arXiv subjects

Simen Å. Ellingsen

Publications and source records attributed to Simen Å. Ellingsen.

At least 37 records · Page 2Linked to original sources

arXiv2017

Transient wave resistance upon a real shear current

We study the waves and wave-making forces acting on ships travelling on currents which vary as a function of depth. Our concern is realism; we consider a real current profile from the Columbia River, and model ships with dimensions and Froude numbers typical of three classes of vessels operating in these waters. To this end we employ the most general theory of waves from free-surface sources on shear current to date, which we derive and present here. Expressions are derived for ship waves which satisfy an arbitrary dispersion relation and are generated by a wave source acting on the free surface, with the source's shape and time-dependence is also being arbitrary. Practical calculation procedures for numerically calculating dispersion on a shear current which may vary arbitrarily with depth both in direction and magnitude, are indicated. For ships travelling at oblique angle to a shear-current, the ship wave pattern is asymmetrical, and wave-making radiation forces have a lateral component in addition to the conventional wave resistance, the sternward component. No corresponding lateral force exists in the absence of shear. We consider the dependence of wave resistance and lateral force for upstream, downstream and cross-stream motion on the Columbia River current, both in steady motion and during two different maneouvres: a ship suddenly set in motion, and a ship turning through 360 deg. We find that for smaller ships (tugboats, fishing-boats) the wave resistance can differ drastically from that in quiescent water, and depends strongly on Froude number and direction of motion. For Froude numbers typical of such boats, wave resistance can vary by a factor 3 between upstream and downstream motion, and the strong Froude number dependence is made more complicated by interference effects. The lateral radiation force ... [abstract truncated due to ArXiV's space restrictions]

physics.flu-dyn↗

arXiv2017

Surface waves on arbitrary vertically-sheared currents

We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for practical calculation. The method has been much used in the past for the case of waves propagating along the same axis as the background current, and we herein extend and apply it to problems with an arbitrary angle between the wave propagation and current directions. Being valid for all wavelengths without loss of accuracy, the scheme is particularly well suited to solve problems involving a broad range of wave vectors, such as ship waves and Cauchy-Poisson initial value problems for example. We examine the group and phase velocities over different wavelength regimes and current profiles, highlighting characteristics due to the depth-variable vorticity. We show an example application to ship waves on an arbitrary current profile, and demonstrate qualitative differences in the wake patterns between concave down and concave up profiles when compared to a constant shear profile with equal depth-averaged vorticity. We also discuss the nature of additional solutions to the dispersion relation when using the piecewise-linear model. These are vorticity waves, drifting vortical structures which are artifacts of the piecewise model. They are absent for a smooth profile and are spurious in the present context.

physics.flu-dyn↗

arXiv2016

Oscillating sources in a shear flow with a free surface

We report on progress on the free surface flow in the presence of submerged oscillating line sources (2D) or point sources (3D) when a simple shear flow is present varying linearly with depth. Such sources are in routine use as Green functions in the realm of potential theory for calculating wave-body interactions, but no such theory exists in for rotational flow. We solve the linearized problem in 2D and 3D from first principles, based on the Euler equations, when the sources are at rest relative to the undisturbed surface. Both in 2D and 3D a new type of solution appears compared to irrotational case, a critical layer-like flow whose surface manifestation ("wave") drifts downstream from the source at the velocity of the flow at the source depth. We analyse the additional vorticity in light of the vorticity equation and provide a simple physical argument why a critical layer is a necessary consequence of Kelvin's circulation theorem. In 3D a related critical layer phenomenon occurs at every depth, whereby a street of counter-rotating vortices in the horizontal plane drift downstream at the local flow velocity.

physics.flu-dyn↗

arXiv2016

Multiple resonances of a moving, oscillating surface disturbance on a shear current

We consider waves radiated by a disturbance of oscillating strength moving at constant velocity along the free surface of a shear flow which, when undisturbed, has uniform horizontal vorticity of magnitude $S$. When no current is present the problem is a classical one and much studied, and in deep water a resonance is known to occur when $τ=|\boldsymbol{V}|ω_0/g$ equals the critical value $1/4$ ($\boldsymbol{V}$: velocity of disturbance, $ω_0$: oscillation frequency, $g$: gravitational acceleration). We show that the presence of the sub-surface shear current can change this picture radically. Not only does the resonant value of $τ$ depend strongly on the angle between $\boldsymbol{V}$ and the current's direction and the "shear-Froude number" $\mathrm{Frs}=|\boldsymbol{V}|S/g$; when $\mathrm{Frs}>1/3$, multiple resonant values --- as many as $4$ --- can occur for some directions of motion. At sufficiently large values of $\mathrm{Frs}$, the smallest resonance frequency tends to zero, representing the phenomenon of critical velocity for ship waves. We provide a detailed analysis of the dispersion relation for the moving, oscillating disturbance, in both finite and infinite water depth, including for the latter case an overview of the different far-field waves which exist in different sectors of wave vector space under different conditions. Owing to the large number of parameters, a detailed discussion of the structure of resonances is provided for infinite depth only, where analytical results are available.

