Emneord:
Fluidmekanikk,
Mekanikk
Publikasjoner

BirknesBerg, Jørn & Pedersen, Geir Kleivstul (2017). The “Chain of Markers” code applied to large scale problems; solitary waves, sloshing and a plunging wave. Research report in mechanics.
ISSN 08019940.
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Jeschke, Anja; Pedersen, Geir Kleivstul; Vater, Stefan & Behrens, Jörn (2017). Depthaveraged nonhydrostatic extension for shallow water equations with quadratic vertical pressure profile: equivalence to Boussinesqtype equations. International Journal for Numerical Methods in Fluids.
ISSN 02712091.
84(10), s 569 583 . doi:
10.1002/fld.4361

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 03783839.
122, s 75 86 . doi:
10.1016/j.coastaleng.2017.01.005
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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, Boussinesqtype models are often used. In this work, a general purpose Boussinesq solver, BoussClaw, is introduced for modeling nonlinear 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 depthaveraged velocity and include enhanced dispersion properties. On the other hand, in the selected formulation only some nonlinearity is retained in the dispersion term. In order to validate BoussClaw, numerical results are compared to analytic solutions, solutions obtained by preexisting 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.

Smith, Lisa; Jensen, Atle & Pedersen, Geir Kleivstul (2017). Investigation of breaking and nonbreaking solitary waves and measurements of swash zone dynamics on a 5° beach. Coastal Engineering.
ISSN 03783839.
120, s 38 46 . doi:
10.1016/j.coastaleng.2016.11.004
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Løvholt, Finn; Pedersen, Geir Kleivstul & Harbitz, Carl Bonnevie (2016). TsunamiGenesis Due to Retrogressive Landslides on an Inclined Seabed, In Geoffrey Lamarche; Joshu Mountjoy; Suzanne Bull & Tom Hubble (ed.),
Submarine Mass Movements and their Consequences: 7th International Symposium.
Springer Publishing Company.
ISBN 9783319209791.
57.
s 569
 578
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Clayrich 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 tsunamigenesis. 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 runup in sloping channels with parabolic cross sections. Natural Hazards.
ISSN 0921030X.
84, s 599 619 . doi:
10.1007/s1106901624480
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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 runup model is adapted to the fully nonlinear set. This model is tested by means of controlled residues and by a wellcontrolled comparison to exact analytic solutions from the literature. Then, runup of solitary waves in simple geometries is simulated and compared to a semianalytic solution that is derived for propagation and runup in a composite channel. The dispersive model retains the higher runup 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 longwave models. Natural hazards and earth system sciences.
ISSN 15618633.
15(3), s 657 669 . doi:
10.5194/nhess156572015
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Tsunamis induced by rock slides constitute a severe hazard towards coastal fjord communities. Fjords are narrow and rugged with steep slopes, and modeling the shortfrequency and highamplitude tsunamis in this environment is demanding. In the present paper, our ability (and the lack thereof) to simulate tsunami propagation and runup in fjords for typical wave characteristics of rockslideinduced 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 1364503X.
373(2053) . doi:
10.1098/rsta.2014.0376
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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 runout 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 03783839.
88, s 101 122 . doi:
10.1016/j.coastaleng.2014.02.003
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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 fromrockslope stability via rockslide and wave mechanics to hazard zoning and risk assessment. The rockslide tsunami hazard and the tsunami earlywarning 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 rockslidegenerated tsunamis fromÅkerneset and Hegguraksla. Two and threedimensional sitespecific laboratory experiments are conducted to study the generation, propagation, and runup 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 nearshore 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 runup 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 landuse 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.

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 03783839.
92, s 12 23 . doi:
10.1016/j.coastaleng.2014.06.010
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An unstable rockslope 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 blocktype. 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.

