16, p. 1913–1920. Full text in Research Archive
• Jensen, Atle & Pedersen, Geir Kleivstul (2004). Optimization of acceleration measurements using PIV. Measurement Science and Technology. ISSN 0957-0233. 15, p. 2275–2283. Full text in Research Archive
• Jensen, Atle; Huseby, Morten; Clamond, Didier; Pedersen, Geir Kleivstul & Grue, John (2004). PIV measurements of accelerations in water waves, PIV and Water Waves. World Scientific. ISSN 9789812389145. p. 279–281. Full text in Research Archive
• Grue, John; Liu, Philip L.-F. & Pedersen, Geir Kleivstul (2004). PIV and Water Waves, PIV and Water Waves. World Scientific. ISSN 9789812389145. p. v–vi. Full text in Research Archive
• Jensen, Atle; Pedersen, Geir Kleivstul & Wood, Deborah (2003). An experimental study of wave run-up at a steep beach. Journal of Fluid Mechanics. ISSN 0022-1120. 486, p. 161–181. Full text in Research Archive
• Wood, Deborah; Pedersen, Geir Kleivstul & Jensen, Atle (2003). Modelling of run up of steep non-breaking waves. Ocean Engineering. ISSN 0029-8018. 30, p. 625–644. Full text in Research Archive
• Pedersen, Geir Kleivstul (2003). Energy conservation and physical optics for discrete long wave equations. Wave motion. ISSN 0165-2125. 37, p. 81–100. Full text in Research Archive
• Langtangen, Hans Petter & Pedersen, Geir Kleivstul (2001). Propagation of Large Destructive Waves. Computational Mechanics. ISSN 0178-7675. Full text in Research Archive
• Pedersen, Geir Kleivstul (2000). An optical theory for discrete media. Wave motion. ISSN 0165-2125. 32, p. 79–92. Full text in Research Archive Show summary

  This paper presents a new kind of analysis of numerical methods for water waves, where asymptotic techniques, previously associated with analytic theory only, are applied to discrete solutions. Observing the close relations between the asymptotic techniques and the basic concepts of wave theory, we realize that this approach directly access the reproduction of physical properties in the discrete description. Herein we focus on one theory of fundamental importance, namely that of geometrical and physical optics. We seek a corresponding description for waves that are discrete, in the sense of being solutions of difference rather than differential equations. Particularly, we address amplification of harmonic waves in shoaling water through an optical theory for discrete solutions, that is derived from a WKBJ type expansion. One of the key results is a discrete counterpart to Green's law. We also find spurious reflection of short waves in shoaling water that can be described by a local expansion. Both the discrete Green's law and the local approximation are verified by comparison to full, computed discrete solutions.

