John Grue

• Mcguire, Karl Henrik; Jacobsen, Håvar R.L. & Grue, John (2025). Wave effects on a floating, flexible and porous plate in 3D. Journal of Fluids and Structures. ISSN 0889-9746. 137. doi: 10.1016/j.jfluidstructs.2025.104361. Full text in Research Archive Show summary

  Motivated by floating solar energy production, we derive by a variational approach the equation of motion of a floating, flexible, and porous plate exposed to incoming waves. The modal representation is orthogonal and complete. The wavenumber 𝐾 is up to 𝐾𝓁𝑥 ≤ 30 (𝓁𝑥 the plate length). The dimensionless stiffness 𝐷∕(𝜌𝑔𝓁2𝑥𝓁2𝑦) is in the range between 10−3 (small plate) and 10−7 (large plate) (𝜌 the density of the fluid, 𝑔 the acceleration due to gravity, 𝓁𝑦 the lateral plate extension). The damping effect of the plate is modeled by a linear Darcy law. Even a small damping coefficient strongly reduces the plate responses. The porous dissipation depends on the flexibility of the plate. The plate-fluid system is connected with a set of integral equations for the radiation and diffraction problems using suitable Green functions in 3D and 2D. The integral equations are developed in two different versions. A set of generalized Haskind relations for the modal exciting force is developed. The damping coefficients are predicted by three different theoretical formulas obtaining convergent results. The overall energy equation is evaluated. The horizontal drift force on a damped plate is essential.

• Grue, John & Röhrs, Johannes (2025). Nonlinear internal wave groups due to the interplay between a coastal current, the tide and a ridge-valley shelf topography. Journal of Nonlinear Waves. 1. doi: 10.1017/jnw.2025.10014. Full text in Research Archive Show summary

  The emitted internal wave groups and generating source at a double ridge-valley topography on the Norwegian Continental Shelf are determined. The location is 69 degrees north and 14 degrees east on the eastern boundary of the Norwegian Sea. Combination of two data sources – an ocean general circulation model and a set of satellite images – predicts the dominant shelf/slope current, the tide and the density stratification. The internal linear long-wave speed provides the reference velocity. The particular flow–topography interaction results in two compact internal tidal troughs, extending across the shelf, orthogonal to the current and separated by the diurnal internal tidal wavelength. The strongly nonlinear trough emits the wave groups advancing upstream at the diurnal frequency. Satellite data determine the spatial frequency and the number of groups. The dimensionless nonlinear excess propagation speed of 0.32 of the wave groups is compared to KdV theory and the model of internal solitary waves. Possible instability and supply of nutrients for a downstream cold-water coral reef are discussed. The data from satellite in combination with ocean model calculations at the mesoscale is general for the identification of nonlinear internal wave generation and propagation.

• Grue, John (2024). Undular Bore Due to a Low Pressure or Bottom Trough Moving at the Critical Speed. Water Waves. ISSN 2523-367X. doi: 10.1007/s42286-024-00105-2. Full text in Research Archive Show summary

  A low pressure or bottom obstacle of negative displacement moves at the critical speed along a fluid layer of constant depth. The disturbance causes a depression of the surface at its forward position. The nonlinear dynamics generates a group of short waves attached to the disturbance. The number of two to six crests have a wavelength of 5.7–12 times the water depth. The wave height increases with the decreasing wavelength. The waves of the group do not follow the dispersion properties of cnoidal waves or Stokes waves. The group is rather characterised as an undular bore. The bore develops during a travel distance of 7–15 times the length of the disturbance. Its front eventually moves ahead of the driving disturbance where the leading crest develops into a solitary wave. A short disturbance is more powerful, but generates fewer crests compared to a long one. Comparison to the generation phase of upstream waves due to a high pressure (ship) or a bottom elevation shows that the wavelength in the two cases is approximately equal.

• Ellevold, Thea Josefine; Grue, John & Sletten, Joakim Soløy (2023). Tracer particle motion driven by vortex formation in the bottom boundary layer underneath internal solitary waves. Frontiers in Marine Science. 10. doi: 10.3389/fmars.2023.1155270. Full text in Research Archive Show summary

  Internal solitary waves (ISWs) of large amplitude moving in the coastal ocean induce sizeable horizontal velocities above the sea bed. In turn, these give rise to instability and vortex formation in the bottom boundary layer (BBL), and sediment resuspension and concentration maintenance in the water column. We present two-dimensional laminar simulations in a numerical tank suitable for internal wave motion, including the processes of the BBL. The combined wave and vorticity field encounters a cloud of tracer particles near the bottom. The tracer particles are moved vertically because of the vorticity field during a first encounter. The reflected wave intercepts a second time with the tracer particles, which are then moved further vertically. Numerical experiments with a kinematic viscosity of 1/100 cm 2 s −1 or 1/1000 cm 2 s -1 are used to manipulate the scale of the Reynolds number at a moderate and great laboratory scale. The final vertical position of the tracer particles is found below a vertical level of approximately 0.23 times the water depth ( H ) after the second passage. The result is independent of the scale. This vertical position matches available field measurements of a summer benthic nepheloid layer reaching a height of 0.19 H . The laminar model predictions compare very well to the ISW-driven vortex formation measured in a three-dimensional laboratory wave tank. Convergence of the calculated vortex formation is documented.