physics.flu-dyn↗

arXiv2016

Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current [Ellingsen, J.~Fluid Mech.\ {\bf 742} R2 (2014)]. We derive the exact criterion for criticality as a function of an intrinsic shear Froude number $S\sqrt{b/g}$ ($S$ is uniform vorticity, $b$ size of source), the water depth, and the angle between the shear current and the ship's motion. Formulae for both the normal and lateral wave resistance force are derived, and we analyse its dependence on the source velocity (or Froude number $Fr$) for different amounts of shear and different directions of motion. The effect of the shear current is to increase wave resistance for upstream ship motion and decrease it for downstream motion. Also the value of $Fr$ at which $R$ is maximal is lowered for upstream and increased for downstream directions of ship motion. For oblique angles between ship motion and current there is a lateral wave resistance component which can amount to $10$-$20\%$ of the normal wave resistance for side-on shear and $S\sqrt{b/g}$ of order unity. (Continues...)

physics.flu-dyn↗

arXiv2016

Oscillating line source in a shear flow with a free surface: critical layer-like contributions

The linearized water-wave radiation problem for an oscillating submerged line source in an inviscid shear flow with a free surface is investigated analytically at finite, constant depth in the presence of a shear flow varying linearly with depth. The surface velocity is taken to be zero relative to the oscillating source, so that Doppler effects are absent. The radiated wave out from the source is calculated based on Euler's equation of motion with the appropriate boundary and radiation conditions, and differs substantially from the solution obtained by assuming potential flow. To wit, an additional wave is found in the downstream direction in addition to the previously known dispersive wave solutions; this wave is non-dispersive and we show how it is the surface manifestation of a critical layer-like flow generated by the combination of shear and mass flux at the source, passively advected with the flow. As seen from a system moving at the fluid velocity at the source's depth, streamlines form closed curves in a manner similar to Kelvin's cat's eye vortices. A resonant frequency exists at which the critical wave resonates with the downstream propagating wave, resulting in a downstream wave pattern diverging linearly in amplitude away from the source.

physics.flu-dyn↗

arXiv2016

Waves from an oscillating point source with a free surface in the presence of a shear current

We investigate analytically the linearized water wave radiation problem for an oscillating submerged point source in an inviscid shear flow with a free surface. A constant depth is taken into account and the shear flow increases linearly with depth. The surface velocity relative to the source is taken to be zero, so that Doppler effects are absent. We solve the linearized Euler equations to calculate the resulting wave field as well as its far-field asymptotics. For values of the Froude number $F^2=ω^2 D/g$ ($ω$: oscillation frequency, $D$ submergence depth) below a resonant value $F^2_\text{res}$ the wave field splits cleanly into separate contributions from regular dispersive propagating waves and non-dispersive "critical waves" resulting from a critical layer-like street of flow structures directly downstream of the source. In the sub-resonant regime the regular waves behave like sheared ring waves while the critical layer wave forms a street of a constant width of order $D\sqrt{S/ω}$ ($S$ is the shear flow vorticity) and is convected downstream at the fluid velocity at the depth of the source. When the Froude number approaches its resonant value, the the downstream critical and regular waves resonate, producing a train of waves of linearly increasing amplitude contained within a downstream wedge.

physics.flu-dyn↗

arXiv2015

Water Waves from General, Time-Dependent Surface Pressure Distribution in the Presence of a Shear Current

We obtain a general solution for the water waves resulting from a general, time-dependent surface pressure distribution, in the presence of a shear current of uniform vorticity beneath the surface, in three dimensions. Linearized governing equations and boundary conditions including the effects of gravity, a distributed external pressure disturbance, and constant finite depth, are solved analytically, and particular attention is paid to classic initial value problems: an initial pressure impulse and a steady pressure distribution which appears suddenly. In the present paper, good agreement with previous results is demonstrated. We subsequently show both analytically and numerically how transient waves from a suddenly appearing steady pressure distribution vanis for large times, and steady ship waves remain. The transient contribution to wave resistance was derived. The results show that a shear current has significant impact on the transient wave motions, resulting in asymmetry between upstream and downstream waves. The case of the suddenly appearing steady pressure is an intermediate case between ring waves and ship waves, starting out as the former and evolving gradually into the latter. The ship's direction of motion relative to the current is found to be crucial in determining how quickly effects of transient waves die out. Transient effects take much longer to doe out for a ship going against the shear flow than for one going downstream, when the two ships have the same velocity relative to the water surface. For ship motion against the shear current, thus, wave effects of transients, e.g., due to maneuvering could accumulate and be far more significant than on a uniform current.