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• Løvholt, Finn; Kim, Jihwan; Harbitz, Carl Bonnevie & Pedersen, Geir Kleivstul (2015). Tsunami generation due to submerged blocks and deformable landslides involving retrogression. Full text in Research Archive
• Lindstrøm, Erika Kristina; Jensen, Atle; Pedersen, Geir Kleivstul; Glimsdal, Sylfest & Sælevik, Gunnstein (2013). Impact and wave generation by sub-aerial slides in a fjord geometry. Full text in Research Archive
• Pedersen, Geir Kleivstul (2013). Waves due to sub-aerial slides in narrow waterways Experiments and computational challenges. Full text in Research Archive
• Verschaeve, Joris C. G.; Pedersen, Geir Kleivstul & Lindstrøm, Erika Kristina (2013). Scale effects and stability of viscous boundary layers in wave tank experiments. Full text in Research Archive
• Lindstrøm, Erika Kristina; Jensen, Atle; Pedersen, Geir Kleivstul & Glimsdal, Sylfest (2013). Scale effects and stability of viscous boundary layers in wave tank experiments. Full text in Research Archive
• Harbitz, Carl Bonnevie; Pedersen, Geir Kleivstul & Glimsdal, Sylfest (2013). Åkerneset – the threat from an unstable rock slope in Storfjorden, western Norway: A review of research and civil protection issues. Full text in Research Archive
• Lindstrøm, Erika Kristina; Pedersen, Geir Kleivstul; Jensen, Atle & Bertelsen, Arnold F (2012). Evolution of boundary layers on beaches. Full text in Research Archive
• Lindstrøm, Erika Kristina; Pedersen, Geir Kleivstul; Jensen, Atle & Bertelsen, Arnold F (2012). Evolution of boundary layers on beaches. Full text in Research Archive
• Wroniszewski, Pawel A.; Verschaeve, Joris C. G.; Pedersen, Geir Kleivstul & Løvholt, Finn (2012). Benchmarking of Navier-Stokes codes for free surface simulations by means of soliton run up. Full text in Research Archive
• Lindstrøm, Erika Kristina; Jensen, Atle; Pedersen, Geir Kleivstul; Sælevik, Gunstein & Glimsdal, Sylfest (2012). Impact and wave generation by sub-aerial slides in a fjord geometry. Full text in Research Archive
• Glimsdal, Sylfest; Pedersen, Geir Kleivstul; Løvholt, Finn & Harbitz, Carl Bonnevie (2012). Dispersive tsunamis; does it really matter? Full text in Research Archive
• Løvholt, Finn & Pedersen, Geir Kleivstul (2012). Modelling highly non-linear waves with depth integrated models. Full text in Research Archive
• Løvholt, Finn & Pedersen, Geir Kleivstul (2012). Capabilities of operational Boussinesq models for simulating the run-up of impact generated tsunamis in fjords. Full text in Research Archive
• Pedersen, Geir Kleivstul (2011). Topics related to tsunamis generated by rock slides Hazards and challenges in computations and experiments. Full text in Research Archive
• Pedersen, Geir Kleivstul (2011). Boundary layers on sloping beaches; Are small scale experiments reliable for verification of models and descripion of full scale events? Full text in Research Archive
• Glimsdal, Sylfest; Dypvik, Henning; Pedersen, Geir Kleivstul; Langtangen, Hans Petter & Shuvalov, Valery (2007). TSUNAMI GENERATED BY THE MJØLNIR IMPACT. Full text in Research Archive
• Glimsdal, Sylfest; Pedersen, Geir Kleivstul; Shuvalov, Valery; Dypvik, Henning & Langtangen, Hans Petter (2006). Tsunami generated by the Mjølnir impact. Full text in Research Archive
• Glimsdal, Sylfest; Pedersen, Geir Kleivstul; Dypvik, Henning; Langtangen, Hans Petter & Kristiansen, Øyvind (2005). Tsunami generated by the Mjølnir impact. Full text in Research Archive
• Jensen, Atle; Mayer, Stefan & Pedersen, Geir Kleivstul (2005). A breaking wave; experiments and computations. Full text in Research Archive
• Jensen, Atle; Pedersen, Geir Kleivstul & Mayer, Stefan (2005). Dynamics of a collapsing breaking wave. Full text in Research Archive
• Gjevik, Bjørn & Pedersen, Geir Kleivstul (2005). Flodbølger fra skred og jordskjelv. Fra Fysikkens Verden. ISSN 0015-9247. p. 4–10. Full text in Research Archive
• Torsvik, Tomas; Dysthe, Kristian & Pedersen, Geir (2005). Waves generated by ships in shallow water at variable Froude numbers. Full text in Research Archive
• Gjevik, Bjørn; Pedersen, Geir Kleivstul & Harbitz, Carl Bonnevie (2005). Flodbølger – kan de varsles? Full text in Research Archive
• Cai, Xing; Pedersen, Geir Kleivstul; Langtangen, Hans Petter & Glimsdal, Sylfest (2005). Parallel Simulation of Tsunamis Using a Hybrid Software Approach. Full text in Research Archive
• Jensen, Atle; Huseby, Morten; Clamond, Didier; Pedersen, Geir Kleivstul & Grue, John (2002). PIV measurements of accelerations in water waves. Full text in Research Archive
• Pedersen, Geir & Hobæk, Halvor (2001). Acoustic streaming generated using low burst repetition frequencies and single bursts. Full text in Research Archive Show summary

