Bjørn Gjevik

• Lynge, Birgit Kjoss; Hjelmervik, Karina Bakkeløkken & Gjevik, Bjørn (2013). Storm surge and tidal interaction in the Tjeldsund channel, northern Norway. Ocean Dynamics. ISSN 1616-7341. 63(7), p. 723–739. doi: 10.1007/s10236-013-0625-1. Full text in Research Archive Show summary

  The aim of this study is to investigate tide–surge interaction in narrow channels with complex and relatively shallow topography. A high-resolution depth-integrated tidal and storm surge model has been implemented for the Tjeldsund channel which is an important sailing lane in northern Norway. A horizontal grid resolution down to 50 m is applied in order to represent the complex bottom topography and the formation of jets and small-scale eddies. Two typically storm surge events in December 2004 have been examined in detail. The tide–surge interaction is found to influence the generation of higher harmonics and the formation of eddies in the current field. In some cases, the magnitude of storm surge currents may reach the same magnitude as the tidal currents enhancing the formation of jets and eddies.

• Bondevik, Stein; Gjevik, Bjørn & Sørensen, Mathilde B. (2013). Norwegian seiches from the giant 2011 Tohoku earthquake. Geophysical Research Letters. ISSN 0094-8276. 40(13), p. 3374–3378. doi: 10.1002/grl.50639. Full text in Research Archive
• Teigen, Sigurd Henrik; Nilsen, Frank; Skogseth, Ragnheid; Gjevik, Bjørn & Beszczynska-Möller, A. (2011). Baroclinic instability in the West Spitsbergen Current. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 116(C7). doi: 10.1029/2011JC006974. Full text in Research Archive Show summary

  Baroclinic instability in the West Spitsbergen Current is investigated, based on data from an array of current meter moorings along 78.83oN, across the deeper (1000-2400 m) section of the continental slope west of Svalbard. Numerical linear stability analyses of the current are presented, utilizing a normal mode two-layer linear model and idealizations of the baroclinic velocity field and the cross-shelf bathymetry. The characteristic period, wave length, and growth rate of unstable vorticity waves are revealed, appearing as two distinct peaks in growth rate, with typical wave periods of 35-75 h and wave lengths 15-30 km. The resulting vorticity wave structure of the dominant unstable mode is centered close to the position of the maximum current. Wavelet and rotary spectrum analysis of the current meter data from September 2007 to July 2009 detect transient signals with significant energy at similar oscillation periods as indicated by the linear stability analysis, which suggests that the baroclinic instability process is active during ∼ 30% of the measurement record and is most pronounced during winter/spring. Unstable vorticity waves represent an effective mechanism for cooling the core of the West Spitsbergen Current by isopycnal transport of water masses from the core to the surface. The heat loss associated with the most unstable mode is estimated to reach 240 W/m2, which is comparable with reported values of winter surface heat loss.

• Lynge, Birgit Kjoss; Berntsen, J & Gjevik, Bjørn (2010). Numerical studies of dispersion due to tidal flow through Moskstraumen, northern Norway. Ocean Dynamics. ISSN 1616-7341. 60(4), p. 907–920. doi: 10.1007/s10236-010-0309-z. Full text in Research Archive
• Teigen, Sigurd Henrik; Nilsen, Frank & Gjevik, Bjørn (2010). Barotropic instability in the West Spitsbergen Current. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 115(C7). doi: 10.1029/2009JC005996. Full text in Research Archive Show summary

  Barotropic instability in the shoreward branch of the West Spitsbergen Current is investigated on the basis of data from an array of current meter moorings along 78.83°N, across the upper continental slope and shelf break west of Svalbard. The slowly varying background current profile is modeled as an along‐slope, asymmetric jet anchored to the shelf break. Numerical linear stability analyses are performed on the idealized current profile and topography, revealing the characteristic period, wavelength, and growth rate of unstable vorticity waves. Detailed analysis of the ambient current profile in 2007–2008 shows that unstable conditions are present during ∼40% of the 10 month measurement record, depending on the localization, width, and amplitude of the current jet. The resulting vorticity waves are localized at the shelf break and are able to exchange water masses across the oceanic Arctic front. Typical wavelengths and periods are 20–40 km and 40–70 h, respectively. Wavelet, coherence, and complex demodulation analyses of the current meter data confirm that transient signals of similar periodicity as predicted by the stability analysis exist in the data record, prominently during the winter and spring months. Estimates of the heat loss contribution from isopycnal diffusion reach 1.4 TW during the time intervals when unstable vorticity waves are active at the shelf break, implying that the dynamics of the West Spitsbergen Current play a significant role in the cooling process of the Atlantic water on the way to the Arctic Ocean. This cooling corresponds to an along‐shelf cooling rate of −0.08°C per 100 km.

• Christensen, Ole; Kostylev, Vladimir; Longva, Oddvar; Thorsnes, Terje; Courtney, Robert C. & Gjevik, Bjørn (2009). Correlations of geological and biological elements in marine habitat mapping in glaciated areas; field tests from the coast of More and Romsdal County, western Norway. Norsk Geologisk Tidsskrift. ISSN 0029-196X. 89(3), p. 229–246. Full text in Research Archive
• Pankratz, Normann; Natvig, Jostein Roald; Gjevik, Bjørn & Noelle, Sebastian (2007). High-order well-balanced finite-volume schemes for barotropic flows: Development and numerical comparisons. Ocean Modelling. ISSN 1463-5003. 18, p. 53–79. doi: 10.1016/j.ocemod.2007.03.005. Full text in Research Archive
• Gjevik, Bjørn (2006). Flo og fjære langs kysten av Norge. In Aksnes, Kaare (Eds.), Almanakk for Norge for året etter Kristi fødsel 2007. Gyldendal Norsk Forlag A/S. ISSN 9788205354944. p. 48–51. Full text in Research Archive
• Thiem, Øyvind; Thiem, O; Berntsen, Jarle & Gjevik, Bjørn (2006). Development of eddies in an idealised shelf slope area due to an along slope barotropic jet. Continental Shelf Research. ISSN 0278-4343. 26, p. 1481–1495. Full text in Research Archive
• Orre, Steinar; Gjevik, Bjørn & LaCasce, Joseph H. (2006). Characterizing chaotic dispersion in a coastal tidal model. Continental Shelf Research. ISSN 0278-4343. 26, p. 1360–1374. doi: 10.1016/j.csr.2005.11.015. Full text in Research Archive Show summary

