Academic Interests
- Air-sea interaction
- Buoyancy-driven convection
- Sea ice formation
- Topographic wave generation and propagation
- Turbulent mixing
- Wind- and wave-induced ocean currents
- Dynamics of very viscous fluids
- Elastic film interaction with surface waves
Higher education and employment history
Education
- 1974: Dr. Philos (Ph.D.) Appl. Math.
- 1969: Cand. Real. (M.S.) Appl. Math.
Positions held
- 1979 - present: Professor, Department of Geophysics, University of Oslo
- 1978 - 1979: Associate Professor, Department of Mathematics, University of Oslo
- 1977 - 1978: Senior Scientist, The Norwegian Meteorological Institute
- 1974 - 1975: Senior Visitor, University of Cambridge, UK
- 1973 - 1977: University Research Fellow. University of Oslo
- 1970 - 1973: Assistant Professor, Department of Mathematics 1970 - 1973
- 1986 (6 mnd), 1997 (3 mnd): Visiting Professor, University of Cambridge, UK
Tags:
Oceanography,
Air-sea interaction,
Buoyancy-driven convection,
Sea ice formation,
Topographic wave,
Turbulent mixing
Publications
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Weber, Jan Erik H.
(2026).
Lagrangian mean drift induced by acoustic waves in a horizontal porous layer with one permeable bounding plane.
Environmental Fluid Mechanics.
ISSN 1567-7419.
26(4).
doi:
10.1007/s10652-026-10105-0.
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We consider a horizontal porous layer of constant thickness with Darcy friction and derive the nonlinear Lagrangian equations for the mean drift of fluid due to plane acoustic waves propagating along the layer. One of the bounding planes is assumed to be impermeable to fluid motion, while the other is permeable. The porous lattice is taken to have the same acoustic impedance as the fluid in the pores. Because the Darcy friction is linear in velocity, the flow in the porous medium is irrotational. However, this friction introduces dissipation in the fluid, so that the Lagrangian drift velocity in irrotational acoustic waves can be uniquely determined. The divergent horizontal Lagrangian mean drift due to spatially damped acoustic waves induces a vertical flow through the permeable boundary which may transport accumulated material into the fluid. Of particular interest here is the possible vertical transport of microplastics from reservoirs in the deep-sea benthic sediments into the ocean water caused by seismic primary waves.
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Weber, Jan Erik H.
(2025).
Eulerian contributions to the particle velocity in Stokes and Gerstner waves.
Wave motion.
ISSN 0165-2125.
139.
doi:
10.1016/j.wavemoti.2025.103627.
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For inviscid periodic wave motion, we derive a novel expression in Lagrangian variables for the Stokes drift, which is valid for rotational as well as irrotational waves. The derivation confirms that the Lagrangian mean velocity can be expressed as the sum of the Eulerian mean velocity and the Stokes drift. However, from the Stokes drift part of this expression, we find that the rotational Gerstner wave has a non-zero Stokes drift. Since the Lagrangian mean velocity is zero for this particular wave, we obviously must have a non-zero Eulerian mean velocity in this case, cancelling the Stokes drift. To discuss this problem in detail, we return to the basic kinematics of periodic wave motion in fluids. We avoid time averaging and consider the classic problem of how the Lagrangian particle velocity develops in time, resulting in a Eulerian velocity (expressed in Lagrangian variables) plus the Stokes velocity. We discuss the implication for irrotational deep-water Stokes waves and rotational Gerstner waves. It is demonstrated that the Eulerian velocity, expressed in Lagrangian variables, is different for the two wave types. This explains why the Lagrangian mean velocity in the Stokes wave is equal to the Stokes drift, while it is zero for the Gerstner wave.
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Weber, Jan Erik H.
(2025).
A note on the similarity between acoustic streaming and gravity wave drift in irrotational fluid motion.
Theoretical and Computational Fluid Dynamics.
ISSN 0935-4964.
39.
doi:
10.1007/s00162-025-00743-3.
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For inviscid irrotational fluid motion, the nonlinear Lagrangian equations for periodic plane acoustic waves and long gravity waves are formally similar. It then follows that the Stokes drift is similar and can be calculated for the two problems. However, the lack of dissipative processes means that the Eulerian mean current cannot be determined, and hence the acoustic streaming velocity and the Lagrangian mean surface-wave drift remain unknown. To remedy this without altering the irrotational character of the fluid motion, we add a small frictional force which is linear in the velocity, or a so-called Rayleigh friction. Then, the Lagrangian mean drift (Stokes drift
Eulerian current) is uniquely determined. With this assumption, the acoustic streaming velocity is times the Stokes drift in sound waves, where is the adiabatic constant. For long gravity waves, the Lagrangian mean drift is 3/2 times the Stokes drift in surface waves. These results are valid whatever small the Rayleigh friction coefficient is, as long as it is not zero.
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Weber, Jan Erik H.
(2024).
Surface wave damping by a Robin boundary condition at a permeable seabed.
European journal of mechanics. B, Fluids.
ISSN 0997-7546.