physics.flu-dyn↗

arXiv2015

Oblique waves on a vertically sheared current are rotational

In the study of surface waves in the presence of a shear current, a useful and much studied model is that in which the shear flow has constant vorticity. Recently it was shown by Constantin [Eur. J. Mech. B/Fluids 30 (2011) 12-16] that a flow of constant vorticity can only permit waves travelling exactly upstream or downstream, but not at oblique angles to the current, and several proofs to the same effect have appeared thereafter. Physical waves cannot possibly adhere to such a restriction, however. We resolve the paradox by showing that an oblique plane wave propagating atop a current of constant vorticity according to the linearized Euler equation carries with it an undulating perturbation of the vorticity field, hence is not prohibited by the Constantin theorem since vorticity is not constant. The perturbation of the vorticity field is readily interpreted in a Lagrangian perspective as the wave motion gently shifting and twisting the vortex lines as the wave passes. In the special case of upstream or downstream propagation, the wave advection of vortex lines does not affect the Eulerian vorticity field, in accordance with the theorem. We conclude that the study of oblique waves on shear currents requires a formalism allowing undulating perturbations of the vorticity field, and the constant vorticity model is helpful only in certain 2D systems.

physics.flu-dyn↗

arXiv2014

Initial surface disturbance on a shear current: the Cauchy--Poisson problem with a twist

We solve for the first time the classical linear Cauchy--Poisson problem for the time evolution an initial surface disturbance when a uniform shear current is present beneath the surface. The solution is general, including the effects of gravity, surface tension and constant finite depth. The particular case of an initially Gaussian disturbance of width $b$ is studied for different values of three system parameters: a "shear Froude number" $S\sqrt{b/g}$ ($S$ is the uniform vorticity), the Bond number and the depth relative to the initial perturbation width. Different phase and group velocity in different directions yield very different wave patterns in different parameter regimes when the shear is strong, and the well known pattern of diverging ring waves in the absence of shear can take on very different qualitative behaviours. For a given shear Froude number, both finite depth and nonzero capillary effects are found to weaken the influence of the shear on the resulting wave pattern. The various patterns are analysed and explained in light of the shear-modified dispersion relation.

physics.flu-dyn↗

arXiv2014

Ship waves in the presence of uniform vorticity

Lord Kelvin's result that waves behind a ship lie within a half-angle 19 deg 28' is perhaps the most famous and striking result in the field of surface waves. We solve the linear ship wave problem in the presence of a shear current of constant vorticity S, and show that the Kelvin angles (one each side of wake) as well as other aspects of the wake depend closely on the "shear Froude number" Frs=VS/g (based on length g/S^2 and the ship's speed V), and on the angle between current and the ship's line of motion. In all directions except exactly along the shear flow there exists a critical value of Frs beyond which no transverse waves are produced, and where the full wake angle reaches 180 deg. Such critical behaviour is previously known from waves at finite depth. For side-on shear, one Kelvin angle can exceed 90 deg. On the other hand, the angle of maximum wave amplitude scales as 1/Fr (Fr based on size of ship) when Fr >> 1, a scaling virtually unaffected by the shear flow.

physics.flu-dyn↗

arXiv2013

Theoretical considerations of laser induced liquid-liquid interface deformation

In the increasingly active field of optofluidics, a series of experiments involving near-critical two-fluid interfaces have shown a number of interesting non-linear effects. We here offer, for the first time to our knowledge, an explanation for one such feature, observed in experiments by Casner and Delville [Phys. Rev. Lett. {\bf 90}, 144503 (2003)], namely the sudden formation of "shoulder"-like shapes in a laser-induced deformation of the liquid-liquid interface at high laser power. Two candidate explanations are the following: firstly, that the shape can be explained by balancing forces of buoyancy, laser pull and surface tension only, and that the observed change of deformation shape is the sudden jump from one solution of the strongly nonlinear governing differential equation to another. Secondly, it might be that the nontrivial shape observed could be the result of temperature gradients due to local absorptive heating of the liquid. We report that a systematic search for solutions of the governing equation in the first case yields no trace of solutions containing such features. By contrast, an investigation of the second option shows that the narrow shape of the tip of the deformation can be explained by a slight {\it heating} of the liquids. The local heating amounts to a few kelvins, with the parameters given, although there are uncertainties here. Our investigations suggest that local temperature variations are the crucial element behind the instability and the shoulder-like deformation.

physics.flu-dyn↗

arXiv2012

Static and dynamic response of a fluid-fluid interface to electric point and line charge