• Ellevold, Thea Josefine & Grue, John (2023). Calculation of internal-wave-driven instability and vortex shedding along a flat bottom. Journal of Fluid Mechanics. ISSN 0022-1120. 966. doi: 10.1017/jfm.2023.476. Full text in Research Archive Show summary

  The instability and vortex shedding in the bottom boundary layer caused by internal solitary waves of depression propagating along a shallow pycnocline of a fluid are computed by finite-volume code in two dimensions. The calculated transition to instability agrees very well with laboratory experiments (Carr et al., Phys. Fluids, vol. 20, issue 6, 2008, 06603) but disagrees with existing computations that give a very conservative instability threshold. The instability boundary expressed by the amplitude depends on the depth d of the pycnocline divided by the water depth H, and decays by a factor of 2.2 when d/H is 0.21, and by a factor of 1.6 when d/H is 0.16, and the stratification Reynolds number increases by a factor of 32. The instability occurs at moderate amplitude at large scale. The calculated oscillatory bed shear stress is strong in the wave phase and increases with the scale. Its non-dimensional magnitude at stratification Reynolds number 650 000 is comparable to the turbulent stress that can be extracted from field measurements of internal solitary waves of similar nonlinearity, moving along a pycnocline of similar relative depth.

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

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

• Antollini, Giulia; Jensen, Atle; Grue, John; Riise, Bjørn & Brochini, Maurizio (2020). Wave-induced vortex generation around a slender vertical cylinder. Physics of Fluids. ISSN 1070-6631. 32. doi: 10.1063/1.5141131. Full text in Research Archive Show summary

  Experimental results of wave-induced vortex generation around a slender, vertical cylinder are discussed. Coherent vortices appear in long waves (kR ∼ 0.1, where k is the wave number and R is the cylinder radius) during the timing of the secondary load cycle, a strongly nonlinear component of the wave force acting on the cylinder, which is also measured. However, the secondary load cycle is also present in moderately long wave cases (kR ∼ 0.3) where there is no vortex formation. The measurement of vortex generation is enabled by particle image velocimetry. The flow downstream the cylinder, in three horizontal planes at different depths, is measured. The vortex formation that occurs in the long waves is attached to the cylinder in the form of thin vortex tubes. These appear symmetrically at angles of 40°–45° off the wave propagation direction. In one weak long wave case, several very thin vortex tubes appear along the back side of the cylinder. Vortex diameters are 20% of the cylinder diameter in four cases and 50% of the cylinder diameter in one case. The measured vorticity emanates from the cylinder’s boundary layer and is an order of magnitude stronger than the vorticity caused by wave breaking. Wave breaking reduces the vortex strength. The fact that the secondary load cycle appears without and with flow separation effects indicates that the load cycle is a gravity wave phenomenon that scales with the Froude number but that flow separation effects also contribute to the magnitude of such suction forces.

• Marchenko, Aleksey; Grue, John; Karulin, Evgeny; Frederking, R.; Lishman, Ben & Chistyakov, Peter [Show all 16 contributors for this article] (2020). Elastic moduli of sea ice and lake ice calculated from in-situ and laboratory experiments. Proceedings of the IAHR International Symposium on Ice. p. 95–106. Full text in Research Archive
• Grue, John (2020). Mini-tsunami made by ship moving across a depth change. Journal of waterway, port, coastal, and ocean engineering. ISSN 0733-950X. 146(5). doi: 10.1061/(ASCE)WW.1943-5460.0000585. Full text in Research Archive
• Grue, John & Osyka, Bogdan (2020). Runup on a vertical column in strong water wave events. Coastal Engineering. ISSN 0378-3839. 163. doi: 10.1016/j.coastaleng.2020.103775. Full text in Research Archive Show summary

  Runup on a slender cylindrical column exposed to long, steep waves, at finite and great depth is quantified by high speed camera technique in wave channel. Ratio between water depth (h) and cylinder diameter (D) is h/D = 10, 4.16, 2.5. Breaking and non-breaking wave events are made by focusing technique. The trough-to-trough period (TTT), crest height (η0.m), frequency (ω = 2π/TTT) and reference speed (g/ω) of each wave event are defined (g denotes acceleration of gravity). Wavenumber (k) is obtained from the dispersion relation. Experimental runup maximum (Rum) is presented in terms of variable Z = [2ω2(Rum - η0,m)/g]1/2. Measurements at finite water depth collapse along a linear relationship kη0,m = a + b Z where coefficients are obtained from the experiments. Results from other studies including large scale measurements fit to this curve, for h/D < 5, kh < 2 and kD < 0.52. Results at great water depth with h/D = 10 show, beyond a threshold wave slope, a similar relationship. Growth factor (1/b) is then much stronger. Gradual transition between results at finite depth and great water depth occurs for 5 < h/D < 10 and kh > 2.5. Measured runup velocity along the column is up to 1.8 times the reference speed at great depth (h/D = 10) and up to 1.2 times the reference speed at finite depth. Wave slope kη0,m is up to 0.56.

