Instability of two-layer film flows due to the interacting effects of surfactants, inertia and gravity

We consider a two-fluid shear flow where the interface between the two fluids is coated with an insoluble surfactant. An asymptotic model is derived in the thin-layer approximation, consisting of a set of nonlinear partial differential equations describing the evolution of the film and surfactant disturbances at the interface. The model includes important physical effects such as Marangoni forces (caused by the presence of surfactant), inertial forces arising in the thick fluid layer, as well as gravitational forces. The aim of this study is to investigate the effect of density stratification or gravity—represented through the Bond number Bo—on the flow stability and the interplay between the different (de)stabilisation mechanisms. It is found that gravity can either stabilise or destabilise the interface (depending on fluid properties) but not always as intuitively anticipated. Different traveling-wave branches are presented for varying Bo, and the destabilising mechanism associated with the Marangoni forces is discussed

The role of soluble surfactants in the linear stability of two-layer flow in a channel

The linear stability of Couette-Poiseuille flow of two superposed fluid layers in a horizontal channel is considered. The lower fluid layer is populated with surfactants that appear either in the form of monomers or micelles and can also get adsorbed at the interface between the fluids. A mathematical model is formulated which combines the Navier- Stokes equations in each fluid layer, convection-diffusion equations for the concentration of monomers (at the interface and in the bulk fluid) and micelles (in the bulk), together with appropriate coupling conditions at the interface. The primary aim of this study is to investigate when the system is unstable to arbitrary wavelength perturbations, and in particular, to determine the influence of surfactant solubility and/or sorption kinetics on the instability. A linear stability analysis is performed and the growth rates are obtained by solving an eigenvalue problem for Stokes flow, both numerically for disturbances of arbitrary wavelength and analytically using long-wave approximations. It is found that the system is stable when the surfactant is sufficiently soluble in the bulk and if the fluid viscosity ratio m and thickness ratio n satisfy the condition m < n2. On the other hand, the effect of surfactant solubility is found to be destabilising if m n2. Both of the aforementioned results are manifested for low bulk concentrations below the critical micelle concentration; however when the equilibrium bulk concentration is sufficiently high (and above the critical micelle concentration) so that micelles are formed in the bulk fluid, the system is stable if m < n2 in all cases examined

Modelling of nonlinear wave-buoy dynamics using constrained variational methods

We consider a comprehensive mathematical and numerical strategy to couple water-wave motion with rigid ship dynamics using variational principles. We present a methodology that applies to three-dimensional potential flow water waves and ship dynamics. For simplicity, in this paper we demonstrate the method for shallow-water waves coupled to buoy motion in two dimensions, the latter being the symmetric motion of a crosssection of a ship. The novelty in the presented model is that it employs a Lagrange multiplier to impose a physical restriction on the water height under the buoy in the form of an inequality constraint. A system of evolution equations can be obtained from the model and consists of the classical shallow-water equations for shallow, incompressible and irrotational waves, and relevant equations for the dynamics of the wave-energy buoy. One of the advantages of the variational approach followed is that, when combined with symplectic integrators, it eliminates any numerical damping and preserves the discrete energy; this is confirmed in our numerical results

Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space dimensions

A Kuramoto–Sivashinsky equation in two space dimensions arising in thin film flows is considered on doubly periodic domains. In the absence of dispersive effects, this anisotropic equation admits chaotic solutions for sufficiently large length scales with fully two-dimensional profiles; the one-dimensional dynamics observed for thin domains are structurally unstable as the transverse length increases. We find that, independent of the domain size, the characteristic length scale of the profiles in the streamwise direction is about 10 space units, with that in the transverse direction being approximately three times larger. Numerical computations in the chaotic regime provide an estimate for the radius of the absorbing ball in ℒ2 in terms of the length scales, from which we conclude that the system possesses a finite energy density. We show the property of equipartition of energy among the low Fourier modes, and report the disappearance of the inertial range when solution profiles are two-dimensional. Consideration of the high-frequency modes allows us to compute an estimate for the analytic extensibility of solutions in ℂ2. We also examine the addition of a physically derived third-order dispersion to the problem; this has a destabilizing effect, in the sense of reducing analyticity and increasing amplitude of solutions. However, sufficiently large dispersion may regularize the spatio-temporal chaos to travelling waves. We focus on dispersion where chaotic dynamics persist, and study its effect on the interfacial structures, absorbing ball and properties of the power spectrum