We consider the behaviour of a dielectric fluid-fluid interface in the presence of a strong electric field from a point charge and line charge, respectively, both statically and, in the latter case, dynamically. The fluid surface is elevated above its undisturbed level until balance is reached between the electromagnetic lifting force, gravity and surface tension. We derive ordinary differential equations for the shape of the fluid-fluid interface which are solved numerically with standard means, demonstrating how the elevation depends on field strength and surface tension coefficient. In the dynamic case of a moving line charge, the surface of an inviscid liquid-liquid interface is left to oscillate behind the moving charge after it has been lifted against the force of gravity. We show how the wavelength of the oscillations depends on the relative strength of the forces of gravity and inertia, whereas the amplitude of the oscillations is a nontrivial function of the velocity at which the line charge moves.

cond-mat.soft↗

arXiv2012

Detection of the Abraham force with a succession of short optical pulses

For over a century, two rival descriptions of electromagnetic field momentum in matter have co-existed, due to Abraham and Minkowski, respectively. We propose a set-up for measuring the difference between Abraham's and Minkowski's predictions in optics. To wit, a set-up is proposed in which the transient "Abraham force", a consequence of the Abraham energy-momentum tensor of 1909 may be measured directly. We show that when a train of short laser pulses is sent through a fiber wound up on a cylindrical drum, the Abraham theory predicts a torque which, by inserting realistic parameters, is found to be detectable. Indeed, the same torque when calculated with the Minkowski tensor takes the opposite sign. Numerical estimates show that with a typical torsion pendulum set-up and standard laser parameters, the angular deflection is in the order of $10^{-3}$ rad, which is easily measurable and even visible to the naked eye. Although its prediction is a century old, the Abraham force has proven experimentally elusive, and to our knowledge no macroscopic experimental demonstration of the difference between the predictions of the two mentioned energy-momentum tensors exists at optical frequencies.

physics.optics↗

arXiv2012

Sign of the Casimir-Polder interaction between atoms and oil-water interfaces: Subtle dependence on dielectric properties

We demonstrate that Casimir-Polder energies between noble gas atoms (dissolved in water) and oil-water interfaces are highly surface specific. Both repulsion (e.g. hexane) and attraction (e.g. glycerine and cyclodecane) is found with different oils. For several intermediate oils (e.g. hexadecane, decane, and cyclohexane) both attraction and repulsion can be found in the same system. Near these oil-water interfaces the interaction is repulsive in the non-retarded limit and turns attractive at larger distances as retardation becomes important. These highly surface specific interactions may have a role to play in biological systems where the surface may be more or less accessible to dissolved atoms.

quant-ph↗

arXiv2012

Mixing layer between two co-current Taylor-Couette flows

A new mixing layer can be generated if the rotation of either of the two cylinders in a Taylor--Couette apparatus varies discontinuously along the symmetry axis. The mixing zone between the two resulting co-current streams gives rise to radial vorticity in addition to the primary axial vorticity. An analytic solution for the azimuthal velocity has been derived from which we show that the width of the mixing zone varies only with radial position.

physics.flu-dyn↗

arXiv2012

Electrostrictive counter-force on fluid microdroplet in short laser pulse

When a micrometer-sized fluid droplet is illuminated by a laser pulse, there is a fundamental distinction between two cases. If the pulse is short in comparison with the transit time for sound across the droplet, the disruptive optical Abraham-Minkowski radiation force is countered by electrostriction and the net stress is compressive. In contrast, if the pulse is long on this scale, electrostriction is cancelled by elastic pressure and the surviving term of the electromagnetic force, the Abraham-Minkowski force, is disruptive and deforms the droplet. Ultrashort laser pulses are routinely used in modern experiments, and impressive progress has moreover been made on laser manipulation of liquid surfaces in recent times, making a theory for combining the two pertinent. We analyze the electrostrictive contribution analytically and numerically for a spherical droplet.

physics.optics↗

arXiv2012

A bilateral shear layer between two parallel Couette flows

We consider a shear layer of a kind not previously studied to our knowledge. Contrary to the classical free shear layer, the width of the shear zone does not vary in the streamwise direction but rather exhibits a lateral variation. Based on some simplifying assumptions, an analytic solution has been derived for the new shear layer. These assumptions have been justified by a comparison with numerical solutions of the full Navier-Stokes equations, which accord with the analytical solution to better than 1% in the entire domain. An explicit formula is found for the width of the shear zone as a function of wall-normal coordinate. This width is independent of wall velocities in the laminar regime. Preliminary results for a co-current laminar-turbulent shear layer in the same geometry are also presented. Shear-layer instabilities were then developed and resulted in an unsteady mixing zone at the interface between the two co-current streams.

physics.flu-dyn↗