  Diverse Lagrangian methods are used to study dispersion and mixing in a model in the Norwegian Trondheim fjord. We focus on the tidally driven currents, neglecting wind-forcing, and generate a large number of particle trajectories. We first consider traditional measures (absolute and relative dispersion) involving averages over all particles. We then contour those measures, to gauge the spatial variations. Then we examine a more recently developed measure, the direct Lyapunov exponent (DLE), to further refine the description of the spatial variability. The results suggest regions of strong mixing adjacent to regions with weak mixing, so that particles in nearby regions may experience very distinct evolutions. And M2 dominates the dispersion; adding additional tidal components affects mainly the amplitude of the particle excursions rather than the character of the mixing.

• Nilsen, F; Gjevik, Bjørn & Schauer, U (2006). Cooling of the West Spitsbergen Current: Isopycnal diffusion by topographic vorticity waves. Journal of Geophysical Research (JGR). ISSN 0148-0227. 111. Full text in Research Archive
• Gjevik, Bjørn; Hareide, D.; Lynge, B.K.; Ommundsen, A; Skailand, J.H. & Urheim, H.B. (2006). Implementation of High Resolution Tidal Current Fields in Electronic Navigational Chart Systems. Marine Geodesy. ISSN 0149-0419. 29, p. 1–17. Full text in Research Archive
• Gjevik, Bjørn; Flather, R.A. & Hareide, D. (2004). Sea level oscillahions with 6-h period in the North Sea 29-31 October 2000. An analysis of data from stations in the northen North Sea and along the western coast of Norway. Ocean Dynamics. ISSN 1616-7341. 54, p. 477–488. doi: 10.1007/S10236-004-0093-8. Full text in Research Archive
• Moe, Halvard; Gjevik, Bjørn & Ommundsen, Atle (2003). A high resolution tidal model for the coast of Møre and Trøndelag, Mid-Norway. Norsk Geografisk Tidsskrift. ISSN 0029-1951. 57, p. 65–82. Full text in Research Archive
• Davies, Alan M.; Xing, Jiuxing & Gjevik, Bjørn (2003). Barotropic eddy generation by flow instability at the shelf edge: Sensitvity to open boundary conditions, inflow and diffusion. Journal of Geophysical Research (JGR). ISSN 0148-0227. 108(C2), p. 17-1–17-15. Full text in Research Archive
• Gjevik, Bjørn; Moe, Halvard & Ommundsen, Atle (2002). Idealized model simulations of barotropic flow on the Catalan shelf. Continental Shelf Research. ISSN 0278-4343. 22, p. 173–198. Full text in Research Archive Show summary

  The effect of along shelf variation in shelf width on barotropic shelf edge flows and topographic shelf waves are investigated with a numerical model. The model topography represents a gradual transition from a narrow straight to a broader straight shelf region. It is designed primary to model the Catalan shelf on the northeastern Mediterranean coast of Spain, but the results obtained here are of general validity and will also apply to shelf flow under similar conditions elsewhere. The numerical experiments are carried out with flow imposed, both steady and oscillatory, at the upstream end of the narrow shelf region. With a prescribed shelf edge flow there is a strong tendency for topographic steering in the transition zone. The adjustment is found to take place on a short time scale of 2-5 days set by propagating wave modes rather than by advection. Bottom friction effects do not lead to significant on-shelf leakage of the flow. Flow instability and eddy formation are found to occur, even in cases where the potential vorticity for the imposed flow does not have a local maximum on the shelf slope. The instability leads to development of anticyclonic eddies on the narrow shelf which undergo strong non-linear adjustment at the transition zone from a narrow to a broader shelf. On the broad section of the shelf near the transition zone there is a tendency for formation of a large anticyclonic eddy. Bottom friction is found to influence the flow instability and the formation of eddies in cases where the flow is marginal for instability and growth of eddies. Particle tracking has been performed in order to study cross shelf mixing and transport. Finally we have studied the current response due to a concentrated wind stress jet acting perpendicular to the coast line in the transition zone between the narrow and the broad shelf regions. A dipolar eddy structure is found to develop with the axis of the dipole tilting about 30 degrees with the axis of the wind jet and with strong current shear in the zone near the dipole axis.

• Moe, Halvard; Ommundsen, Atle & Gjevik, Bjørn (2002). A high resolution tidal model for the area around The Lofoten Islands, Northern Norway. Continental Shelf Research. ISSN 0278-4343. 22, p. 485–504. Full text in Research Archive Show summary

  A depth-integrated numerical model with grid resolution 500 m has been used to simulate tides around The Lofoten Islands in northern Norway. The model spans more than 3 deg latitude and covers a sea area of approximately 1.2*10^5 km^2. The fine spatial resolution resolves the important fine scale features of the bottom topography on the shelf and the complex coastline with fjords and islands. Boundary conditions at the oceanic sides of the model domain are obtained by interpolation from a large scale tidal model covering the Nordic Seas and implemented with the flow relaxation scheme (FRS). The semi-diurnal components M2, S2 and N2 and the diurnal component K1 are simulated. Harmonic constants for sea level are compared with observations from 21 stations. The best fit is found for the M2 component with a standard deviation between the observed and modelled amplitude and phase of 2.3 cm and 2.5 degrees, respectively. The standard deviation for the other smaller components ranges between 1.5 to 2.8 cm and 5.3 to 16.7 degrees. Current fields from the model are compared with observations in four locations; the Moskenes sound, the Gimsøy channel, the Tjeldsund channel and the Sortland channel. In the Sortland channel the model predicts a dominant diurnal K1 current in agreement with observations.