• Riise, Bjørn; Grue, John; Jensen, Atle & Johannessen, Thomas Berge (2018). High frequency resonant response of a monopile in irregular deep water waves. Journal of Fluid Mechanics. ISSN 0022-1120. 853, p. 564–586. doi: 10.1017/jfm.2018.499. Full text in Research Archive Show summary

  Experiments with a weakly damped monopile, either fixed or free to oscillate, exposed to irregular waves in deep water, obtain the wave-exciting moment and motion response. The nonlinearity and peak wavenumber cover the ranges: 𝜖P∼0.10−0.14 and kPr∼0.09−0.14 where 𝜖P=0.5HSkP is an estimate of the spectral wave slope, HS the significant wave height, kP the peak wavenumber and r the cylinder radius. The response and its statistics, expressed in terms of the exceedance probability, are discussed as a function of the resonance frequency, 𝜔0 in the range 𝜔0∼3−5 times the spectral peak frequency, 𝜔P. For small wave slope, long waves and 𝜔0/𝜔P=3, the nonlinear response deviates only very little from its linear counterpart. However, the nonlinearity becomes important for increasing wave slope, wavenumber and resonance frequency ratio. The extreme response events are found in a region where the Keulegan–Carpenter number exceeds KC>5, indicating the importance of possible flow separation effects. A similar region is also covered by a Froude number exceeding Fr>0.4, pointing to surface gravity wave effects at the scale of the cylinder diameter. Regarding contributions to the higher harmonic forces, different wave load mechanisms are identified, including: (i) wave-exciting inertia forces, a function of the fluid acceleration; (ii) wave slamming due to both non-breaking and breaking wave events; (iii) a secondary load cycle; and (iv) possible drag forces, a function of the fluid velocity. Also, history effects due to the inertia of the moving pile, contribute to the large response events. The ensemble means of the third, fourth and fifth harmonic wave-exciting force components extracted from the irregular wave results are compared to the third harmonic FNV (Faltinsen, Newman and Vinje) theory as well as other available experiments and calculations. The present irregular wave measurements generalize results obtained in deep water regular waves.

• Riise, Bjørn; Grue, John; Jensen, Atle & Johannessen, Thomas Berge (2018). A note on the secondary load cycle for a monopile in irregular deep water waves. Journal of Fluid Mechanics. ISSN 0022-1120. 849, p. R1–R12. doi: 10.1017/jfm.2018.450. Full text in Research Archive Show summary

  Laboratory experiments with a bottom hinged surface-piercing cylinder, exposed to irregular deep water waves, are used to investigate high-frequency forcing. The focus is on the secondary load cycle, a strongly nonlinear phenomenon regarding the wave load on a vertical cylinder, first identified by Grue et al. (1993 Preprint Series. Mechanics and Applied Mathematics, pp. 1–30. University of Oslo, available at http://urn.nb.no/URN:NBN:no-52740; 1994 Ninth International Workshop on Water Waves and Floating Bodies (ed. M. Ohkusu), pp. 77–81, available at http://iwwwfb.org). For a total of 2166 single wave events, the force above 3ω (where ω is the governing wave frequency) is used to identify and split the strongly nonlinear forces into two peaks: a high-frequency peak closely correlated in time with the wave crest when the total load is positive and a high-frequency peak defining the secondary load cycle which occurs close in time to the wave zero downcrossing when the total load is negative. The two peaks are studied by regression analysis as a function of either the Keulegan–Carpenter number (KC) or the Froude number (Fr). Regarding the secondary load cycle, the best correlation is found with Fr. The speed of the travelling edge of the undisturbed wave approximates the fluid velocity. A threshold value separating between small and large forces is found for KC∼4–5, indicating effects of flow separation. Alternatively, the threshold occurs for Fr∼0.3–0.4, indicating local wave effects at the scale of the cylinder diameter. The findings suggest that both effects are present and important.

• Grue, John (2017). Ship generated mini-tsunamis. Journal of Fluid Mechanics. ISSN 0022-1120. 816, p. 142–166. doi: 10.1017/jfm.2017.67. Full text in Research Archive Show summary

  Very long waves are generated when a ship moves across an appreciable depth change ∆h comparable to the average and relatively shallow water depth h at the location, with ∆h/h ≃ 1. The phenomenon is new and the waves are recently observed in the Oslofjord in Norway. The 0.5-1 km long waves, extending across the 2-3 km wide fjord, are observed as run-ups and run-downs along the shore, of periods of 30-60 seconds, where a wave height up to 1.4 m has been measured. The waves travelling with the shallow water speed, found ahead of the ships moving at subcritical depth Froude number, behave like a mini-tsunami. A qualitative explanation of the linear generation mechanism is provided by an asymptotic analysis, valid for ∆h/h << 1 and long waves, expressing the generation in terms of a pressure impulse at the depth change. Complementary fully dispersive calculations for ∆h/h ≃ 1 document symmetries of the waves at positive or negative ∆h. The wave height grows with the ship speed U according to U n with n in the range 3 − 4, for ∆h/h ≃ 1, while the growth in U is only very weak for ∆h/h << 1 (the asymptotics). Calculations show good agreement with observations.