  In a previous meeting (15th ISNA, Göttingen 1999) we reported to have observed a new type of acoustic streaming which only occurred near a needle probe positioned near the focus of a focusing ultrasound transducer. The streaming was observed even at pulse rates as low as 1 Hz. In an attempt to find the origin of this streaming attention was focused on possible excitation of evanescent waves on the probe surface. Presently we report results from a new experiment on this subject. Streaming was observed and measured by using tiny tracer particles of polyamide which were recorded with a CCD-video camera and a frame grabber in a PC. The frames were analyzed with a Matlab-program for obtaining stream lines and velocity measurements in a vertical plane through the sound axis. The results show that the streaming is not connected with the probe: We observe single burst streaming in free field, even with burst repetitions longer than 1 second.

• Pedersen, Geir & Hobæk, Halvor (2001). Single burst acoustic streaming. Full text in Research Archive Show summary

  On a previous occasion we reported observations of a new type of acoustic streaming which only occurred around a needle hydrophone positioned near the focus of a focusing ultrasound transducer. The streaming was observed even at burst repetition frequencies as low as 1 Hz. In an attempt to find the origin of this streaming attention was focused on possible excitation of evanescent waves on the probe surface. Presently we report results from a new experiment on this subject. Streaming was observed and measured using tiny tracer particles of polyamid which were recorded with a CCD-video camera and a frame grabberin a PC. The frames were analysed with a Matlab-program for obtaining stream lines and velocity measurements in a vertical plane through the sound axis. The results show that we also observe streaming in free field when using burst repetition frequencies lower than 1 Hz, and even when using single bursts.

• Langtangen, Hans Petter & Pedersen, Geir Kleivstul (2001). Propagation of Large Destructive Waves (Tsunamies). Full text in Research Archive
• Pedersen, Geir Kleivstul (1999). CHALLENGES IN TSUNAMI MODELING. Full text in Research Archive Show summary

  Some challenges in tsunami research Tsunamis are huge devastating Ocean waves that occasionally causes deaths and widespread destruction. The lecture starts with a very brief overview of tsunamis as a natural hazard and a topic for research. Then hydrodynamic aspects of tsunami generation and propagations are demonstrated through a set of animations. On basis of the experiences reflected in the animations, a few selected themes of current tsunami research are discussed.

• Langtangen, Hans Petter & Pedersen, Geir Kleivstul (1999). Propagation of destructive flood waves. Full text in Research Archive
• Langtangen, Hans Petter & Pedersen, Geir Kleivstul (1999). Finite Element Models for Tsunami Simulation. Full text in Research Archive
• Pedersen, Geir Kleivstul; Moe, Halvard; Brown, Mike; Dybesland, Elen & Nordby, Roger Otten (1999). Official GITEC-TWO video on tsunamis. Full text in Research Archive
• Pedersen, Geir Kleivstul & Brown, Mike (1999). The story of a tsunami. Full text in Research Archive Show summary

  The story of a tsumani. An educational video, animation + speech, that demonstrates different phases in the generation, propagation and shorline impact of destructive ocean waves (tsunamis) due to eartquakes. Quicktime versions or video-cassettes are available from the Author

• Langtangen, Hans Petter & Pedersen, Geir Kleivstul (1999). Effects of Dispersion on Generation and Propagation of Tsunamis. Full text in Research Archive
• Langtangen, Hans Petter & Pedersen, Geir Kleivstul (1999). An Analytic Approach to Tsunami Modeling. Full text in Research Archive
• Birknes-Berg, Jørn & Pedersen, Geir Kleivstul (2017). The “Chain of Markers” code applied to large scale problems; solitary waves, sloshing and a plunging wave. Universitetet i Oslo. Full text in Research Archive Show summary

  There are many different numerical methods for solving the Navier-Stokes equations for problems with a free surface. Some examples are volume of fluid (VOF), Marker and cell (MAC), level set, smooth particle hydrodynamics (SPH), boundary element methods (BEM) and weighted residual methods. One important element when solving problems with a free surface is how the free surface is treated. One of the most popular techniques is the VOF method. Another approach is to have markers on the free surface and this method is pursued in this study.