109,
p. 243–252.
doi:
10.1016/j.euromechflu.2024.10.010.
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We investigate the damping of inviscid surface gravity waves when they propagate over a permeable seabed. Traditionally, this problem is solved by considering the wave motion in the upper water layer interacting with the Darcy flow in the porous bottom layer through matching of the solutions at the permeable interface. The novel approach in this study is that we describe the interaction between the upper fluid layer and the permeable bottom layer by the application of a Robin boundary condition. By varying the magnitude of the Robin parameter , we can model the bottom structure of the fluid layer from rigid to completely permeable. In the case when the bottom is a porous medium where Darcy’s law applies, or composed by densely packed vertical Hele-Shaw cells,
is small, and can by determined by comparison with analytical results for a two-layer structure. In this case the wave damping is small. For larger values of , the damping increases, and for very large , the wave is almost critically damped. For the nonlinear transport in spatially damped shallow-water waves, increasing bottom permeability (larger ), reduces the magnitude of the horizontal Stokes drift velocity, while the drift profile tends to become parabolic with height. The vertical Stokes drift in the limit of large permeability is linear with height, with a magnitude that is larger than the horizontal drift. It is suggested that the implementation of a permeable bottom bed in some cases could prevent shorelines from damaging erosion by incoming surface waves.
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Weber, Jan Erik H. & Brostrøm, Gøran
(2024).
Continental shelf wave generation due to surface stress anomalies in the wake of offshore wind farms.
Continental Shelf Research.
ISSN 0278-4343.
279,
p. 1–8.
doi:
10.1016/j.csr.2024.105278.
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For isolated oceanic structures above sea level in synoptic-scale wind fields, shielding causes a wind wake with reduced wind intensity on the lee side of the structure. This generates a wind-stress curl that may act as a source term for continental shelf waves (CSWs) propagating around the structure, if the bottom is sloping. We investigate CSW propagation in the case where the structure (a wind farm or an island) is circular and the depth over the shelf slope increases exponentially with radial distance. For free waves, the wave number, and hence the frequency, is quantized. We demonstrate that for circular banks with narrow continental margins, the resulting eigenfrequencies are close to those obtained for a straight shelf. Modelling the stress in the wind wake as a solitary pulse that moves along a straight shelf, we find, in the absence of friction, a forced solution that increases linearly in time when the pulse moves with the same speed as the free wave speed. For strong winds over longer periods of time, the along-shore wave velocity in the case of resonance may be of the order for topographic parameters characteristic of the Taiwan Bank. Velocities of this magnitude could potentially cause harmful erosion as well as affect the ecosystem on the bank slopes.
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Weber, Jan Erik H. & Isachsen, Pål Erik
(2023).
Energy transfer from sub-inertial Kelvin waves to continental shelf waves at a transverse bottom escarpment.
Continental Shelf Research.
ISSN 0278-4343.
258.
doi:
10.1016/j.csr.2023.104985.
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We consider barotropic coastally-trapped Kelvin waves of tidal origin along a straight coast that propagate from deeper water across a transverse bottom escarpment into a more shallow region. The component, which has a frequency above the inertial frequency, is modified by crossing the escarpment, but continues basically as a Kelvin wave into the shallow region. For tidal components that have frequencies smaller than, like, some of the energy in the Kelvin wave is converted into a continental shelf wave (CSW) that follows the escarpment with shallow water to the right (in the northern hemisphere). The theory is applied to the shelf north-west of Norway where the deep Norwegian Sea is separated from the much shallower Barents Sea by an escarpment reaching from the north-Norwegian coast towards Spitsbergen. By introducing an idealized bottom topography and coastal geometry, analytical calculations and numerical modeling are used to investigate the energy flux in CSWs towards Spitsbergen caused by sub-inertial Kelvin wave motion along the west coast of Norway. Both analytical and numerical calculations indicate that the CSW energy flux towards Spitsbergen is about eighty percent of the incident sub-inertial Kelvin wave energy flux, and that only twenty percent of the energy flux is transmitted into the Barents Sea in the form of sub-inertial Kelvin waves.
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Weber, Jan Erik H.; Whitchelo, Yiyi; Pirolt, Jon Alexander; Christensen, Kai Håkon; Rabault, Jean & Jensen, Atle
(2023).
Observations of transient wave-induced mean drift profiles caused by virtual wave stresses in a two-layer system.
Journal of Fluid Mechanics.
ISSN 0022-1120.
975( A12).
doi:
10.1017/jfm.2023.864.
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An experimental study of long interfacial gravity waves was conducted in a closed wave tank containing two layers of viscous immiscible fluids. The study focuses on the development in time of the mean particle drift that occurs close to the interface where the two fluids meet. From a theoretical analysis by Weber & Christensen ( Eur. J. Mech.- B/ Fluids , vol. 77, 2019, pp. 162–170) it is predicted that the growing drift in this region is associated with the action of the virtual wave stress. This effect has not been explored experimentally before. Interfacial waves of different amplitudes and frequencies were produced by a D-shaped paddle. Particle tracking velocimetry was used to track the time development of the Lagrangian mean drift. The finite geometry of the wave tank causes a mean return flow that is resolved by mass transport considerations. The measurements clearly demonstrate the importance of the virtual wave stress mechanism in generating wave drift currents near the interface.