• Grue, John & Kolaas, Jostein (2017). Experimental particle paths and drift velocity in steep waves at finite water depth. Journal of Fluid Mechanics. ISSN 0022-1120. 810:R1, p. 1–10. doi: 10.1017/jfm.2016.726. Full text in Research Archive Show summary

  The Lagrangian paths, horizontal Lagrangian drift velocity, U L , and the Lagrangian excess period, T L − T 0 , where T L is the Lagrangian period and T 0 the Eulerian linear period, are obtained by particle tracking velocimetry (PTV) in non-breaking periodic laboratory waves at a finite water depth of h = 0 . 2 m, wave height of H = 0 . 49 h and wavenumber of k = 0 . 785 / h . Both U L and T L − T 0 are functions of the average vertical position of the paths, ̄ Y , where − 1 < ̄ Y / h < 0. The functional relationships U L ( ̄ Y ) and T L − T 0 = f ( ̄ Y ) are very similar. Comparisons to calculations by the inviscid strongly nonlinear Fenton method and the second-order theory show that the streaming velocities in the boundary layers below the wave surface and above the fluid bottom contribute to a strongly enhanced forward drift velocity and excess period. The experimental drift velocity shear becomes more than twice that obtained by the Fenton method, which again is approximately twice that of the second-order theory close to the surface. There is no mass flux of the periodic experimental waves and no pressure gradient. The results from a total number of 80 000 experimental particle paths in the different phases and vertical positions of the waves show a strong collapse. The particle paths are closed at the two vertical positions where U L = 0.

• Carr, Magda; Franklin, James; King, Stuart E.; Davies, Peter A.; Grue, John & Dritschel, David G (2017). The characteristics of billows generated by internal solitary waves. Journal of Fluid Mechanics. ISSN 0022-1120. 812, p. 541–577. doi: 10.1017/jfm.2016.823. Full text in Research Archive Show summary

  The spatial and temporal development of shear-induced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contour-advective semi-Lagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying wave-induced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their long-wave counterparts for a given stratification.

• Dokken, Jorgen S.; Grue, John & Karstensen, Lasse (2017). Wave analysis of porous geometry with linear resistance law. Journal of Marine Science and Application. ISSN 1671-9433. 16(4), p. 480–489. doi: 10.1007/s11804-017-1438-2. Full text in Research Archive Show summary

  The wave diffraction-radiation problem of a porous geometry of arbitrary shape located in the free surface of a fluid is formulated by a set of integral equations, assuming a linear resistance law at the geometry. The linear forces, the energy relation and the mean horizontal drift force are evaluated for non-porous and porous geometries. A geometry of large porosity has an almost vanishing added mass. The exciting forces are a factor of 5–20 smaller compared to a solid geometry. In the long wave regime, the porous geometry significantly enhances both the damping and the mean drift force, where the latter grows linearly with the wavenumber. The calculated mean drift force on a porous hemisphere and a vertical truncated cylinder, relevant to the construction of fish cages, is compared to available published results. This research has been published in Journal of Marine Science and Application. ©2017 Springer Verlag

• Grue, John; Bourgault, Daniel & Galbraith, Peter S (2016). Supercritical dead water: Effect of nonlinearity and comparison with observations. Journal of Fluid Mechanics. ISSN 0022-1120. 803, p. 436–465. doi: 10.1017/jfm.2016.518. Full text in Research Archive
• Grue, John (2015). Nonlinear evaluation of the kinematics of directional field waves (Realistliku lainevälja üksiklainete kinemaatiliste parameetrite arvutamine veepinna salvestustest). Academy Journal. ISSN 1736-6046. 64(3), p. 270–277. doi: 10.3176/proc.2015.3.10. Full text in Research Archive
• Grue, John (2015). Nonlinear interfacial wave formation in three dimensions. Journal of Fluid Mechanics. ISSN 0022-1120. 767, p. 735–762. doi: 10.1017/jfm.2015.42. Full text in Research Archive
• Grue, John (2015). Nonlinear dead water resistance at subcritical speed. Physics of Fluids. ISSN 1070-6631. 27(8). doi: 10.1063/1.4928411. Full text in Research Archive
• Landet, Tormod; Mortensen, Mikael & Grue, John (2015). Towards a continuous and discontinuous Galerkin method for multi-phase flows. In Skallerud, Bjørn Helge & Andersson, Helge Ingolf (Ed.), Proceedings of MekIT'15 Eighth National Conference on Computational Mechanics. International Center for Numerical Methods in Engineering (CIMNE). ISSN 9788494424496. p. 275–294. Full text in Research Archive Show summary

  We present an overview of the continuous and discontinuous Galerkin finite element methods (CG-FEM, DG-FEM) for numerical solution of the transport equation and show how the Navier-Stokes equations can be solved with CG-FEM in both a coupled and segregated manner. We show convergence of the implemented Navier-Stokes solvers for single-phase ows on the well known Taylor-Green vortex and also show how the volume of uid (VOF) method for tracking the interface between two uids can be implemented in DG-FEM. Our work is aimed towards creating a method for looking at the impact forces from water waves on structures and comments are made on how to evolve the presented solution methods into a two-phase solver that can handle the physics involved in highly non-linear free surface simulations.