• Gjevik, Bjørn; Moe, Halvard & Ommundsen, Atle (2002). Idealized Model Simulations of Barotopic Flow on the Catalan Shelf. Continental Shelf Research. ISSN 0278-4343. Full text in Research Archive
• Gjevik, Bjørn; Pedersen, Geir Kleivstul; Dybesland, Elen; Harbitz, Carl Bonnevie; Miranda, P.M.A. & Baptista, M.A. [Show all 10 contributors for this article] (1997). Modeling tsunamis from earthquake sources near Gorringe Bank southwest of Portugal. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 102(C13), p. 931–949. doi: 10.1029/97JC02179. Full text in Research Archive Show summary

  The Azores-Gibraltar 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 well-documented 1969 tsunami event is examined both with a ray-tracing 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 half-space 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.

• Gjevik, Bjørn; Moe, Halvard & Ommundsen, Atle (1997). Sources of the Maelstrom. Nature. ISSN 0028-0836. 388, p. 837–838. Full text in Research Archive
• Hackett, Bruce; Røed, Lars Petter; Gjevik, Bjørn; Martinsen, Eivind A. & Eide, Lars Ingolf (1995). A review of the Metocean Modeling Project (MOMOP) Part 2: Model validation study. In Lynch, Daniel R. & Davies, Alan M. (Ed.), Quantitative Skill Assessment for Coastal Ocean Models. American Geophysical Union (AGU). ISSN 9780875902616. p. 307–327. Full text in Research Archive Show summary

  Two fully three-dimensional, primitive equation, baroclinic level models are applied to the mid-Norwegian shelf, and their simulations for a period in March 1988 are validated against observations from the NORCSEX'88 field experiment. The main concern is currents, but salinity and temperature fields are also compared. This validation study has elements not only for a model-data comparison, but also a model-model comparison. Thus, a model-model comparison verification study, using two idealized test cases appropriate for the Norwegian Shelf, is performed as a forerunner to the validation proper. A third, layered, model is also included in the verification study for comparison. The idealized test cases consider 1) the baroclinic response to the storm passage across a shelf and 2) flow over a sea mountain. The main difference between the model responses in these test cases lies in the spatial structure of the currents over long time scales, and is attributed to differences in the parameterizations of the horizontal and vertical eddy viscosities and bottom friction. The validation against data uses a hierarchical procedure, in which the overall features of the fields are compared first, followed by comparisons of more detailed features. Three specific comparison products are used here: transports through vertical sections, horizontal distributions and vertical distributions. It is concluded that both models are able to qualitatively generate many of the observed features of the flow, but neither is able to quantitatively reproduce the detailed currents. The model's successes are attributable to their inclusion of required mechanisms for generating and maintaining the currents on the shelf: the barotropic mode, baroclinic modes and nonlinearity. Their shortcomings are inaccurate placement and timing of the mesoscale features and overly weak gradients, especially in the vertical. These are mainly attributable to inadequate parameterizations of subgrid-scale turbulent mixing, to lack of horizontal resolution and to imperfect initial and boundary conditions.

• Røed, Lars Petter; Hackett, Bruce; Gjevik, Bjørn & Eide, Lars Ingolf (1995). A review of the Metocean Modeling Project (MOMOP) Part 1: Model comparison study. In Lynch, Daniel R. & Davies, Alan M. (Ed.), Quantitative Skill Assessment for Coastal Ocean Models. American Geophysical Union (AGU). ISSN 9780875902616. p. 285–305. Full text in Research Archive Show summary

  Considered are the results of a model comparison study performed as part of the Metocean Modeling Project (MOMOP). The study involves the design of five test cases, relevant to the Norwegian Shelf, by which three-dimensional, baroclinic numerical ocean models can be verified. The first two of these are two-dimensional, in which processes connected to the geostrophic adjustment problem and wind-driven upwelling in a stratified ocean are considered. The remaining cases are three-dimensional and reveal the model's response to flow over a sea mountain (Case 3) and wind-driven flow in the presence of a shelf topography including a steep shelf slope (Cases 4 and 5). Six models participated, including level models, layered models and spectral (in the vertical) models. Two of the models are in sigma-coordinates. The remaining models are straightforward Cartesian coordinate models. The comparison exercise turned out to be as important for the development and design of appropriate test cases as for studying and comparing model results. It was concluded that only the upwelling case was appropriatly designed for the the desired physical processes, while the remaining test cases needed some modification. In retrospect, it would have been useful to test the design a priori using a proven model. Nevertheless, it was found that a model comparison study is a powerful verification tool, in particular for complex, nonlinear, baroclinic ocean models. Concerning the models themselves, it was felt that, given enough time and resources, most, if not all, of the models could have produced acceptable results.

• Harbitz, Carl Bonnevie; Pedersen, Geir Kleivstul & Gjevik, Bjørn (1993). Numerical Simulations of Large Water Waves due to Landslides. Journal of Hydraulic Engineering. ISSN 0733-9429. 1119(12). doi: 10.1061/12(1325. Full text in Research Archive Show summary

  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.

• Martinsen, Eivind A.; Gjevik, Bjørn & Røed, Lars Petter (1979). A numerical model for long barotropic waves and storm surges along the western coast of Norway. Journal of Physical Oceanography. ISSN 0022-3670. 9, p. 1126–1138. Full text in Research Archive
• Gjevik, Bjørn & Røed, Lars Petter (1976). Storm surges along the western coast of Norway. Tellus A: Dynamic Meteorology and Oceanography. ISSN 0280-6495. 28(2), p. 166–182. Full text in Research Archive Show summary

  Storm surge situations along the western coast of Norway between 62oN and 68oN are examined. The observations show that large storm surges are caused by strong south westerly winds acting along a large section of the coast. This situation occurs when an intense low pressure center moves relatively close to the coast and in a direction nearly parallel to it. A model of surge generation by propagating wind fields acting along a straight coast is studied. Analytical solutions for the surge amplitude along the coast are obtained and discussed. The theory is applied to storm surge situations along the western coast of Norway, and it shows that the wind stress in the direction along the coast and the Coriolis force are important forces for the generation of large surges. The wind stress component normal to the coast (i.e., north westerly winds) and the changes in the atmospheric pressure contribute less to the surge.