Løvholt, Finn; Harbitz, Carl Bonnevie; Vanneste, Maarten; De Blasio, Fabio V; Urgeles, Roger; Iglesias, Olaia; Canals, Miquel; Lastras, Galderic; Pedersen, Geir Kleivstul & Glimsdal, Sylfest (2014). Modeling Potential Tsunami Generation by the BIG’95 Landslide, In S. Krastel; J.H. Behrmann; D. Völker; Michael Stipp; C. Berndt; R. Urgeles; J. Chaytor; K. Huhn; M. Strasser & Carl Bonnevie Harbitz (ed.),
Submarine Mass Movements and Their Consequences: 6th International Symposium.
Springer.
ISBN 9783319009711.
VII.
s 507
 515

Park, Yong Sung; Verschaeve, Joris C. G.; Pedersen, Geir Kleivstul & Liu, Phil LinFan (2014). Boundarylayer flow and bed shear stress under a solitary wave: revision. Journal of Fluid Mechanics.
ISSN 00221120.
753, s 554 559 . doi:
10.1017/jfm.2014.52
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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 boundarylayer under a solitary wave.

Verschaeve, Joris C. G. & Pedersen, Geir Kleivstul (2014). Linear stability of boundary layers under solitary waves. Journal of Fluid Mechanics.
ISSN 00221120.
761, s 62 104 . doi:
10.1017/jfm.2014.617

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 03783839.
91, s 1 17 . doi:
10.1016/j.coastaleng.2014.04.012
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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 volumeoffluid (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, JeanSébastien; Harbitz, Carl Bonnevie & Pedersen, Geir Kleivstul (2013). Modelling of the 1888 landslide tsunami, Trondheim, Norway, In Claudio Margottini; Paolo Canuti & Kyoji Sassa (ed.),
Landslide Science and Practice, Volume 5: Complex Environment.
Springer.
ISBN 9783642314261.
x.
s 73
 79

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 15618633.
13(6), s 1507 1526 . doi:
10.5194/nhess1315072013
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This article focuses on the effect of dispersion in the field of tsunami modeling. Frequency dispersion in the linear longwave 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 longtime 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 semiidealized study of a moderatestrength 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 landslidegenerated 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 10706631.
25(12) . doi:
10.1063/1.4847035

Løvholt, Finn; Lynett, P. & Pedersen, Geir Kleivstul (2013). Simulating runup on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities. Nonlinear processes in geophysics.
ISSN 10235809.
20(3), s 379 395 . doi:
10.5194/npg203792013

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 10706631.
25(1) . doi:
10.1063/1.4773327

Sælevik, Gunnstein; Jensen, Atle & Pedersen, Geir Kleivstul (2013). Runup of solitary waves on a straight and a composite beach. Coastal Engineering.
ISSN 03783839.
77, s 40 48 . doi: http://dx.doi.org/10.1016/j.coastaleng.2013.02.007

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 15618633.
12(4), s 1017 1028 . doi:
10.5194/nhess1210172012
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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 runup 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, mediumresolution 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 runup correctly, though.

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  Oceans.
ISSN 21699275.
117 . doi:
10.1029/2011JC007616
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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.

Pedersen, Geir Kleivstul (2011). Oblique runup of nonbreaking solitary waves on an inclined plane. Journal of Fluid Mechanics.
ISSN 00221120.
668, s 582 606 . doi:
10.1017/S0022112010005343

Glimsdal, S.; Pedersen, Geir Kleivstul; Langtangen, Hans Petter; Shuvalov, Valery & Dypvik, Henning (2010). The Mjølnir tsunami, In Henning Dypvik; Filippos Tsikalas & Morten Smelror (ed.),
The Mjølnir impact event and its consequences. Geology and geophysics of a Late Jurassic/Early Cretaceous marine impact event.
Springer.
ISBN 9783540882596.
Chapter 10.
s 257
 271

Løvholt, Finn; Pedersen, Geir Kleivstul & Glimsdal, Sylfest (2010). Coupling of dispersive tsunami propagation and shallow water coastal response. The Open Oceanography Journal.
ISSN 18742521.
4, s 71 82 . doi:
10.2174/1874252101004010071
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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, flankcollapse 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.