• Grue, John; Kolaas, Jostein & Jensen, Atle (2014). Velocity fields in breaking-limited waves of finite depth. European journal of mechanics. B, Fluids. ISSN 0997-7546. 47, p. 97–107. doi: 10.1016/j.euromechflu.2014.03.014. Full text in Research Archive Show summary

  The kinematics below the strongest possible periodic water waves on intermediate depth, for wave periods Tg/h=8.75 and 11.7 (g acceleration of gravity, h water depth), is measured by PTV. The largest possible uniform waves far away from the wave maker have a height of H/h≃0.49 and a fluid velocity up to 0.5gh for these periods. Moderately breaking waves measured close to the wave maker have a turbulent surface region riding on top of a smooth flow with horizontal fluid velocity of 0.62gh at maximum, and wave height up to H/h=0.63. Strongly breaking waves have a thicker turbulent surface region, smaller maximum height (H/h=0.56) and a horizontal fluid velocity of 0.72gh at maximum. Measurement of the flow below 72 breaking wave crests illustrate the range and variation of the elevation and kinematics. Experiments are compared to fully nonlinear and second-order theories, where the former is valid for regular nonbreaking waves, and the latter gives conservative predictions for the very strong waves. Secondary streaming in the bottom boundary layer below the waves is measured.

• Grue, John & Tyvand, Peder A. (2014). Foreword to the Enok Palm Memorial Volume. European journal of mechanics. B, Fluids. ISSN 0997-7546. 47, p. 1–3. Full text in Research Archive
• Shiskina, Olga D.; Sveen, Johan Kristian & Grue, John (2013). Transformation of internal solitary waves at the "deep" and "shallow" shelf: satellite observations and laboratory experiment. Nonlinear processes in geophysics. ISSN 1023-5809. 20(5), p. 743–757. doi: 10.5194/npg-20-743-2013. Full text in Research Archive Show summary

  An interaction of internal solitary waves with the shelf edge in the time periods related to the presence of a pronounced seasonal pycnocline in the Red Sea and in the Alboran Sea is analysed via satellite photos and SAR images. Laboratory data on transformation of a solitary wave of depression while passing along the transverse bottom step were obtained in a tank with a two-layer stratified fluid. The certain difference between two characteristic types of hydrophysical phenomena was revealed both in the field observations and in experiments. The hydrological conditions for these two processes were named the “deep” and the “shallow” shelf respectively. The first one provides the generation of the secondary periodic short internal waves – “runaway” edge waves – due to change in the polarity of a part of a soliton approaching the shelf normally. Another one causes a periodic shear flow in the upper quasi-homogeneous water layer with the period of incident solitary wave. The strength of the revealed mechanisms depends on the thickness of the water layer between the pycnocline and the shelf bottom as well as on the amplitude of the incident solitary wave.

• Grue, John (2013). Interfacial Wave Motion of Very Large Amplitude: Formulation in Three Dimensions and Numerical Experiments. Procedia IUTAM. 8, p. 129–143. doi: 10.1016/j.piutam.2013.04.017. Full text in Research Archive
• Grue, John & Jensen, Atle (2012). Orbital velocity and breaking in steep random gravity waves. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 117. doi: 10.1029/2012JC008024. Full text in Research Archive
• Grue, John (2011). Internal wave induced breaking and strong bottom currents. AIP Conference Proceedings. ISSN 0094-243X. 1376. doi: 10.1063/1.3651824. Full text in Research Archive Show summary

  Source: Recent progresses in fluid dynamics research - proceeding of the sixth international conference on fluid mechanics. ISBN: 978-0-7354-0936-1