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• Gjevik, Bjørn (2009). Flo og fjære langs kysten av Norge og Svalbard. Farleia Forlag. ISBN 9788299803106. 351 p. Full text in Research Archive
• Grue, John; Gjevik, Bjørn & Weber, Jan Erik (1996). Waves and Nonlinear Processes in Hydrodynamics. Kluwer Academic Publishers. ISBN 9780792340317. 402 p. Full text in Research Archive

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• Gjevik, Bjørn (2016). Ulykken på Ona i 1670 - Kan noe liknende skje i dag? In Sanden, Jarle (Eds.), Årbok 2016 Romsdalsmuseet- Naturkatastrofer. Romsdalsmuseet. ISSN 9788290251944. p. 35–48. Full text in Research Archive
• Gjevik, Bjørn & Nilsen, Steinar (2014). Beretninger om linefiske på bankene utenfor Midt-NorgeBeretninger om linefiske på bankene utenfor Midt-Norge. In Aune, Kolbjørn & Bjørkvik, Eilert (Ed.), Årbok for Fosen 2014. Fosen Historielag. ISSN 9788290341447. p. 115–140. Full text in Research Archive
• Hjelmervik, Karina Bakkeløkken; Lynge, Birgit Kjoss & Gjevik, Bjørn (2013). Modelling of tides and storm surges in Theldsund channel. Full text in Research Archive
• Bondevik, Stein; Sørensen, Mathilde B. & Gjevik, Bjørn (2012). Norwegian fjords sang along – observations of seiches following the 2011 Tohoku, Japan, earthquake. Full text in Research Archive
• Sørensen, Mathilde B.; Bondevik, Stein & Gjevik, Bjørn (2012). Norwegian fjords sang along – observations of seiches following the 2011 Tohoku, Japan, earthquake. Full text in Research Archive
• Gjevik, Bjørn (2011). Månen nær jorda 19.mars. Forskning.no. ISSN 1891-635X. Full text in Research Archive
• Gjevik, Bjørn (2011). Vær, vind og sjø - fra Petter Dass til moderne forskning. In Skorpen, Knut & Severinsen, Anne (Ed.), Årbok for Helgeland 2011. Helgeland Historielag. ISSN 9788290148411. p. 10–18. Full text in Research Archive
• Gjevik, Bjørn (2010). Flo og fjære langs norskekysten. Kysten. ISSN 0332-9550. p. 16–20. Full text in Research Archive
• Gjevik, Bjørn (2010). Flo og fjære langs kysten av Norge. Almanakk for Norge. ISSN 0806-5632. p. 48–51. Full text in Research Archive
• Gjevik, Bjørn (2010). Tidevannet - Et mangfoldig og komplekst fenomen. Fra Fysikkens Verden. ISSN 0015-9247. Full text in Research Archive
• Hjelmervik, Karina Bakkeløkken; Lynge, Birgit Kjoss; Ommundsen, Atle & Gjevik, Bjørn (2009). Modelling of tides and storm surges in the Tjeldsund channel in northern Norway. Full text in Research Archive
• Weber, Jan Erik H. & Gjevik, Bjørn (2008). Havnivået langs Norskekysten. Forskning.no. ISSN 1891-635X. Full text in Research Archive
• Hjelmervik, Karina Bakkeløkken; Ommundsen, Atle & Gjevik, Bjørn (2007). Model simulations of tidal currents in Tjeldsundet and Ramsundet, northern Norway. 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
• Gjevik, Bjørn; Pedersen, Geir Kleivstul & Harbitz, Carl Bonnevie (2005). Flodbølger – kan de varsles? Full text in Research Archive
• Gjevik, Bjørn (2005). Flodbølge-faren i Norge. Full text in Research Archive
• Gjevik, Bjørn (2000). Modeller for tidevann og tidevannstrømmer langs norskekysten. Full text in Research Archive Show summary

  Tidevann og tidevannsstrømmer kan beregnes ved hjelp av matematiske modeller og datamaskiner. I foredraget forklares det hvordan slike beregninger blir gjennomført. Resultatene sammenlignes med målinger langs norskekysten og visualiseres ved videoanimasjoner. Beregnet strømfelt vil i fremtiden inngå i den nye generasjon av elekroniske sjøkart og strømfelter vil kunne sees på kartmonitoren når man seiler i strømsterke farvann.

• Gjevik, Bjørn & Hareide, Daniel (2000). Ekstrem vannstandsendring og strøm i Oslofjorden. Natten mellom 3. og 4. desember 1999. Naturen. ISSN 0028-0887. p. 258–263. Full text in Research Archive Show summary

  I Oslofjorden er tidevannet, altså de regelmessige skiftningene i vannstand som følge av månen og solas virkning, mindre enn 36 cm. Atmosfærisk pådrag som lufttrykkendringer og sterk vind kan enkelte ganger føre til mye større utslag enn dette. Når vannstanden endrer seg mye over forholdsvis kort tid må storevannmasser transporteres gjennom Drøbaksundet og det vil medføre meget sterk strøm i det trange sundet. Manuskript finnes på: http://www.math.uio.no/~bjorng/oslofjord/manus.pdf

• Gjevik, Bjørn; Moe, Halvard & Ommundsen, Atle (2000). Venturing into the vortex. [Radio]. Channel Four, Equinox Lethal Seas : Northlight Productions. Full text in Research Archive Show summary

  The whirlpool occupies a mythical place in our consciousness. It is an oceanic phenomenon which inspires worldwide awe and terror. Every culture which witnesses this rare spectacle has its legends of monsters of the deep, seizing seafarers and dragging them to their doom. But what are the scientific facts behind the legend? Equinox ventures into the eye of the Maelstrom to capture unique footage of the world's most lethal seas, showing the whirlpool in all its mighty grandeur.