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Christensen, Kai Håkon & Weber, Jan Erik H.
(2023).
Application of a Robin boundary condition to surface waves.
Frontiers in Marine Science.
10.
doi:
10.3389/fmars.2023.1129643.
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Surface effects on deep-water gravity waves are investigated theoretically by the application of a Robin boundary condition with a complex Robin parameter, R=Rr+iRi. The Robin condition combines the shear stress and the horizontal velocity at the ocean surface. We show that this condition describes wave damping related to surface phenomena like elastic films or thin viscous fluid layers. It may also model wave generation by oscillating surface stresses depending on the signs and magnitudes of Rr and Ri.
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Weber, Jan Erik H. & Børve, Eli
(2022).
On group velocity and spatial damping of diurnal continental shelf waves.
Continental Shelf Research.
ISSN 0278-4343.
232.
doi:
10.1016/j.csr.2021.104630.
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Diurnal continental shelf waves (CSWs) are studied theoretically for an idealized shelf topography. Wave attenuation is caused by the exchange of fluid on the sloping shelf with an inner region through a permeable coastline. As an example, we consider the region outside Lofoten-Vesterålen in north Norway. Here CSWs with diurnal tidal frequencies are possible in a small wave number range centered around zero group velocity. A previous investigation with a Robin condition (a weighted combination of Dirichlet and Neumann conditions) at the permeable boundary has shown that the spatial damping coefficient becomes infinitely large when the group velocity of the CSWs approaches zero. Here we demonstrate that this is not a result of the mathematical formulation, but reflects a physical reality. We show this by modelling the highly convoluted inner archipelagic region as a series of densely packed vertical Hele Shaw cells. By comparing the two ways of describing a permeable coastal boundary (Robin/Hele Shaw), we may express the Robin parameter in terms of the physical parameters (permeability, eddy viscosity) that characterize the flow on the inner porous shelf. The radiation stresses that drive the Lagrangian mean currents are the same in the two cases. This means that the spatial mean current distribution over the sloping shelf becomes unaltered when we compare the Robin case and the porous inner shelf case.
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Weber, Jan Erik H.
(2022).
On the coupling between surface waves and the motion in a flexible porous surface layer.
Ocean Modelling.
ISSN 1463-5003.
174.
doi:
10.1016/j.ocemod.2022.102013.
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The coupling between surface waves and the motion in a flexible porous surface layer is investigated theoretically. We apply a Lagrangian formulation for the viscous fluid and the fluid-saturated porous medium. In the floating porous layer, which we assume to be much thinner than the wavelength, we apply a macroscopic version of Darcy’s law. The interface between the porous layer and the underlying fluid is permeable, and the wave-induced vertical motion at the interface leads to wave damping. In addition, the viscous shear stress at the interface also dampens the waves. We here investigate the relative strength of the two mechanisms. Furthermore, we calculate the Lagrangian mean drift in the porous surface layer. The present study may provide a physical model for wave damping in the presence of unconsolidated rubble ice and the slow particle drift in rubble-ice layers.
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Weber, Jan Erik H.
(2022).
A note on the temporal and spatial attenuation of ocean waves.
Ocean Modelling.
ISSN 1463-5003.
175.
doi:
10.1016/j.ocemod.2022.102027.
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We study attenuation of free waves in the homogeneous ocean. Using the Cauchy–Riemann relations and then energy equation, we derive a novel equation that relates temporal and spatial decay to the energy dissipation in the fluid. In particular, for spatially damped waves we find that the attenuation coefficient is inversely proportional to the group velocity. We discuss the consequences of this for continental shelf waves where the group velocity may tend to zero in wave number space, and hence the spatial attenuation coefficient may become infinitely large. We show that generally for a travelling wave solution, the spatial damping will remain unchanged in a frame of reference moving with the group velocity, revealing the different physics behind temporal wave damping and spatial wave damping.
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Weber, Jan Erik H. & Børve, Eli
(2021).
Diurnal continental shelf waves with a permeable coastal boundary: Application to the shelf northwest of Norway.
European journal of mechanics. B, Fluids.
ISSN 0997-7546.
89,
p. 64–71.
doi:
10.1016/j.euromechflu.2021.05.003.
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Spatially damped continental shelf waves (CSWs) with diurnal tidal frequency outside Lofoten–Vesterålen in north-west Norway are studied theoretically for an idealized shelf topography. Wave damping is caused by the exchange of fluid on the shelf with an inner archipelago through a permeable coastline. This exchange is modelled by the application of a Robin condition at the coastal boundary. It is shown that CSWs with diurnal frequencies are possible in a small wave number range centred around zero group velocity. By calculating the nonlinear radiation stress components in the spatially damped CSWs, we find the time- and depth averaged Lagrangian mean drift current to second order along the coast. We show that the Lagrangian mean drift current is independent of the value of the damping coefficient, however small, as long as it is nonzero. This illustrates the singular behaviour of the Lagrangian wave drift problem for CSWs.