• Rashid, Farah; Vartdal, Magnus & Grue, John (2011). Oscillating cylinder in viscous fluid: calculation of flow patterns and forces. Journal of Engineering Mathematics. ISSN 0022-0833. 70(1-3), p. 281–295. doi: 10.1007/s10665-010-9395-7. Full text in Research Archive
• Grue, John (2011). Two phenomena: Honji instability, and ringing of offshore structures. Theoretical and Applied Mechanics Letters. ISSN 2095-0349. 1(6). doi: 10.1063/2.1106201. Full text in Research Archive
• Grue, John & Sveen, Johan Kristian (2010). A scaling law of internal run-up duration. Ocean Dynamics. ISSN 1616-7341. 60(4), p. 993–1006. doi: 10.1007/s10236-010-0284-4. Full text in Research Archive
• Grue, John (2010). Editorial. Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics. ISSN 1755-0777. 163, p. 225–226. Full text in Research Archive
• Wåhlin, Anna Kristine; Johansson, A. M.; Aas, Eyvind; Brostrøm, G.; Weber, Jan Erik H. & Grue, John (2010). Horizontal convection in water heated by infrared radiation and cooled by evaporation: scaling analysis and experimental results. Tellus A: Dynamic Meteorology and Oceanography. ISSN 0280-6495. 62A(2), p. 154–169. doi: 10.1111/j.1600-0870.2009.00427.x. Full text in Research Archive
• Grue, John (2010). Computation formulas by FFT of the nonlinear orbital velocity in three-dimensional surface wave fields. Journal of Engineering Mathematics. ISSN 0022-0833. 67(1-2), p. 55–69. doi: 10.1007/s10665-009-9334-7. Full text in Research Archive
• Grue, John (2009). Computation formulas by FFT of the nonlinear orbital velocity in three-dimensional surface wave fields. Journal of Engineering Mathematics. ISSN 0022-0833. doi: 10.1007/s10665-009-93347. Full text in Research Archive
• Fructus, Dorian; Carr, M; Grue, John; Jensen, Atle & Davies, PA (2009). Shear-induced breaking of large internal solitary waves. Journal of Fluid Mechanics. ISSN 0022-1120. 620, p. 1–29. doi: 10.1017/S0022112008004898. Full text in Research Archive
• Grue, John (2008). Nonlinear Surface Waves interacting with a Vertical Cylinder. The first few Steps of a General Method. In Kreuzer, Edwin (Eds.), IUTAM Symposium on Fluid-Structure Interaction in Ocean Engineering. Springer. ISSN 9781402086298. p. 79–92. Full text in Research Archive
• Sanchis, Arnaud Clovis Marcel; Sælevik, Gunnstein & Grue, John (2008). Two-degree-of-freedom vortex-induced vibrations of a spring-mounted rigid cylinder with low mass ratio. Journal of Fluids and Structures. ISSN 0889-9746. 24(6), p. 907–919. doi: 10.1016/j.jfluidstructs.2007.12.008. Full text in Research Archive
• Grue, John (2008). Current trends in engineering mechanics; fluid mechanics for sub-sea developments. Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics. ISSN 1755-0777. 161(1), p. 47–47. Full text in Research Archive
• Grue, John; Pelinovsky, Efim; Fructus, Dorian; Talipova, Tania & Kharif, Christian (2008). Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami. Journal of Geophysical Research (JGR): Oceans. ISSN 2169-9275. 113(C5). doi: 10.1029/2007JC004343. Full text in Research Archive
• Carr, Magda; Fructus, Dorian; Grue, John; Jensen, Atle & Davies, Peter A. (2008). Convectively induced shear instability in large amplitude internal solitary waves. Physics of Fluids. ISSN 1070-6631. 20(126601). Full text in Research Archive
• Fructus, Dorian & Grue, John (2007). An explicit method for the nonlinear interaction between water waves and variable and moving bottom topography. Journal of Computational Physics. ISSN 0021-9991. 222(1), p. 720–739. doi: 10.1016/j.jcp.2006.08.014. Full text in Research Archive
• Clamond, D; Fructus, Dorian & Grue, John (2007). A note on time integrators in water-wave simulations. Journal of Engineering Mathematics. ISSN 0022-0833. 58, p. 149–156. doi: 10.1007/s10665-006-9106-6. Full text in Research Archive
• Jensen, Atle; Clamond, Didier; Huseby, Morten & Grue, John (2007). On local and convective accelerations in steep wave events. Ocean Engineering. ISSN 0029-8018. 34. doi: 10.1016/j.oceaneng.2006.03.013. Full text in Research Archive
• Grue, John & Jensen, Atle (2006). Experimental velocities and accelerations in very steep wave events in deep water. European journal of mechanics. B, Fluids. ISSN 0997-7546. 25, p. 554–564. Full text in Research Archive
• Clamond, Didier; Francius, M; Grue, John & Kharif, C (2006). Long time interaction of envelope solitons and freak wave formations. European journal of mechanics. B, Fluids. ISSN 0997-7546. 25, p. 536–553. Full text in Research Archive
• Grue, John (2006). Very large internal waves in the ocean – observations and nonlinear models. In Grue, John & Trulsen, Karsten (Ed.), Waves in Geophysical Fluids Tsunamis, Rogue Waves, Internal Waves and Internal Tides. Springer Science+Business Media B.V.. ISSN 9783211374603. p. 205–265. Full text in Research Archive
• Grue, John (2006). Rapid computations of steep surface waves in three dimensions, and comparison with experiments. In Grue, John & Trulsen, Karsten (Ed.), Waves in Geophysical Fluids Tsunamis, Rogue Waves, Internal Waves and Internal Tides. Springer Science+Business Media B.V.. ISSN 9783211374603. p. 173–204. Full text in Research Archive
• Clamond, Didier; Fructus, Dorian; Grue, John & Kristiansen, Øyvind (2005). An efficient model for three-dimensional surface wave simulations. Part II: Generation and absorption. Journal of Computational Physics. ISSN 0021-9991. 205, p. 686–705. doi: 10.1016/j.jcp.2004.11.038. Full text in Research Archive
• Fructus, Dorian; Clamond, Didier; Grue, John & Kristiansen, Øyvind (2005). An efficient model for three-dimensional surface wave simulations - Part 1: Free space problems. Journal of Computational Physics. ISSN 0021-9991. 205. Full text in Research Archive
• Fructus, Dorian; Kharif, C; Francius, M; Kristiansen, Øyvind; Clamond, Didier & Grue, John (2005). Dynamics of crescent water wave patterns. Journal of Fluid Mechanics. ISSN 0022-1120. 537. Full text in Research Archive
• Kristiansen, Øyvind; Fructus, Dorian; Clamond, Didier & Grue, John (2005). Simulations of crescent water wave patterns on finite depth. Physics of Fluids. ISSN 1070-6631. 17. Full text in Research Archive
• Grue, John (2005). Generation, propagation and breaking of internal solitary waves. Chaos. ISSN 1054-1500. 15(3). Full text in Research Archive
• Fructus, Dorian & Grue, John (2004). Fully nonlinear solitary waves in a layered stratified fluid. Journal of Fluid Mechanics. ISSN 0022-1120. 505, p. 323–347. Full text in Research Archive
• Guo, Yakun; Sveen, Johan Kristian; Davies, Peter; Grue, John & Dong, Ping (2004). Modelling the motion of an internal solitary wave over a bottom ridge in a stratified fluid. Environmental Fluid Mechanics. ISSN 1567-7419. 4, p. 417–443. Full text in Research Archive
• Jensen, Atle; Huseby, Morten; Clamond, Didier; Pedersen, Geir Kleivstul & Grue, John (2004). PIV measurements of accelerations in water waves, PIV and Water Waves. World Scientific. ISSN 9789812389145. p. 279–281. Full text in Research Archive
• Grue, John; Liu, Philip L.-F. & Pedersen, Geir Kleivstul (2004). PIV and Water Waves, PIV and Water Waves. World Scientific. ISSN 9789812389145. p. v–vi. Full text in Research Archive
• Clamond, Didier; Grue, John; Jensen, Atle & Huseby, Morten (2004). PIV measurements of the velocity field in steep wave events, PIV and Water Waves. World Scientific. ISSN 9789812389145. p. 282–284. Full text in Research Archive
• Grue, John (2004). Internal Wave Fields Analyzed by Imaging Velocimetry, PIV and Water Waves. World Scientific. ISSN 9789812389145. p. 239–279. Full text in Research Archive
• Sveen, Johan Kristian & Grue, John (2004). Measurements of velocities during run-up of long internal waves on a gently sloping beach, PIV and Water Waves. World Scientific. ISSN 9789812389145. p. 334–336. Full text in Research Archive
• Wood, Deborah; Sveen, Johan Kristian & Grue, John (2004). Comparison of modelling of strong internal wave events with PIV studies of the phenomenon, PIV and Water Waves. World Scientific. ISSN 9789812389145. p. 337–339. Full text in Research Archive
• Grue, John; Clamond, Didier; Huseby, Morten & Jensen, Atle (2003). Kinematics of extreme waves in deep water. Applied Ocean Research. ISSN 0141-1187. 25, p. 355–366. Full text in Research Archive