• Gjevik, Bjørn (2000). Summary and assessment of the NDP MetOcean project. Full text in Research Archive
• Gjevik, Bjørn (2000). Hva vet vi om Golfstrømmen utenfor norskekysten ? Full text in Research Archive
• Gjevik, Bjørn; Moe, Halvard & Ommundsen, Atle (1999). Idealized model simulations of barotropic flow on the Catalan shelf. Full text in Research Archive Show summary

  The effect of longshelf variation in shelf width on barotropic shelf edge flows and topographic shelf waves are investigated with a numerical model. The model topography represents a gradual transition from a narrow straight to a broader straight shelf region. It is designed primary to model the Catalan shelf on the northeastern Mediterranean coast of Spain, but the results obtained here are of general validity and will also apply to shelf flow under similar conditions elsewhere. The numerical experiments are carried out with flow imposed, both steady and oscillatory, at the upstream end of the narrow shelf region. With a prescribed shelf edge flow there is a strong tendency for topographic steering in the transition zone. The adjustment is found to take place on a short time scale of 2-5 days set by propagating wave modes rather than by advection. Bottom friction effects do not lead to significant on-shelf leakage of the flow. Flow instability and eddy formation are found to occur, even in cases where the potential vorticity for the imposed flow does not have a local maximum on the shelf slope. The instability leads to development of anticyclonic eddies on the narrow shelf which undergo strong non-linear adjustment at the transition zone from a narrow to a broader shelf. On the broad section of the shelf near the transition zone there is a tendency for formation of a large anticyclonic eddy. Bottom friction is found to influence the flow instability and the formation of eddies in cases where the flow is marginal for instability and growth of eddies. Particle tracking has been performed in order to study cross shelf mixing and transport. Finally we have studied the current response due to a concentrated wind stress jet acting perpendicular to the coast line in the transition zone between the narrow and the broad shelf regions. A dipolar eddy structure is found to develop with the axis of the dipole tilting about 30 degrees with the axis of the wind jet and with strong current shear in the zone near the dipole axis.

• Gjevik, Bjørn (1999). Effect of along shelf variation in bathymetry on shelf slope currents and tides. Full text in Research Archive
• Gjevik, Bjørn & Moe, Halvard (1999). Idealized model simulations of barotropic flow on the Catalan shelf. Full text in Research Archive Show summary

  The effect of a shelf width increase on barotropic shelf edge flows and topographic shelf waves are investigated with a numerical model. The numerical experiments are carried out with flow imposed upstream, both steady and oscillatory, at the narrow shelf. A prescribed shelf edge flow gives a strong tendency for topographic steering in the transition zone. The adjustment is found to take place on a short time scale of 2-5 days set by propagating wave modes rather than by advection. Bottom friction effects do not lead to significant on-shelf leakage of the flow. Flow instability and eddy formation is found to occur, even in cases when the potential vorticity for the imposed flow does not have a local maximum on the shelf slope. The instability lead to development of anticyclonic eddies on the narrow shelf which undergo a strong non-linear adjustment at the transition zone from a narrow to a broader shelf. On the broad section of the shelf near the transition zone there is a tendency for formation of a large anticyclonic eddy. Bottom friction influences the flow instability and eddy formation in cases where the situation is marginal for flow instability and growth of eddies. Finally we have studied the current response due to a consentrated wind stress jet acting perpendicular to the coast line in the zone between the narrow and the broad shelf regions. A dipole eddy structure is found to develop with the axis tilting about 30 degrees with the axis of the wind jet and with strong current shear in the zone near the dipole axis.

• Gjevik, Bjørn (1999). Moskstraumen; Myter Diktning og Virkelighet. Full text in Research Archive
• Hjelmervik, Karina Bakkeløkken; Ommundsen, Atle & Gjevik, Bjørn (2006). Modellsimuleringer av tidevannstrømmen i Tjeldsundet og Ramsundet. Universitetet i Oslo. Full text in Research Archive Show summary

  Tidevannsstrømmen i Tjeldsundet og Ramsundet i Ofoten er simulert med en numerisk havmodell med horisontal gitteroppløsning 25-50 meter. Middelstrømmen i vannsøylen er beregnet for de tre viktigste halvdaglige tidevannskomponentene <I>M</I><SUB>2</SUB>, <I>S</I><SUB>2</SUB>, og <I>N</I><SUB>2</SUB>, og den største heldaglige komponenten <I>K</I><SUB>1</SUB>. For å vise resultatene, er det tegnet strømkart for områdene med sterkeste strøm; Ballstadstraumen, Sandtorgstraumen og Steinslandsstraumen i Tjeldsundet og Spannbogstraumen i Ramsundet. Kartene viser strømfeltene hver time gjennom en tidevannsyklus. I tillegg er det tegnet konturkart for sterkest strøm ved middels stor flo. Kartene viser at det er store variasjoner i strømstyrke og at det i forskjellige faser av tidevannsyklusen opptrer virvler og bakevjer i strømfeltene. Det opptrer virvler flere steder blant annet i nordgående flostrøm ved Evenskjœr nord for Sandtorg, i området ved Tjeldsundbrua, langs land øst og vest Ballstad, og i kjølvannet av Holsflua i Tjeldsundet, nord for innløpet til Ramsund ved sørvestgående fallstrøm. Noen av disse virvelstrukturene er dokumentert også ved observasjoner. Det er foretatt sammenlikninger med både vannstands- og strømmålinger. Modellen viser god overensstemmelse med vannstandsmålingene og prediksjoner av tidspunktene for strømvending mellom nordgående flostrøm og sørgående fallstrøm stemmer også godt overens med målinger. Strømstyrken i modellen viser dessuten god overenstemmelse med tidligere målinger av strømmen i overflatelaget (øvre 10-15 meter av vannsøylen). Strømmålingene utført under prosjektperioden av FFI i dypere vannlag (10-20 meter over bunnen) viser derimot vesentlig lavere strøm enn den middelstrømmen for vannsøylen som modellen predikterer. FFI-målingene er periodevis beheftet med stor usikkerhet på grunn av nedbøyninger og svingninger i måleriggen. Strømfeltene fra modellsimuleringene er forsøksvis implementert for visning i Forsvarets kartsystem MARIA og i serveren METOC WMS for å gjøre resultatene tilgjengelige for operativt bruk.