Handegard, Nils Olav; Pedersen, Geir & Brix, Ole (2009). Estimating tailbeat frequency using splitbeam echosounders. ICES Journal of Marine Science.
ISSN 10543139.
66(6), s 1252 1258 . doi:
10.1093/icesjms/fsp003

Løvholt, Finn & Pedersen, Geir Kleivstul (2009). Instabilities of Boussinesq models in nonuniform depth. International Journal for Numerical Methods in Fluids.
ISSN 02712091.
61(6), s 606 637 . doi:
10.1002/fld.1968

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 03783839.
56(9), s 897 906 . doi:
10.1016/j.coastaleng.2009.04.007

Torsvik, Tomas; Pedersen, Geir Kleivstul; Pedersen, Geir & Dysthe, Kristian (2009). Waves Generated by a Pressure Disturbance Moving in a Channel with a Variable CrossSectional Topography. Journal of waterway, port, coastal, and ocean engineering.
ISSN 0733950X.
135(3), s 120 123 . doi:
10.1061/(ASCE)0733950X(2009)135:3(120)

Løvholt, Finn; Pedersen, Geir Kleivstul & Gisler, Galen Ross (2008). Oceanic propagation of a potential tsunami from the La Palma Island. Journal of Geophysical Research.
ISSN 01480227.
113 . doi:
10.1029/2007JC004603

Pedersen, Geir Kleivstul (2008). A Lagrangian Model Applied to Runup Problems, In Philip LF Liu; Harry Yeh & Costas Synolakis (ed.),
ADVANCED NUMERICAL MODELS FOR SIMULATING TSUNAMI WAVES AND RUNUP.
World Scientific.
ISBN 9812700129.
Chapter 17.
s 311
 315

Pedersen, Geir Kleivstul (2008). Modeling runup with depth integrated equation models, In Philip LF Liu; Harry Yeh & Costas Synolakis (ed.),
ADVANCED NUMERICAL MODELS FOR SIMULATING TSUNAMI WAVES AND RUNUP.
World Scientific.
ISBN 9812700129.
Chapter 1.
s 3
 41

Bredesen, Rolv Erlend; Langtangen, Hans Petter & Pedersen, Geir Kleivstul (2007). Benchmark of a Tsunami RunUp Code, In B Skallerud & H. I. Andersson (ed.),
MekIT'07.
Tapir Akademisk Forlag.
ISBN 9788251922357.
kap.
s 127
 134

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 10869379.
42(9), s 1473 1493

Birknes, Jørn & Pedersen, Geir Kleivstul (2006). A particle finite element method applied to long wave runup. International Journal for Numerical Methods in Fluids.
ISSN 02712091.
52(3), s 237 261 . doi:
10.1002/fld.1172
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This paper presents a LagrangianEulerian finite element formulation for solving fluid dynamics problems with moving boundaries and employs the method to long wave runup. 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 threedimensional dam break and long wave runup 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.

Cai, Xing; Pedersen, Geir Kleivstul; Langtangen, Hans Petter & Glimsdal, Sylfest (2006). Parallel Simulation of Tsunamis Using a Hybrid Software Approach, In G. R. Joubert; F. J. Peters; P Tirado; W. E. Nagel; O. Plata & E. Zapata (ed.),
Parallel Computing: Current and Future Issues of Highe End Computing.
John von Neumann Institute for Computing.
ISBN 3000173528.
Kapittel i bok.
s 383
 390

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 0029196X.
86, s 255 264

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 15618633.
6, s 979 997

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 1364503X.
364, s 2009 2039

Tomas, Torsvik; Dysthe, Kristian & Pedersen, Geir (2006). Influence of variable Froude number on waves generated by ships in shallow water. Physics of fluids.
ISSN 10706631.
18