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Weber, Jan Erik H.
(2021).
On the Stokes drift in traveling surface pulses.
Ocean Modelling.
ISSN 1463-5003.
166.
doi:
10.1016/j.ocemod.2021.101847.
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Similar to the Stokes drift in periodic gravity waves, we introduce a second-order Stokes effect on the particle drift in isolated linear surface disturbances (pulses) in shallow water. For a linear disturbance with the shape and length scale of a KdV solitary wave, the model results agree surprisingly well with the observed drift in moderately steep solitary waves in the laboratory, as well as with more comprehensive theory for surface drift in solitary waves.
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Weber, Jan Erik H.
(2021).
Lagrangian drift in a permeable bottom layer
induced by internal gravity waves.
Tellus A: Dynamic Meteorology and Oceanography.
ISSN 0280-6495.
73(1),
p. 1–9.
doi:
10.1080/16000870.2021.1877461.
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The mean drift in a permeable homogeneous bottom layer caused by internal gravity waves in an overlying stratified fluid, is investigated theoretically. We apply a Lagrangian formulation, together with the long-wave approximation, for the motion in the fluid and the fluid-saturated permeable layer. In the stratified fluid, we assume a constant Brunt-Väisälä frequency and inviscid flow. In the permeable bed, the density is constant. Here we apply a simple macroscopic version of Darcy’s law. For internal waves with frequency ω, a fundamental small parameter in the permeable bed is R=ωK/ν2. Here K is the effective permeability, and ν2 is the overall eddy viscosity, representing the small-scale turbulence of the interstitial fluid. The Lagrangian mean flow in each layer is weakly damped, with a damping rate proportional to R, and composed of contributions from an infinite, but discrete set of eigen-modes. For each mode the mean drift in the permeable bed is an order R2 smaller than the Stokes drift in internal waves at the bottom of the fluid layer. For spatially damped waves, it is particularly interesting that the wave-induced Eulerian mean current in the permeable bed may exceed the Stokes drift if the bed thickness is smaller than the upper layer thickness. It is suggested that the explored wave-induced particle drift in the permeable bottom layer could provide a physical model for the slow net transport of bio aerosols and smoke particles in the tropical rainforest.
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Weber, Jan Erik H. & Christensen, Kai Håkon
(2021).
On the analogy between rigid plate motion and mean momentum transfer in surface gravity waves.
AIP Advances.
11(4).
doi:
10.1063/5.0043751.
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The transfer of mean momentum from surface gravity waves to Eulerian mean fluxes is investigated by modeling the total wave momentum (the Stokes flux) as a thin surface layer moving with the phase speed c of the waves and with a thickness Z derived from the divergence effect. The bulk of the fluid receiving momentum from the waves is modeled by a rigid lower layer acted upon by the virtual wave stress, where the latter is related to the form stress from the wind and the time rate of change in Z through −cdZ/dt. In addition, the effects of surface wind and bottom stress are included in the model. Through the combination with measurements, this robust model may yield information about the Eulerian fluxes when the ocean surface is covered by a combination of ice and oil, and the constitutive equations for the surface cover are not easily obtained.
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Weber, Jan Erik H. & Ghaffari, Peygham
(2021).
Wave-induced Lagrangian drift in a porous seabed.
Environmental Fluid Mechanics.
ISSN 1567-7419.
doi:
10.1007/s10652-021-09823-4.
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Abstract The mean drift in a porous seabed caused by long surface waves in the overlying fluid is investigated theoretically. We use a Lagrangian formulation for the fluid and the porous bed. For the wave field we assume inviscid flow, and in the seabed, we apply Darcy’s law. Throughout the analysis, we assume that the long-wave approximation is valid. Since the pressure gradient is nonlinear in the Lagrangian formulation, the balance of forces in the porous bed now contains nonlinear terms that yield the mean horizontal Stokes drift. In addition, if the waves are spatially damped due to interaction with the underlying bed, there must be a nonlinear balance in the fluid layer between the mean surface gradient and the gradient of the radiation stress. This causes, through continuity of pressure, an additional force in the porous layer. The corresponding drift is larger than the Stokes drift if the depth of the porous bed is more than twice that of the fluid layer. The interaction between the fluid layer and the seabed can also cause the waves to become temporally attenuated. Again, through nonlinearity, this leads to a horizontal Stokes drift in the porous layer, but now damped in time. In the long-wave approximation only the horizontal component of the permeability in the porous medium appears, so our analysis is valid for a medium that has different permeabilities in the horizontal and vertical directions. It is suggested that the drift results may have an application to the transport of microplastics in the porous oceanic seabed.
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Weber, Jan Erik H. & Christensen, Kai Håkon
(2021).
On the singular behavior of the Stokes drift in layered miscible fluids.
Wave motion.
ISSN 0165-2125.
102,
p. 1–8.
doi:
10.1016/j.wavemoti.2021.102712.