• Hjelmervik, Karina Bakkeløkken; Ommundsen, Atle & Gjevik, Bjørn (2005). Implementation of non-linear advection terms in a high resolution tidal model. Universitetet i Oslo. Full text in Research Archive Show summary

  Various methods for approximating the non-linear advection terms in a high resolution tidal model with complex coastal boundaries have been implemented and tested. The model, driven by the dominant <I>M</I><SUB>2</SUB> tidal component at the open boundaries, has been applied to a model domain with 100 meter grid resolution for the Tjeldsundet channel in northern Norway. Overtides, intensivated jets and eddy structures appear in the current fields of the full non-linear simulations. How these flow features depend on the way the friction terms are calculated and the way the non-linear advection terms are calculated in a zone near the coastal boundaries, are discussed. Some comparison with field measurements have also been made.

• Ommundsen, Atle; Hjelmervik, Karina Bakkeløkken & Gjevik, Bjørn (2005). Tidevannstrømmen i Tjeldsund-Ramsund, 1.-3. november 2005. Forsvarets forskningsinstitutt. Full text in Research Archive
• Orre, Steinar; Åkervik, Espen & Gjevik, Bjørn (2004). Analysis of current and sea level observations from Trondheimsleia. Universitetet i Oslo. Full text in Research Archive Show summary

  Sea level and current measurements from Trondheimsleia have been analysed and the parameters of the tidal ellipses for the major tidal components <I>M</I><SUB>2</SUB>, <I>S</I><SUB>2</SUB>, <I>N</I> SUB>2</SUB>, and <I>K</I><SUB>1</SUB> have been calculated. Harmonic constants for sea level and tidal ellipse parameters have been compared with the corresponding data from a high resolution tidal model in order to validate the performance of the model. Short periodic oscillations with period about 40 minutes are observed at the time of peak tidal current at one station located in a channel with relatively strong tidal currents.

• Gjevik, Bjørn; Hareide, Daniel; Lynge, Birgit Kjoss; Ommundsen, Atle; Skailand, Jan Helge & Urheim, H.B. (2004). Implementation of high resolution tidal current fields in electronic navigational chart systems. Universitetet i Oslo. Full text in Research Archive Show summary

  A system for displaying tidal currents in an electronic chart display and information system (ECDIS) has been developed and implemented in compliance with the standards of the International Hydrographic Organization (IHO). The tidal current fields can be displayed in real time on the electronic navigational chart and several options and functions for updating and zooming have been designed. The current fields are calculated from a data base with the harmonic constants for the four major tidal constituents. The harmonic constants are obtained from a high resolution numerical model which is validated by comparing with sea level and current measurements. The depth matrix for the central part of the model domain was calculated from data from multi-beam bathymetric surveys. An application example of the implementation is given for Trondheimsleia, a part of the main sailing route along the western coast of Norway.

• Gjevik, Bjørn & Fagerland, Morten Wang (2003). Felteori og vektoranalyse. Forelesninger og oppgaver i MEK1100. Universitetet i Oslo. Full text in Research Archive
• Gjevik, Bjørn (2002). Unstable and neutrally stable modes in barotropic and baroclinic shelf slope currents. Universitetet i Oslo. Full text in Research Archive Show summary

  The stability of barotropic and baroclinic shelf slope currents currents is investigated. Assuming periodic small amplitude perturbation in along shelf direction the stability problem is reduced to an eigenvalue problem by discretization in the across shelf direction. The eigenvalue problem for the wave frequency when along shelf wave number is specified is solved numerically by using NAG-routines. Two applications are considered, one corresponding to the conditions along the Catalan shelf, northwestern Mediterranean, the other to the shelf slope west of Norway.

• Moe, Halvard; Ommundsen, Atle & Gjevik, Bjørn (2000). A high resolution tidal model for the area around The Lofoten Islands, Northern Norway. Universitetet i Oslo. ISSN 9788255312376. Full text in Research Archive Show summary

  A numerical model with grid resolution 500 m has been used to simulate tides around The Lofoten Islands in northern Norway. The model spans more than 3 degrees latitude and covers a sea area of approximately 1.2x10^5 km^2. The fine spatial resolution resolves the important fine scale features of the bottom topography on the shelf and the complex coastline with fjords and islands. Boundary conditions at the oceanic sides of the model domain are obtained by interpolation from a large scale tidal model covering the Nordic Seas. The semi-diurnal components M_2, S_2 and N_2 and the diurnal component K_1 are simulated. Harmonic constants for sea level are compared with observations from 21 stations. The best fit is found for the M_2 component with a standard deviation between the observed and modelled amplitude and phase of respectively 2.3 cm and 2.5 degrees. The standard deviation for the other smaller components ranges 1.5-2.8 cm and 5.3-16.7 degrees. Current fields from the model are compared with observations in four locations; the Moskenes sound, the Gimsøy channel, the Tjeldsund channel and the Sortland channel. Current speed is found to be in good agreement with observations. In the Sortland channel the model predicts a dominant diurnal K_1 current in agreement with observations.

• Gjevik, Bjørn; Moe, Halvard & Ommundsen, Atle (2000). Idealized model simulations of barotropic flow on the Catalan shelf. Universitetet i Oslo. Full text in Research Archive
• Ommundsen, Atle & Gjevik, Bjørn (2000). Scattering of tidal Kelvin waves along shelves which vary in their lengthwise direction. Universitetet i Oslo. ISSN 9788255312451. Full text in Research Archive Show summary

  The effect of along shelf variation in shelf width on the propagation of Kevin waves with semi-diurnal, M2, or diurnal, K1, period is studied using a numerical model. Two idealized cases are considered characterized by either a transition zone from a broad to a narrow shelf or vice versa. Simulations show that the semi-diurnal Kelvin waves adjust gradually in the transition zone to a transmitted Kelvin wave matching the downstream depth profile. The simulations of a propagating diurnal Kelvin wave show mode conversion and the development of shelf waves. This may lead to regions on the shelf with dominant diurnal currents even in cases where the sea surface amplitude of the diurnal tide is much smaller than the semi-diurnal.