A novel wave-energy device with enhanced wave amplification and induction actuator

© 2020, European Wave and Tidal Energy Conference. All rights reserved. A novel wave-energy device is presented. Both a preliminary proof-of-principle of a working, scaled laboratory version of the energy device is shown as well as the derivation and analysis of a comprehensive mathematical and numerical model of the new device. The wave-energy device includes a convergence in which the waves are amplified, a constrained wave buoy with a (curved) mast and direct energy conversion of the buoy motion into electrical power via an electro-magnetic generator. The device is designed for use in breakwaters and it is possible to be taken out of action during severe weather. The new design is a deconstruction of elements of existing waveenergy devices, such as the TapChan, IP wave-buoy and the Berkeley Wedge, put together in a different manner to enhance energy conversion and, hence, efficiency. The idea of wave-focusing in a contraction emerged from our work on creating and simulating rogue waves in crossing seas, including a “bore-soliton-splash”. Such crossing seas have been recreated and modelled in the laboratory and in simulations by using a geometric channel convergence. The mathematical and numerical modelling is also novel. One monolithic variational principle governs the dynamics including the combined (potential-flow) hydrodynamics, the buoy motion and the power generation, to which the dissipative elements such as the electrical resistance of the circuits, coils and loads have been added a posteriori. The numerical model is a direct and consistent discretisation of this comprehensive variational principle. Preliminary numerical calculations are shown for the case of linearised dynamics; optimisation of efficiency is a target of future work

Nonlinear dynamics of two-layer channel flow with soluble surfactant below or above the critical micelle concentration

The nonlinear stability of an inertialess two-layer surfactant-laden Couette flow is considered. The two fluids are immiscible and have different thicknesses, viscosities and densities. One of the fluids is contaminated with a soluble surfactant whose concentration may be above the critical micelle concentration, in which case micelles are formed in the bulk of the fluid. A surfactant kinetic model is adopted that includes the adsorption and desorption of molecules to and from the interface, and the formation and breakup of micelles in the bulk. The lubrication approximation is applied and a strongly nonlinear system of equations is derived for the evolution of the interface and surfactant concentration at the interface, as well as the vertically averaged monomer and micelle concentrations in the bulk (as a result of fast vertical diffusion). The primary aim of this study is to determine the influence of surfactant solubility on the nonlinear dynamics. The nonlinear lubrication model is solved numerically in periodic domains and saturated travelling waves are obtained at large times. It is found that a sufficiently soluble surfactant can either destabilise or stabilise the interface depending on certain fluid properties. The stability behaviour of the system depends crucially on the values of the fluid viscosity ratio and thickness ratio in reference to the boundary. If the surfactant exists at large concentrations that exceed the critical micelle concentration, then long waves are stable at large times, unless density stratification effects overcome the stabilising influence of micelles. Travelling wave bifurcation branches are also calculated and the impact of various parameters (such as the domain length or fluid thickness ratio) on the wave shapes, amplitudes and speeds is examined. The mechanism responsible for interfacial (in)stability is explained in terms of the phase difference between the interface deformation and concentration waves, which is shifted according to the sign of the crucial factor and the strength of the surfactant solubility

Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows

The nonlinear dynamics of two immiscible superposed viscous fluid layers in a channel is examined using asymptotic modelling and direct numerical simulations (DNS). The flow is driven by an imposed axial pressure gradient. Working on the assumption that one of the layers is thin, a weakly-nonlinear evolution equation for the interfacial shape is derived that couples the dynamics in the two layers via a nonlocal integral term whose kernel is determined by solving the linearised Navier–Stokes equations in the thicker fluid. The model equation incorporates salient physical effects including inertia, gravity, and surface tension, and allows for comparison with DNS at finite Reynolds numbers. Direct comparison of travelling-wave solutions obtained from the model equation and from DNS show good agreement for both stably and unstably stratified flows. Both the model and the DNS indicate regions in parameter space where unimodal, bimodal and trimodal waves co-exist. Nevertheless, the asymptotic model cannot capture the dynamics for a sufficiently strong unstable density stratification when interfacial break-up and eventual dripping occurs. In this case, complicated interfacial dynamics arise from the dominance of the gravitational force over the shear force due to the underlying flow, and this is investigated in detail using DNS

Variational finite element methods for waves in a Hele–Shaw tank

The damped motion of driven water waves in a Hele-Shaw tank is investigated variationally and numerically. The equations governing the hydrodynamics of the problem are derived from a variational principle for shallow water. The variational principle includes the effects of surface tension, linear momentum damping due to the proximity of the tank walls and incoming volume flux through one of the boundaries representing the generation of waves by a wave pump. The model equations are solved numerically using (dis)continuous Galerkin finite element methods and are compared to exact linear wave sloshing and driven wave sloshing results. Numerical solutions of the nonlinear shallow water-wave equations are also validated against laboratory experiments of artificially driven waves in the Hele-Shaw tank

Unpublished Mediterranean records of marine alien and cryptogenic species

Good datasets of geo-referenced records of alien species are a prerequisite for assessing the spatio-temporal dynamics of biological invasions, their invasive potential, and the magnitude of their impacts. However, with the exception of first records on a country level or wider regions, observations of species presence tend to remain unpublished, buried in scattered repositories or in the personal databases of experts. Through an initiative to collect, harmonize and make such unpublished data for marine alien and cryptogenic species in the Mediterranean Sea available, a large dataset comprising 5376 records was created. It includes records of 239 alien or cryptogenic taxa (192 Animalia, 24 Plantae, 23 Chromista) from 19 countries surrounding the Mediterranean Sea. In terms of records, the most reported Phyla in descending order were Chordata, Mollusca, Chlorophyta, Arthropoda, and Rhodophyta. The most recorded species was Caulerpa cylindracea, followed by Siganus luridus, Magallana sp. (cf. gigas or angulata) and Pterois miles. The dataset includes records from 1972 to 2020, with the highest number of records observed in 2018. Among the records of the dataset, Dictyota acutiloba is a first record for the Mediterranean Sea. Nine first country records are also included: the alga Caulerpa taxifolia var. distichophylla, the cube boxfish Ostracion cubicus, and the cleaner shrimp Urocaridella pulchella from Israel; the sponge Paraleucilla magna from Libya and Slovenia; the lumpfish Cyclopterus lumpus from Cyprus; the bryozoan Celleporaria vermiformis and the polychaetes Prionospio depauperata and Notomastus aberans from Malta

A MSFD complementary approach for the assessment of pressures, knowledge and data gaps in Southern European Seas : the PERSEUS experience

PERSEUS project aims to identify the most relevant pressures exerted on the ecosystems of the Southern European Seas (SES), highlighting knowledge and data gaps that endanger the achievement of SES Good Environmental Status (GES) as mandated by the Marine Strategy Framework Directive (MSFD). A complementary approach has been adopted, by a meta-analysis of existing literature on pressure/impact/knowledge gaps summarized in tables related to the MSFD descriptors, discriminating open waters from coastal areas. A comparative assessment of the Initial Assessments (IAs) for five SES countries has been also independently performed. The comparison between meta-analysis results and IAs shows similarities for coastal areas only. Major knowledge gaps have been detected for the biodiversity, marine food web, marine litter and underwater noise descriptors. The meta-analysis also allowed the identification of additional research themes targeting research topics that are requested to the achievement of GES. 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license.peer-reviewe