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• Grue, John & Kolstø, Anne-Brit (2014). Medical Technology - Meeting Tomorrow's Health Care Challenges. Novus Forlag. ISBN 9788270997916. 66 p. Full text in Research Archive
• Grue, John & Almås, Karl Andreas (2013). Food from the Ocean - Norway's Opportunities. Novus Forlag. ISBN 9788270997299. 151 p. Full text in Research Archive
• Gabrielsen, Roy H. & Grue, John (2012). Norwegian Energy Policy in Context of the Global Energy Situation. Novus Forlag. ISBN 9788270997053. 129 p. Full text in Research Archive Show summary

  The symposium was held in the House of the Academy (DNVA) in Oslo on 1st February, 2012 and had 150 participants. His Majesty King Harald V attended the complete meeting. Ola Borten Moe, Minister of Petroleum and Energy, gave the intro­ductory talk. He was followed by CEO Helge Lund of Statoil and CEO Christian Rynning-Tønnesen of Statkraft. Experts invited by the learned societies contributed with talks on: the transition from conventional to renewable energy, the power-intensive metallurgical industry, and challenges in energy and climate policy. The volume includes a chapter on energy efficiency that has been added after the symposium.

• Grue, John & Gabrielsen, Roy H. (2011). Marine Transport in the High North. Novus Forlag. ISBN 9788270996414. 124 p. Full text in Research Archive
• Grue, John & Trulsen, Karsten (2006). Waves in Geophysical Fluids Tsunamis, Rogue Waves, Internal Waves and Internal Tides. Springer Science+Business Media B.V.. ISBN 9783211374603. 344 p. Full text in Research Archive
• Grue, John; Liu, Phil L. F. & Pedersen, Geir (2004). PIV and Water Waves. World Scientific. ISBN 9789812389145. 350 p. Full text in Research Archive