• Moe, Halvard; Gjevik, Bjørn & Ommundsen, Atle (2000). A high resolution tidal model for the coast of Møre and Trøndelag, Mid Norway. Universitetet i Oslo. ISSN 9788255312369. Full text in Research Archive Show summary

  A numerical model with grid resolution 500 m has been used to simulate tides on a section of the shelf off the coast of Møre and Trøndelag in western Norway. The model spans about 3 degrees latitude and covers a sea area of approximately 8x10^4 km^2. The fine spatial resolution resolves the important fine scale features of the bottom topography on the shelf and the complex coastline with fjords and islands. Boundary conditions at the oceanic sides of the model domain are obtained by interpolation from a larger scale tidal model covering the Nordic Seas. The semi-diurnal components M_2, S_2 and N_2 and the diurnal component K_1 are simulated. Harmonic constants for sea level are compared with observations from 28 stations. The standard deviations between the observed and modelled amplitudes and phases for the dominant semi-diurnal component, M_2, are 1.7 cm and 5.1 degrees respectively. Current fields from the model are compared with observations from stations along the pipeline from Tjeldbergodden on the coast to the oil and gas fields on the northern rim of Haltenbanken.

• Gjevik, Bjørn (2000). Summary and assessment of the NDP MetOcean project. Norwegian Depwater Programme, Norske Shell, Stavanger. Full text in Research Archive
• Pedersen, Geir; Langtangen, Hans Petter; Johnsgard, Helge & Gjevik, Bjørn (1998). Mid term report for GITEC-TWO. Universitetet i Oslo. Full text in Research Archive Show summary

  The report summarizes the work performed at the Department of Mathematics, during the first year of the European research project GITEC-TWO (contract ENV4-U96-0297). Some of the result will subsequently be published elsewhere in a more complete form. We start with the brief presentation of hydrostatic and dispersive long wave equations, in Eulerian as well as Lagrangian description, and a family of somewhat related numerical techniques. The effect of dispersion on the 1969 tsunami, originating in deep sea south-west of Portugal, is extensively discussed in relation to numerical solutions and discretization errors. We find strong indications that dispersive effects are significant for this tsunami. In the project work emphasis has been put on the analysis of numerical methods by analytic tools. To the knowledge of the writers this is a new approach. First an optical theory for discrete waves is established. Then the effects of a staircase boundary on run-up is investigated through separation of variables in a non-orthogonal coordinate system. Two finite element model are presented: a technique for solution of the Boussinesq equations in Eulerian coordinates and a run-up model in Lagrangian description. The latter is verified through comparison to analytic results and a previously developed finite difference method. The results are promising.

• Pedersen, Geir; Langtangen, Hans Petter; Johnsgard, Helge & Gjevik, Bjørn (1998). Final report for GITEC-TWO. Universitetet i Oslo. Full text in Research Archive Show summary

  The report summarizes the work performed at the Department of Mathematics, during the first two years of the European research project GITEC-TWO (contract ENV4-U96-0297). Some of the result will subsequently be published elsewhere in a more complete form. The project work will continue to the end of 1998. The report adresses the following topics - Development of an optical theory for discrete waves - Run-up and staircase boundaries - Finite element techniques for the Boussinesq equations - Lagrangian finite difference technique for run-up of long waves - Lagrangian finite element technique for run-up of long waves - Testing of run-up models by comparison to analytical solutions - Parallel models - Domain decomposition; multiphysics - Bore propagation and ru-up - Boundary element method for full potential theory - Discusion of physichal effects and validity of long wave approximations Introduction: In the first GITEC project the UiO group performed a series of case studies concerning tsunami events in the Atlantic, the eastern Mediterranean and the Norwegian sea. During the project the focus was slightly shifted towards general model analysis and development. Preliminary Lagrangian run-up models and finite element (FE) techniques for Boussinesq equations were reported. Moreover, tests concerning the convergence and applicability of the standard long wave models were included in the case studies or carried out as separate tasks. Continuing this line of investigation, we have focused mainly on model activities in GITEC-TWO, even though the work on the 1969 tsunami outside Portugal has continued and the study of the Tafjord event (1934) has been renewed. All the model activities rely heavily upon the experience from these and other case studies from the preceding project and elsewhere. Moreover, we have addressed a set of idealized, but challenging test cases, to obtain an improved insight in physics as well as numerics. This will enable us to exploit our new modeling tools in full studies of actual events with better results and control. A number of test cases have been established, including wave generation and interaction with a shallow seamount, run-up on an idealized headland, slides in fjords, and wave propagation in several two dimensional geometries, usually corresponding to cross sections of actual bathymetries. Some of these problems are also addressed by the LDG group. The prolonged study of the 1969 tsunami, originating near the Gorringe Bank, is linked to the publication of a joint journal paper (Gjevik et al. 1997) with the ICTE and the LDG groups. Due to the complexity of the problem and the diversity of the subtopics involved, the paper has been substantially revised during GITEC-TWO before being finally accepted. This is described further in section 8. In all simulations, concerning real as well as idealized test cases, emphasis has been put on grid refinement tests. Unless otherwise explicitly noted all the presented simulations herein are close to convergence. It might seem surprising, but some of the properties of the most standard tsunami models are insufficiently documented in the literature. This is alarming since much of the tsunami work world wide still have to rely on the standard methods. Naturally, many of the features will also be inherited by more advanced models. Facing this problem during the preceding project, we have undertaken a study of the optical properties of finite difference (FD) and FE models, as well as on the influence of so called staircase (sawtooth) boundaries on the coastal response to incident waves. The results are summarized in section 2. Together with section 8 these topics form a fairly broad analysis on the shortcomings and accuracy of linear hydrostatic models. Other investigations concerning properties of finite element discretizations, domain decomposition etc. are described in other sections, the references or in manuscripts in progress. The FE model for the Boussinesq equations has been upgraded, analyzed and fully documented in the journal paper Langtangen and Pedersen (1998b). Evaluation and verification of the method are partly based on the test cases outlined above. More details are given in section 3. Particular emphasis has been put the on run-up models, that are described in the sections 4 and 6. The FD Lagrangian model for run-up, initiated under the first GITEC project, has been further developed, tested and documented in journal papers Johnsgard and Pedersen (1997)(ab). Bore treatment and bottom drag have been included as new features. Careful investigations have revealed both conceptual and practical problems concerning bore run-up (section 6). A related, but more general, FE technique has been implemented and compared to analytical solutions as well as to the pre-existing FD method. Both these results and additional simplified case studies are promising. This is elaborated in section 4. Preliminary model description and test results are published in a conference proceedings Langtangen and Pedersen (1998)(a). The FE software has been implemented in C++ using object-oriented design techniques and the Diffpack library. As is usual in tsunami research, our modeling has been based mainly on hydrostatic and dispersive long wave equations. In order to check the validity of such equations, as well to investigate short wave features of tsunamis, we have developed a model that solves the equations of full nonlinear potential theory as described in section 7. Two essential themes in the tsunami computation of the near future are parallel computing and automatic coupling of models with different numerical and physical characteristics. Both problems reduce to the development of flexible and general software components for implementing domain decomposition methods on top of existing solvers. Our work in this field, within GITEC-TWO, is sketched in section 5. In the GITEC project we produced a video cassette describing some results concerning the 1969 Portuguese event and the Storegga tsunami, in collaboration with the Computer Center of the University of Oslo. Also in the new project we will produce animations and videos. However, significant upgrading of both hardware and software has been necessary. In combination with vacancy in the Department's position as computer engineer, with particular responsibility for scientific visualization, this has led to substantial delays. Anyway, sufficient resources is now allocated to the visualization task and the work is in steady progress and should be completed within the extended deadline of the GITEC-TWO project.