Glimsdal, Sylfest; Pedersen, Geir Kleivstul & Langtangen, Hans Petter (2005). An Investigation of Domain Decomposition Methods for OneDimensional Dispersive Long Wave Equations. Advances in Water Resources.
ISSN 03091708.
27(11), s 1111 1133

Jensen, Atle; Mayer, Stefan & Pedersen, Geir Kleivstul (2005). Experiments and computation of onshore breaking solitary waves. Measurement science and technology.
ISSN 09570233.
16, s 1913 1920

Cai, Xing; Pedersen, Geir Kleivstul & Langtangen, Hans Petter (2005). A parallel multisubdomain strategy for solving Boussinesq water wave equations. Advances in Water Resources.
ISSN 03091708.
28(3), s 215 233

Grue, John; Liu, Philip L.F. & Pedersen, Geir Kleivstul (2004). PIV and Water Waves, In
PIV and Water Waves.
World Scientific.
ISBN 9812389148.
Preface.
s v
 vi

Jensen, Atle; Huseby, Morten; Clamond, Didier; Pedersen, Geir Kleivstul & Grue, John (2004). PIV measurements of accelerations in water waves, In
PIV and Water Waves.
World Scientific.
ISBN 9812389148.
7.1.
s 279
 281

Jensen, Atle & Pedersen, Geir Kleivstul (2004). Optimization of acceleration measurements using PIV. Measurement science and technology.
ISSN 09570233.
15, s 2275 2283

Jensen, Atle; Pedersen, Geir Kleivstul & Wood, Deborah (2003). An experimental study of wave runup at a steep beach. Journal of Fluid Mechanics.
ISSN 00221120.
486, s 161 181

Pedersen, Geir Kleivstul (2003). Energy conservation and physical optics for discrete long wave equations. Wave motion.
ISSN 01652125.
37, s 81 100

Wood, Deborah; Pedersen, Geir Kleivstul & Jensen, Atle (2003). Modelling of run up of steep nonbreaking waves. Ocean Engineering.
ISSN 00298018.
30, s 625 644

Langtangen, Hans Petter & Pedersen, Geir Kleivstul (2001). Propagation of Large Destructive Waves. Computational Mechanics.
ISSN 01787675.

Pedersen, Geir Kleivstul (2000). An optical theory for discrete media. Wave motion.
ISSN 01652125.
32, s 79 92
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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.

Gjevik, Bjørn; Pedersen, Geir Kleivstul; Dybesland, Elen; Harbitz, Carl Bonnevie; Miranda, P.M.A.; Baptista, M.A.; MendesVictor, L.; Heinrich, P.; Roche, R. & Guesmia, M. (1997). Modeling tsunamis from earthquake sources near Gorringe Bank southwest of Portugal. Journal of Geophysical Research  Oceans.
ISSN 21699275.
102(C13), s 931 949 . doi:
10.1029/97JC02179
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The AzoresGibraltar fracture zone with the huge bathymetric reliefs in the area southwest of Portugal is believed to have been the source of large historic tsunami events. This report describes simulations of tsunami generation and propagation from sources near the Gorringe Bank. The welldocumented 1969 tsunami event is examined both with a raytracing technique and with finite difference models based on various shallow water equations. Both methods show that the most likely source location is southeast of the Gorringe Bank near the epicenter location determined from seismic data. The tsunami source is calculated by formulas given by Okada [1985] for surface deformation of an elastic halfspace caused by faulting. Observed wave amplitude and travel time and values computed from an initial wave field according to Okada [1985] formulas show acceptable agreement for most stations along the coast of Portugal and Spain. However, in order to explain a large primary wave with downward displacement observed on the coast of Morocco, an alternative source model with a larger area of downward displacement has been introduced. This also leads to a better overall fit with observed travel time. Implications for disastrous events, as the one in 1755, are also discussed. Linear hydrostatic shallow water models are used for most of the simulations, but the importance of nonlinearity and dispersion is examined with the Boussinesq equations. The sensitivity of the solution to changes in the location and the strength of the source is discussed, and a series of grid refinement studies are performed in order to assess the accuracy of the simulations.