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• Ellevold, Thea Josefine & Grue, John (2022). Bottom boundary instability driven by internal solitary waves at a flat bottom. Full text in Research Archive
• Grue, John & Röhrs, Johannes (2022). Groups of short internal waves driven by interacting coastal current and internal tide at ridge-canyon topography. Full text in Research Archive
• Antolloni, Giulia; Jensen, Atle; Grue, John; Riise, Bjørn H. & Brocchini, Maurizio (2020). Erratum: Wave-induced vortex generation around a slender vertical cylinder (Physics of Fluids (2020) 32 (042105) DOI: 10.1063/1.5141131). Physics of Fluids. ISSN 1070-6631. 32(10). doi: 10.1063/5.0027156. Full text in Research Archive
• Grue, John (2014). The limiting effect of breaking in strongly nonlinear waves on intermediate water depth, with emphasis on the kinematics. Full text in Research Archive
• Grue, John (2014). Finite depth waves; what are the maximum height, maximum kinematics, and the effect of strong breaking? Full text in Research Archive
• Grue, John (2014). Maximum finite depth waves: breaking, kinematics and particle drift. Full text in Research Archive
• Grue, John (2014). Nonlinear evaluation of the kinematics of directional field waves. Full text in Research Archive
• Grue, John (2014). Enok Palm - Pioneer in mathematical hydrodynamics. 47, p. 4–8. Full text in Research Archive
• Grue, John (2014). Backward Wave Drift. Full text in Research Archive
• Grue, John & Almås, Karl Andreas (2013). Introduction - Norway, a Maritime Country and a Global Seafood Producer. In Grue, John & Almås, Karl Andreas (Ed.), Food from the Ocean - Norway's Opportunities. Novus Forlag. ISSN 9788270997299. p. 13–22. Full text in Research Archive
• Grue, John & Almås, Karl Andreas (2013). Preface. In Grue, John & Almås, Karl Andreas (Ed.), Food from the Ocean - Norway's Opportunities. Novus Forlag. ISSN 9788270997299. p. 5–9. Full text in Research Archive
• Grue, John (2013). Kinematics in extreme waves on finite water depth. Full text in Research Archive
• Grue, John (2013). Havets indre bølger. Naturen. ISSN 0028-0887. p. 210–227. Full text in Research Archive
• Grue, John & Gabrielsen, Roy H. (2012). Introduction - The Norwegian Energy System and the Global Perspective, Norwegian Energy Policy in Context of the Global Energy Situation. Novus Forlag. ISSN 9788270997053. p. 13–19. Full text in Research Archive Show summary

  The symposium was held in the House of the Academy (DNVA) in Oslo on 1st February, 2012 and had 150 participants. His Majesty King Harald V attended the complete meeting. Ola Borten Moe, Minister of Petroleum and Energy, gave the intro­ductory talk. He was followed by CEO Helge Lund of Statoil and CEO Christian Rynning-Tønnesen of Statkraft. Experts invited by the learned societies contributed with talks on: the transition from conventional to renewable energy, the power-intensive metallurgical industry, and challenges in energy and climate policy. The volume includes a chapter on energy efficiency that has been added after the symposium.

• Grue, John (2011). Internal wave induced breaking ans strong bottom currents. Full text in Research Archive
• Grue, John (2011). NORD! Unterwasserwellen im meer. In Christensen, Olav (Eds.), Arven etter Nansen. Universitetet i Oslo. ISSN 9788282350518. p. 72–89. Full text in Research Archive
• Grue, John (2011). Havets indre bølger. In Christensen, Olav (Eds.), Arven etter Nansen. Universitetet i Oslo. ISSN 9788282350518. p. 72–89. Full text in Research Archive
• Grue, John (2011). Havets indre bølger, i 'Arven etter Nansen', ref. O. Christensen. Full text in Research Archive
• Grue, John (2010). Special issue in honor of Professor Bjorn Gjevik. Ocean Dynamics. ISSN 1616-7341. 60(4), p. 901–905. doi: 10.1007/s10236-010-0318-y. Full text in Research Archive
• Wåhlin, Anna Kristine; Ericsson, A.M.; Aas, Eyvind; Brostrøm, G.; Weber, Jan Erik H. & Grue, John (2008). Horizontal convection in water heated by infrared radiation and cooled by evaporation. Full text in Research Archive
• Trulsen, Karsten; Jensen, Atle & Grue, John (2005). Water wave kinematics of steep irregular waves - systematic perturbation approach, empirical law, PIV measurements and engineering practice. Full text in Research Archive
• Clamond, Didier; Fructus, Dorian & Grue, John (2004). A new absorbing boundary condition for three-dimensional surface wave simulations. Full text in Research Archive
• Grue, John; Gramstad, Odin & Sanchis, Arnaud (2004). PIV experiments on vortex induced vibrating cylinders at high Reynolds numbers. Full text in Research Archive
• Grue, John (2004). Sinus, cosinus, eksponensialfunksjonen i matematikk og bølger. Full text in Research Archive
• Fructus, Dorian; Clamond, Didier & Grue, John (2004). Unsteady simulations of fully nonlinear wave patters in 3D. Full text in Research Archive
• Grue, John (2003). Fast fully nonlinear simulation models of ocean surface waves and internal waves in 3D. Full text in Research Archive
• Clamond, Didier; Grue, John; Huseby, Morten & Jensen, Atle (2003). Theoretical and experimental analysis of the velocity profile under crest of extreme water waves. Full text in Research Archive
• Grue, John (2003). Kjempebølgene matematisk bevist. [Journal]. Teknisk Ukeblad. Full text in Research Archive
• Grue, John (2003). Monsterbølger. [TV]. NRK Dagsrevyen. Full text in Research Archive
• Grue, John (2003). Matematikken bak nettsiden SINUS paa http://viten.no. Full text in Research Archive
• Grue, John (2003). Nettbasert læring i trigonometri og elementær bølgefysikk i vgs. Fra Fysikkens Verden. ISSN 0015-9247. Full text in Research Archive
• Clamond, Didier; Fructus, Dorian & Grue, John (2003). A fast method for fully nonlinear three-dimensional water wave simulations. Full text in Research Archive
• Shiskina, Olga; Sveen, Johan Kristian & Grue, John (2003). Propagation of a solitary wave along the shelf. Russian Academy of Sciences. Full text in Research Archive

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