• Gjevik, Bjørn; Pedersen, Geir; Dybesland, E.; Johnsgard, Helge; Langtangen, Hans Petter & Harbitz, Carl Bonnevie (1995). Model development and simulation of tsunamis outside Portugal and Greece; Second GITEC status report. Universitetet i Oslo. Full text in Research Archive
• Pedersen, Geir; Gjevik, Bjørn; Harbitz, Carl Bonnevie; Dybesland, E.; Johnsgard, Helge & Langtangen, Hans Petter (1995). Tsunami case studies and model analysis; Final GITEC-report. Universitetet i Oslo. Full text in Research Archive
• Gjevik, Bjørn; Pedersen, Geir Kleivstul; Dybesland, E. & Harbitz, Carl Bonnevie (1994). Numerical simulations of tsunami waves: Preliminary results of the Storegga, the Gorringe bank and the Thera case studies. Universitetet i Oslo. Full text in Research Archive
• Gjevik, Bjørn; Nøst, Elisabeth & Straume, T. (1992). Model simulations of the tides in the Barents. Universitetet i Oslo. Full text in Research Archive
• Harbitz, Carl Bonnevie; Pedersen, Geir Kleivstul & Gjevik, Bjørn (1991). Model simulations of large water waves due to landslides. Universitetet i Oslo. Full text in Research Archive
• Gjevik, Bjørn (1990). Simulations of shelf sea response due to traveling storms. Universitetet i Oslo. ISSN 9788255306993. Full text in Research Archive
• Gjevik, Bjørn & Pedersen, Geir Kleivstul (1981). RUN-UP OF LONG WAVES ON AN INCLINED PLANE. Universitetet i Oslo. Full text in Research Archive Show summary

  Non-linear wave reflection on inclined planes is studied. Analytical expressions which describe the run-up and the back-wash are obtained both for single and periodic waves. The maximum run-up height for a single harmonic wave compare well with observations of solitary waves on relatively steep slopes. A simple breaking criterion for the collapse of a solitary wave during the back-wash is deviced. The criterion is found to agree well with observations. From the form of the water surface during the run-up we have estimated the possible water spill-over into a reservoir. Energy consideration indicate that less than 30 per cent of the wave energy may be available for power production.

• Martinsen, E. A.; Gjevik, Bjørn & Røed, Lars Petter (1978). A NUMERICAL MODEL FOR LONG BAROTROPIC WAVES AND STORM SURGES ALONG THE WESTERN COAST OF NORWAY. Universitetet i Oslo. ISSN 9788255303633. Full text in Research Archive
• Gjevik, Bjørn & Marthinsen, Tom (1977). THREE-DIMENSIONAL LEE-WAVE PATTERN. Universitetet i Oslo. ISSN 9788255303329. Full text in Research Archive
• Gjevik, Bjørn (1971). On the non-linear stability of a liquid film flowing down an inclined plane. Universitetet i Oslo. Full text in Research Archive
• Gjevik, Bjørn (1970). Spatially varying finite-amplitude wave trains on falling liquid films. Universitetet i Oslo. Full text in Research Archive Show summary

  In a previous paper the occurrence of steady finite-amplitude waves on falling liquid films has been studied by a long wave expansion technique. This analysis is now extended to include spatially varying wave trains. The solutions presented may correspond to the forced wave trains occurring downstream from a wave generator. Moreover the second order terms in the long wave expansion are reported and their effect on the finite-amplitude wave motion is studied, Numerical results for finite-amplitude waves on thin films of water or alcohol are presented.

• Gjevik, Bjørn (1970). The effect of viscosity on long capillary-gravity waves. Universitetet i Oslo. Full text in Research Archive Show summary

  The effect of viscosity on capillary-gravity waves is examined by a long wave expansion. The phase velocity differs little from that for an inviscid fluid unless the depth is close to the boundary layer thickness. Numerical results for water are in agreement with measurements.

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