Murison, Robert; Pedersen, Geir; Baug, Ine Marlen; Milde, Anne Marita & Overmier, Bruce (1995). Dopaminergic system sensitivity, shockinduced stress and stressinduced gastric ulceration may be interdependent. Homeostasis.
ISSN 09607560.
36, s 6 11

Harbitz, Carl Bonnevie; Pedersen, Geir Kleivstul & Gjevik, Bjørn (1993). Numerical Simulations of Large Water Waves due to Landslides. Journal of Hydraulic Engineering.
ISSN 07339429.
1119(12) . doi:
10.1061/(ASCE)07339429(1993)119:12(1325)
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A mathematical model based on the hydrodynamic shallow water equations is developed for numerical simulation of slide generated waves in fjords. The equations are solved numerically by a finite difference technique. To examine the performance of the numerical model we have simulated the slide catastrophe in Tafjord, western Norway, 1934. The predicted runup heights are in good agreement with measured runup heights. The effects of wave amplification are estimated in runup zones with gentle beach slopes. The model results reveal wave energy trapping due to the fjord geometry. This causes standing wave oscillations in accordance with the observations.
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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. Fulltekst i vitenarkiv.

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. Preprint series (Universitetet i Oslo. Matematisk institutt), Mechanic. 01. Fulltekst i vitenarkiv.
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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 OrrSommerfeld 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 TollmienSchlichting waves destabilizing the flow.

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..

Lindstrøm, Erika Kristina; Jensen, Atle; Pedersen, Geir Kleivstul & Glimsdal, Sylfest (2013). Scale effects and stability of viscous boundary layers in wave tank experiments.

Lindstrøm, Erika Kristina; Jensen, Atle; Pedersen, Geir Kleivstul; Glimsdal, Sylfest & Sælevik, Gunnstein (2013). Impact and wave generation by subaerial slides in a fjord geometry.

Pedersen, Geir Kleivstul (2013). Waves due to subaerial slides in narrow waterways Experiments and computational challenges.

Verschaeve, Joris C. G.; Pedersen, Geir Kleivstul & Lindstrøm, Erika Kristina (2013). Scale effects and stability of viscous boundary layers in wave tank experiments.

Glimsdal, Sylfest; Pedersen, Geir Kleivstul; Løvholt, Finn & Harbitz, Carl Bonnevie (2012). Dispersive tsunamis; does it really matter?.

Lindstrøm, Erika Kristina; Jensen, Atle; Pedersen, Geir Kleivstul; Sælevik, Gunstein & Glimsdal, Sylfest (2012). Impact and wave generation by subaerial slides in a fjord geometry.

Lindstrøm, Erika Kristina; Pedersen, Geir Kleivstul; Jensen, Atle & Bertelsen, Arnold F (2012). Evolution of boundary layers on beaches.

Lindstrøm, Erika Kristina; Pedersen, Geir Kleivstul; Jensen, Atle & Bertelsen, Arnold F (2012). Evolution of boundary layers on beaches.

Løvholt, Finn & Pedersen, Geir Kleivstul (2012). Capabilities of operational Boussinesq models for simulating the runup of impact generated tsunamis in fjords.

Løvholt, Finn & Pedersen, Geir Kleivstul (2012). Modelling highly nonlinear waves with depth integrated models.

Wroniszewski, Pawel A.; Verschaeve, Joris C. G.; Pedersen, Geir Kleivstul & Løvholt, Finn (2012). Benchmarking of NavierStokes codes for free surface simulations by means of soliton run up.

Pedersen, Geir Kleivstul (2011). Boundary layers on sloping beaches; Are small scale experiments reliable for verification of models and descripion of full scale events?.

Pedersen, Geir Kleivstul (2011). Topics related to tsunamis generated by rock slides Hazards and challenges in computations and experiments.