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Gravity waves of the Stokes-type in a system of two horizontal layers of inviscid, stratified and miscible fluids are studied by applying a Lagrangian description of fluid motion. It is shown that for the total vertically-integrated Stokes drift (the Stokes flux) to become zero, the density must be continuous at the interface. This is not the case in a system of two immiscible homogeneous layers of different densities. For miscible fluids, however, one can extend the density of the lower layer continuously to that of the upper layer through an infinitely thin interface. This introduces a negative Stokes drift with a delta-function behavior. The corresponding finite negative Stokes flux obtained by integrating the Stokes drift across this infinitely thin layer adds to the original positive Stokes fluxes in the upper and lower layer, yielding the required vanishing total Stokes flux between the bounding planes of the model. The delta-function behavior of the Stokes drift at the interface also induces additional Lagrangian mean displacements in the vertical so that the position of the Lagrangian mean interfacial level is the same as in the absence of waves.
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Weber, Jan Erik H. & Broström, Göran
(2021).
Convection in conditionally unstable seawater.
AIP Advances.
11(7).
doi:
10.1063/5.0053629.
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Buoyancy-driven convection in a conditionally unstable ocean is studied theoretically. Conditionally unstable conditions are related to supercooled seawater. The freezing point is depressed due to increasing pressure, and upward motion (reduced pressure) leads to the formation of ice crystals in the form of frazil ice and hence a reduced bulk density of the rising mass parcel. For downward motion (increasing pressure), freezing does not occur. To model this one-way process, we take that rising parcels become lighter as they follow the adiabatic density lapse rate due to freezing. Through the action of a unit step function, we can model the fact that frazil ice is added only in the upward motion. Supercooled seawater is observed in the proximity of ice shelf fronts. We consider an idealized ice shelf and take the front to be vertical. For this geometry, we present linear analytical solutions as well as numerical results for nonlinear two-dimensional steady conditional convection in the presence of a stable environmental density gradient. With a parallel to moist convection in the atmosphere, we find convection cells near the ice front with rising fluid in a narrow region and sinking fluid over a much broader region.
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Ghaffari, Peygham; Weber, Jan Erik H.; Nøst, Ole Anders & Drivdal, Magnus
(2020).
Stokes drift in topographic waves over an enclosed basin shelf.
Journal of Physical Oceanography.
ISSN 0022-3670.
50(5),
p. 1197–1211.
doi:
10.1175/JPO-D-19-0126.1.
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The effect of the continental shelf wave on the flow field over the southern shelf of the Caspian Sea (CS) as the largest enclosed basin of the world, is investigated. Considerable currents with subinertial time scales are observed over the continental shelf in the southern CS. For variations in the surface layer with typical periods of 1 day, local episodic wind events appear to be the driving force. For longer time scales, it is suggested that the observed currents are due to passing continental shelf waves. Measurements over the continental shelf and shelf slope, showing periods of 2–6 days, indicate the presence of such waves. Combined with theory and numerical modeling, the amplitude of the continental shelf wave modes at the coast is assessed from current meter observations. It is demonstrated that the mean drift velocity (the Stokes drift) for long continental shelf waves is determined entirely by the shelf geometry. For the actual shelf mode, it is shown that the associated Stokes drift constitute a nonnegligible mean current along the shelf. This current should be taken into account when assessing the transport of biological material and neutral tracers along the southern coast of the CS.
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Weber, Jan Erik H.
(2019).
A Lagrangian study of internal Gerstner- and Stokes-type gravity waves.
Wave motion.
ISSN 0165-2125.
88,
p. 257–264.
doi:
10.1016/j.wavemoti.2019.06.002.
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By using a direct Lagrangian formulation, two different solutions for the nonlinear motion in inviscid internal gravity waves between horizontal planes in a non-rotating fluid are discussed. The first solution assumes a constant Brunt–Väisälä frequency N. The main findings are that the vertical mean displacement of the isopycnals and the horizontal mean drift are both zero to second order (Sanderson, 1985). We here point out that this is characteristic for a Gerstner-type wave. Attention is drawn to a second solution for arbitrary stable stratification which yields a non-zero vertical mean isopycnal displacement. Although internal waves are rotational, this solution characterizes a Stokes-type wave. The vertical mean displacement, which can be positive or negative depending on the spatial location and the wave mode in question, is due to the divergence effect in Lagrangian terms. It is shown that the vertical mean displacement at a certain level is proportional to the depth-dependent, or partial Stokes flux. Finally, it is demonstrated that the two wave types have different mean vorticities to second order. For constant , they are equal in magnitude, but have opposite signs. In the Appendix the existence of a mean drift in internal waves of the Stokes-type is verified by a direct Lagrangian calculation for a slightly viscous fluid with constant N.
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Weber, Jan Erik H. & Christensen, Kai Håkon
(2019).
Virtual wave stress and transient mean drift in spatially damped long interfacial waves.
European journal of mechanics. B, Fluids.
ISSN 0997-7546.
77,
p. 162–170.
doi:
10.1016/j.euromechflu.2019.04.004.