• Lindstrøm, Erika Kristina; Verschaeve, Joris C. G. & Pedersen, Geir Kleivstul (2014). A note on instabilities in the boundary layer during runup of solitary waves on a plane slope. Universitetet i Oslo. Full text in Research Archive Show summary

  The present report is concerned with the evolution of boundary layers during runup of solitary waves on a beach in a wave tank of depth 0.2m. It comprises both theory and high resolution PIV measurements of velocity profiles. A linear stability analysis of the boundary layer for solitary waves running up a sloping beach is performed by means of the Orr-Sommerfeld equation. Due to the increased retardation phase during runup, the amplification of disturbances in the boundary layer is increased as compared to that of solitary waves traveling on constant depth. On the basis of these results, we reexamine the experimental results by Pedersen et al. [11] and find some experimental evidence for Tollmien-Schlichting waves destabilizing the flow.

• Pedersen, Geir Kleivstul & Løvholt, Finn (2008). "Documentation of a global Boussinesq solver. Universitetet i Oslo. Full text in Research Archive Show summary

  This report is the documentation of a new model for large scale solution of the Boussinesq equations. The equations are briefly presented with emphasis on the inclusion of spherical coordinates and the Coriolis force. We have chosen to start with the standard Boussinesq formulation, but have modified it to achieve improved dispersion properties for moderately short waves. This formulation is put into the context of Boussinesq equations in general in an appendix. Describing first the discretization in detail, we design higher order numerical differences, analyse dispersion, stability and the convergence rate of the iteration scheme used at each time step. The performance of the present model is also compared to state of the art models (FUNWAVE/COULWAVE). A selection of tests are performed to validate the code and assess the applicability and accuracy of the method. The tests include eigenoscillations in basins, solitary wave propagation, comparison with pre-existing models, diffraction of incident solitary waves by a vertical cylinder and trans-Atlantic propagation of a hypothetical tsunami from the La Palma island. The latter case is pursued further in a companion paper. All tests indicate that the model is correctly coded, efficient and robust.

• Torsvik, Tomas; Pedersen, Geir & Dysthe, Kristian (2008). Influence of Cross Channel Depth Variation on Ship Wave Patterns. Universitetet i Oslo. Full text in Research Archive Show summary

  The present work is a numerical investigation on waves generated by a pressure disturbance moving at constant speed in a channel with a variable cross-channel depth profile. The channel profile, which is uniform in the along-channel direction, has a deep trench located in the vicinity of the center line of the channel, and shallow banks near the channel walls. Wave fields generated upstream and downstream of the moving pressure disturbance are described, and the characteristic features present in the wave patterns are related to the parameters governing the speed of the pressure disturbance and the shape of the cross-channel profile. Our numerical investigation is based on the COULWAVE long wave model, which solves a set of Boussinesq type equations in two horizontal dimensions.

• Pedersen, Geir Kleivstul (2005). Variable depth and the validity of Boussinesq-type models. Universitetet i Oslo. Full text in Research Archive Show summary

  The main issue of this report is comparison and verification of long wave models with emphasis on variable depth effects. A selection of dispersive long wave theories are reviewed. Included are the so-called standard Boussinesq equations and the much celebrated counterpart where the velocities are prescribed at an optimal vertical position, namely at 0.531 times the depth down from the equilibrium surface. The latter option, referred to as improved Boussinesq equations, displays substantially improved dispersion properties on constant depth. We also address formulations with the velocity potential as primary unknown and where approximations linked to a mild bottom slope have been invoked. One of the potential formulations are modified in a very simple way to yield dispersion properties equal to the "improved Boussinesq equations". First the different Boussinesq models are assessed for constant depth propagation. Then testing is extended to wave motion in an idealized bathymetry with two horizontal planes joined by a smooth slope. The length of the waves incident on the slope as well as the slope steepness are systematically varied. It turns out that the new potential formulation, with improved dispersion properties, performs well even in presence of steep bottom gradients.