Pedersen, Geir Kleivstul & Løvholt, Finn (2008). "Documentation of a global Boussinesq solver. Preprint series. Mechanics and Applied Mathematics. 1.

Torsvik, Tomas; Pedersen, Geir & Dysthe, Kristian (2008). Influence of Cross Channel Depth Variation on Ship Wave Patterns. Preprint series. Mechanics and Applied Mathematics. 2.

Glimsdal, Sylfest; Dypvik, Henning; Pedersen, Geir Kleivstul; Langtangen, Hans Petter & Shuvalov, Valery (2007). TSUNAMI GENERATED BY THE MJØLNIR IMPACT.

Glimsdal, Sylfest; Pedersen, Geir Kleivstul; Shuvalov, Valery; Dypvik, Henning & Langtangen, Hans Petter (2006). Tsunami generated by the Mjølnir impact.

Cai, Xing; Pedersen, Geir Kleivstul; Langtangen, Hans Petter & Glimsdal, Sylfest (2005). Parallel Simulation of Tsunamis Using a Hybrid Software Approach.

Gjevik, Bjørn & Pedersen, Geir Kleivstul (2005). Flodbølger fra skred og jordskjelv. Fra Fysikkens Verden.
ISSN 00159247.
(1), s 4 10

Glimsdal, Sylfest; Pedersen, Geir Kleivstul; Dypvik, Henning; Langtangen, Hans Petter & Kristiansen, Øyvind (2005). Tsunami generated by the Mjølnir impact.

Jensen, Atle; Mayer, Stefan & Pedersen, Geir Kleivstul (2005). A breaking wave; experiments and computations.

Jensen, Atle; Pedersen, Geir Kleivstul & Mayer, Stefan (2005). Dynamics of a collapsing breaking wave.

Torsvik, Tomas; Dysthe, Kristian & Pedersen, Geir (2005). Waves generated by ships in shallow water at variable Froude numbers.

Gjevik, Bjørn; Pedersen, Geir Kleivstul & Harbitz, Carl Bonnevie (2005). Flodbølger – kan de varsles?. Aftenposten (morgenutg. : trykt utg.).
ISSN 08043116.

Jensen, Atle; Huseby, Morten; Clamond, Didier; Pedersen, Geir Kleivstul & Grue, John (2002). PIV measurements of accelerations in water waves.

Pedersen, Geir (2001). Akustisk Strømning.

Pedersen, Geir & Hobæk, Halvor (2001). Acoustic streaming generated using low burst repetition frequencies and single bursts.
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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 CCDvideo camera and a frame grabber in a PC. The frames were analyzed with a Matlabprogram 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.
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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 CCDvideo camera and a frame grabberin a PC. The frames were analysed with a Matlabprogram 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).

Langtangen, Hans Petter & Pedersen, Geir Kleivstul (1999). An Analytic Approach to Tsunami Modeling.

Langtangen, Hans Petter & Pedersen, Geir Kleivstul (1999). Effects of Dispersion on Generation and Propagation of Tsunamis.

Langtangen, Hans Petter & Pedersen, Geir Kleivstul (1999). Finite Element Models for Tsunami Simulation.

Langtangen, Hans Petter & Pedersen, Geir Kleivstul (1999). Propagation of destructive flood waves.

Pedersen, Geir Kleivstul (1999). CHALLENGES IN TSUNAMI MODELING.
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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.

Pedersen, Geir Kleivstul & Brown, Mike (1999). The story of a tsunami.
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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 videocassettes are available from the Author

Pedersen, Geir Kleivstul; Moe, Halvard; Brown, Mike; Dybesland, Elen & Nordby, Roger Otten (1999). Official GITECTWO video on tsunamis.

Pedersen, Geir Kleivstul & Langtangen, Hans Petter (1998). An analytical approach to tsunami modeling.

Pedersen, Geir Kleivstul & Langtangen, Hans Petter (1998). Dispersive effects on tsunamis.
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Publisert 13. nov. 2010 14:05
 Sist endret 12. aug. 2014 13:33