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The mean drift in spatially damped long gravity waves at the boundary between two layers of immiscible viscous fluids is investigated theoretically by applying a Lagrangian description of motion. The focus of the paper is on the development of the drift near the interface. The initial drift (inviscid Stokes drift + viscous boundary-layer terms) associated with the instantaneously imposed wave field does not generally fulfill the conditions at the common boundary between the layers. Hence, transient Eulerian mean currents develop on both sides of the interface to ensure continuity of velocities and viscous stresses. The development of strong jet-like Eulerian currents increasing with time in this problem is related to the action of the virtual wave stress (VWS). Very soon (after a few wave periods) the transient Eulerian part dominates in the Lagrangian mean current. This effect is similar to that found for the drift in short gravity waves with a film-covered surface. A new relation is derived showing that the difference between the VWS’s at the interface is given by the divergence of the total horizontal wave momentum flux in a two-layer system. Our analysis with spatially damped waves also yields the Lagrangian change of the mean surface level and mean interfacial level (the divergence effect) due to periodic baroclinic wave motion.
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Weber, Jan Erik H.
(2018).
An interfacial Gerstner-type trapped wave.
Wave motion.
ISSN 0165-2125.
77,
p. 186–194.
doi:
10.1016/j.wavemoti.2017.12.002.
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Coastally trapped rotational interfacial waves are studied theoretically by using a Lagrangian formulation of fluid motion in a rotating ocean. The waves propagate along the interface between two immiscible inviscid incompressible fluid layers of finite depths and different densities, and are trapped at a straight wall due to the Coriolis force. For layers of finite depth, solutions are sought as series expansions after a small parameter. Comparison is made with the irrotational interfacial Kelvin wave. Both types of waves are identical to first order, having zero vorticity. The second order solution yields a relation between the vorticity and the velocity shear in the wave motion. Requiring that the mean motion in both layers is irrotational, then follows the well-known Stokes drift for interfacial Kelvin waves. On the other hand, if the mean forward drift is identically zero, we obtain the second order vorticity in the Gerstner-type wave. The solutions in both layers for the Gerstner-type interfacial wave are given analytically to second order. It is shown that small density differences and thin upper layers both act to yield a shape of the material interfacial with broader crests and sharper troughs. These effects also tend to make the particle trajectories at the interface in both layers become distorted ellipses which are flatter on the upper side. It is concluded that the effect of air excludes the possibility of observing the exact Gerstner wave in deep water.
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Ghaffari, Peygham; Isachsen, Pål Erik; Nøst, Ole Anders & Weber, Jan Erik H.
(2018).
The influence of topography on the stability of the Norwegian Atlantic Current off Northern Norway.
Journal of Physical Oceanography.
ISSN 0022-3670.
48(11),
p. 2761–2777.
doi:
10.1175/JPO-D-17-0235.1.
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The steep continental slope off the Lofoten–Vesterålen islands of northern Norway appears to be the source of the most intense mesoscale eddy field in all of the Nordic Seas. Here we use linearized two-layer shallow-water equations to study the stability of the Norwegian Atlantic Current in this region. The study extends previous works that used linearized quasigeostrophic vertical mode equations to examine the effects of bottom topography on baroclinic instability here. We find evidence of baroclinic instability in the stacked shallow-water model but also of barotropic instability that is associated with the upper-layer lateral shear. The calculations give an indication that growth rates of barotropic instability may be comparable to or larger than those of baroclinic instability over the steepest parts of the continental slope.
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Weber, Jan Erik H.
(2017).
Vertically varying Eulerian mean currents induced by internal coastal Kelvin waves.
Journal of Geophysical Research (JGR): Oceans.
ISSN 2169-9275.
122(2),
p. 1222–1231.
doi:
10.1002/2016JC012377.
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The lost momentum in spatially damped internal Kelvin waves reappears as Eulerian mean currents through the action of the nonlinear wave-wave interaction terms. A novel expression is derived for the steady balance between the frictional force on the coastally trapped horizontal Eulerian mean flow, and the forcing from the wave field in terms of the mean wave Reynolds stresses and the horizontal divergence of the Stokes drift. The forcing can be expressed in terms of orthogonal eigenfunctions for internal waves, yielding the vertical variation of the Eulerian mean flow. For arbitrary values of the Brunt-Väisälä frequency , it is shown that the wave forcing on the Eulerian mean is always negative, yielding a Poiseuille type flow. Therefore, unlike the Stokes drift velocity in internal Kelvin waves which exhibits a backward drift for the first mode in the region of maximum , the wave-induced horizontal Eulerian mean current is always in the direction of the waves. The results are illustrated by an example from Van Mijenfjorden in Svalbard, which is an arctic sill fjord where internal waves are generated by the action of the barotropic semi-diurnal tide.
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Weber, Jan Erik H.
(2017).
Equatorial Stokes drift and Rossby rip currents.
Journal of Geophysical Research (JGR): Oceans.
ISSN 2169-9275.
122(6),
p. 4819–4828.
doi:
10.1002/2016JC012653.