• Pedersen, Geir Kleivstul (2001). A note on tsunami generation by earthquakes. Universitetet i Oslo. Full text in Research Archive Show summary

  We formulate generation of tsunamis by earthquakes as a linear potential flow problem with rapid in and out-flux at the sea bottom. Starting from solutions for a few simplified bottom deformations we proceed to establish a closed form solution for a more complex source by application of matched asymptotics. The results are verified by comparison with numerical solutions.

• Wood, Deborah J.; Pedersen, Geir Kleivstul & Jensen, Atle (2001). Modelling of run up of steep non-breaking waves by fluent. Universitetet i Oslo. Full text in Research Archive Show summary

  An industrial Navier-Stokes solver (FLUENT) is used to examine steep waves as they run up a steep beach (10.54$^0$). The volume of fluid method (VOF) is used to model the free surface. Comparison with experimental results shows reasonable overall agreement in the prediction of the free-surface, velocities and accelerations within the flow. However, a spurious boundary feature at the free-surface was also found which does reduce the quality of the results. For a steep wave we see the transition from a steep wave front to a smooth run-up tongue at the beach that is in qualitative agreement with the experiments.

• Jensen, Atle; Pedersen, Geir Kleivstul & Wood, Deborah J. (2001). An experimental study of wave run-up at a steep beach. Universitetet i Oslo. Full text in Research Archive Show summary

  This paper focus on experiments on run-up of strongly nonlinear waves on a moderately steep beach of 10.5deg inclination. Velocity fields are obtained by the PIV (Particle Image Velocimetry) technique. Acceleration measurements are also attempted, but it is difficult to obtain useful results in every case. In addition free surface profiles are extracted from digital images and wave resistance probes. Several non-breaking incident waves are measured and compared with theory in deep water as well as under run-up. However, the main theme is run-up of steep waves at the brink of breaking, that is assumed to be a good starting point approaching a detailed study of bore run-up. In some cases these are found to be temporarily slightly overturning in the first stages of run-up, without developing neither a plunger nor appreciable spilling. This feature is discussed in view of acceleration measurements and with reference to the dam-break problem. Effects of scaling, as well as three dimensional features observed for the steepest waves, are also briefly discussed.

• Pedersen, Geir Kleivstul (2001). Energy conservation and physical optics for discrete long wave equations. Universitetet i Oslo. Full text in Research Archive Show summary

  In a preceding paper, [7], physical optics was developed for a selection of discrete long wave solutions by application a perturbation expansion. Herein, we approach discrete optics from analysis of discrete energy, in the sense of discrete expressions fulfilling a local energy conservation law. The expressions for energy density and flux are found from finite difference and element discretizations of linear and non-linear shallow water equations as well as linear Boussinesq equations with constant depth. The discrete energies are generally not perfectly positive definite and ambiguity in their definition is encountered and discussed. Still, the discrete energies appear as well behaved, which is confirmed through calculation of averaged energy quantities for harmonics, that reproduces the physical optics from [7] under the assumption of negligible diffraction. The optics and the derived expressions for the energies are verified through direct solution of discrete long wave equations. Discrete energies are also discussed in relation to Hamilton's principle. The discrete momentum equation can be obtained from Hamilton's principle inserted energy like quadratures. However, those energy forms are not consistent with the energies that are conserved. [7] Pedersen G. An optical theory for discrete media. Wave Motion, 32:79--92, 2000.

• Pedersen, Geir (2001). Akustisk Strømning. Universitetet i Bergen. Full text in Research Archive

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