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The Stokes drift in long baroclinic equatorial Rossby waves is investigated theoretically by using eigenfunction expansions in the vertical. These waves are non-dispersive and propagate westward along the equator. Particular attention is paid to the first baroclinic, first meridional Rossby wave mode which has been observed in the equatorial Pacific. It is demonstrated that the Stokes drift depends very much on the depth-variation of the Brunt-Väisälä frequency. Even more importantly, it is found that, for arbitrary stable stratification, the total zonal Stokes volume transport induced by the Rossby wave mode (1,1) is identically zero. The eastward drift due reflected wave energy in the form of internal equatorial Kelvin waves is also addressed. Due to the very long period of the incident Rossby wave mode (1,1), the reflected equatorial Kelvin wave must at least be a 2. mode component in the vertical. The corresponding Stokes drift only induces a minor change near the surface of the total westward drift velocity at the equator. The implication for the existence of compensating Rossby rip currents along the equator is discussed.
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Drivdal, Magnus Bjørn; Weber, Jan Erik H. & Debernard, Jens B.
(2016).
Dispersion relation for continental shelf waves when the shallow shelf part has an arbitrary width: Application to the shelf west of Norway.
Journal of Physical Oceanography.
ISSN 0022-3670.
46(2),
p. 537–549.
doi:
10.1175/JPO-D-15-0023.1.
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Weber, Jan Erik H.; Drivdal, Magnus Bjørn; Christensen, Kai Håkon & Brostrøm, Gøran
(2015).
Some aspects of the Coriolis-Stokes forcing in the oceanic momentum and energy budgets.
Journal of Geophysical Research (JGR): Oceans.
ISSN 2169-9275.
120(8),
p. 5589–5596.
doi:
10.1002/2015JC010717.
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Ghaffari, Peygham & Weber, Jan Erik H.
(2014).
Mass transport in the Stokes edge wave for constant arbitrary bottom slope in a rotating ocean.
Journal of Physical Oceanography.
ISSN 0022-3670.
44(4),
p. 1161–1174.
doi:
10.1175/JPO-D-13-0171.1.
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Weber, Jan Erik H.; Christensen, Kai Håkon & Broström, Göran
(2014).
Stokes drift in internal equatorial Kelvin waves; continuous stratification versus two-layer models.
Journal of Physical Oceanography.
ISSN 0022-3670.
44(2),
p. 591–599.
doi:
10.1175/JPO-D-13-0135.1.
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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.
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Støylen, Eivind & Weber, Jan Erik H.
(2010).
Mass transport induced by internal Kelvin waves beneath shore-fast ice.
Journal of Geophysical Research (JGR): Oceans.
ISSN 2169-9275.
115(C03022).
doi:
10.1029/2009JC005298.
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A one-layer reduced-gravity model is used to investigate the wave-induced mass flux in internal Kelvin waves along a straight coast beneath shore-fast ice. The waves are generated by barotropic tidal pumping at narrow sounds, and the ice lid introduces a no-slip condition for the horizontal wave motion. The mean Lagrangian fluxes to second order in wave steepness are obtained by integrating the equations of momentum and mass between the material interface and the surface. The mean flow is forced by the conventional radiation stress for internal wave motion, the mean pressure gradient due to the sloping surface, and the frictional drag at the boundaries. The equations that govern the mean fluxes are expressed in terms of mean Eulerian variables, while the wave forcing terms are given by the horizontal divergence of the Stokes flux. Analytical results show that the effect of friction induces a mean Eulerian flux along the coast that is comparable to the Stokes flux. In addition, the horizontal divergence of the total mean flux along the coast induces a small mass flux in the cross-shore direction. This flux changes the mean thickness of the upper layer outside the trapping region and may facilitate geostrophically balanced boundary currents in enclosed basins. This is indeed demonstrated by numerical solutions of the flux equations for confined areas larger than the trapping region. Application of the theory to Arctic waters is discussed, with emphasis on the transport of biological material and pollutants in nearshore regions.
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Brostrøm, Gøran; Christensen, Kai Håkon & Weber, Jan Erik H.
(2008).
A quasi-Eulerian, quasi-Lagrangian view of surface-wave- induced flow in the ocean.
Journal of Physical Oceanography.
ISSN 0022-3670.
38,
p. 1122–1130.
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Weber, Jan Erik H.; Brostrom, G & Christensen, Kai Håkon
(2008).
Radiation stress and depth-dependent drift in surface waves with dissipation.
International Journal of Offshore and Polar Engineering.
ISSN 1053-5381.
18(1),
p. 8–13.
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Weber, Jan Erik; Brostrøm, Gøran & Saetra, Øyvind
(2006).
Eulerian versus Lagrangian approaches to the wave-induced transport in the upper ocean.
Journal of Physical Oceanography.
ISSN 0022-3670.
36(11),
p. 2106–2118.
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Weber, Jan Erik & Løyning, Terje B.
(2006).
Thermobaric effect on slantwise convection in cold seawater.
Tellus A: Dynamic Meteorology and Oceanography.
ISSN 0280-6495.
58(3),
p. 385–391.
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Christensen, Kai Håkon & Weber, Jan Erik
(2005).
Wave-induced drift of large floating sheets.
Geophysical and Astrophysical Fluid Dynamics.
ISSN 0309-1929.
99(6),
p. 433–443.
doi:
10.1080/03091920500357119.
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In this article we study the wave-induced drift of large, flexible shallow floating objects, referred
to as sheets. When surface waves propagate through a sheet, they provide a mean stress on the
sheet, resulting in a mean drift. In response, the sheet generates an Ekman current. The drift
velocity of the sheet is determined by (i) the wave-induced stress, (ii) the viscous stress due to
the Ekman current, and (iii) the Coriolis force. The sheet velocity and the current beneath
the sheet are determined for constant and depth-varying eddy viscosities.
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Weber, Jan Erik
(2005).
Mean drift velocity in viscous flow over a corrugated bottom.
Physics of Fluids.
ISSN 1070-6631.
17,
p. 113102-1–113102-8.
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Weber, Jan Erik H.
(2018).
Lagrangian approach to wave-induced flow in a viscous rotating ocean.
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The presence of viscosity has a profound effect on the wave-induced drift. In a pioneering paper (Longuet-Higgins, 1953) it was demonstrated that the inclusion of a small viscosity not only modified the motion in thin boundary layers near the surface and at the bottom, but also produced significant changes from Stokes (1847) irrotational solution in the interior. We here present results for wave-induced drift in a fluid layer of finite depth by applying a direct Lagrangian description of fluid motion. The Lagrangian form is (usually) more mathematically demanding than the traditional Eulerian approach. However, it yields directly the mean particle drift velocity in periodic motion. The solution to the wave-drift problem in a Lagrangian description depends crucially on the viscosity ν being non-zero, however small. It exemplifies the singular nature of this problem, in which the limit of solutions as ν→0 is different from solutions obtained with ν=0.
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Weber, Jan Erik H.
(2018).
Virtual wave stress and transient particle drift in spatially damped long interfacial waves.
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Weber, Jan Erik H. & Ghaffari, Peygham
(2016).
Mean currents induced by spatially damped internal Kelvin waves: Application to Van Mijenfjorden in Svalbard.
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Weber, Jan Erik H. & Christensen, Kai Håkon
(2016).
Mean particle drift in long gravity waves at the interface between immiscible viscous fluids.
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Weber, Jan Erik H.; Christensen, Kai Håkon & Broström, Göran
(2013).
Stokes drift in internal equatorial Kelvin waves.
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Weber, Jan Erik H.
(2011).
Minnetale over professor dr. philos. Hans Ragnar Kristian Økland.
Årbok / Det norske videnskaps-akademi.
ISSN 0332-6209.
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Støylen, Eivind & Weber, Jan Erik H.
(2009).
Mass transport induced by internal Kelvin waves beneath shorefast ice.
Geophysical Research Abstracts.
ISSN 1029-7006.
11.
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Weber, Jan Erik H. & Brostrøm, Gøran
(2009).
Density-driven convection between horizontal planes in a conditionally unstable fluid.
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Weber, Jan Erik H. & Støylen, Eivind
(2009).
Mass transport induced by internal Kelvin waves beneath shore fast ice.
Full text in Research Archive
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Weber, Jan Erik H.
(2008).
Mixing due to surface-wave breaking.
Geophysical Research Abstracts.
ISSN 1029-7006.
10.
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Støylen, Eivind & Weber, Jan Erik H.
(2008).
Mean mass transport induced by internal Kelvin waves, with application to the circulation in the Van Mijen fjord in Svalbard.
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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
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Brostrøm, Gøran; Christensen, Kai Håkon & Weber, Jan Erik H.
(2008).
How to include surfaces waves in an ocean model.
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Christensen, Kai Håkon; Brostrøm, Gøran & Weber, Jan Erik H.
(2007).
A new model for the drift in progressive surface gravity waves.
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Christensen, Kai Håkon; Brostrøm, Gøran & Weber, Jan Erik
(2006).
A new model for the mean drift in surface gravity waves.
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Weber, Jan Erik; Christensen, Kai Håkon & Brostrøm, Gøran
(2006).
Radiation stress and the drift in gravity waves with Rayleigh friction.
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Weber, Jan Erik
(2006).
How shallow-water waves induce an anti-cyclonic mean drift around banks and islands in an inviscid rotating ocean.
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Weber, Jan Erik; Brostrøm, Gøran & Saetra, Øyvind
(2006).
A wave-driven surge model for the deep ocean.
Geophysical Research Abstracts.
ISSN 1029-7006.
8.
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Weber, Jan Erik; Brostrøm, Gøran & Christensen, Kai Håkon
(2006).
Radiation stress and the drift in gravity waves with weak friction.
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Wåhlin, Anna Kristine; Ericsson, A. M.; Aas, Eyvind & Weber, Jan Erik
(2005).
Horizontal convection in water heated by infra-red radiation and cooled by evaporation.
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Published
Dec. 10, 2013 7:55 PM
- Last modified
May 5, 2023 4:26 PM
