Two-layer Fluid Research Articles

Stability analysis of finite amplitude interfacial waves in a two-layer fluid in the presence of depth uniform current

Stability analysis of finite amplitude interfacial waves in a two-layer fluid in the presence of depth uniform current

Transient Two-Layer Electroosmotic Flow and Heat Transfer of Power-Law Nanofluids in a Microchannel.

To achieve the optimum use and efficient thermal management of two-layer electroosmosis pumping systems in microdevices, this paper studies the transient hydrodynamical features in two-layer electroosmotic flow of power-law nanofluids in a slit microchannel and the corresponding heat transfer characteristics in the presence of viscous dissipation. The governing equations are established based on the Cauchy momentum equation, continuity equation, energy equation, and power-law nanofluid model, which are analytically solved in the limiting case of two-layer Newtonian fluid flow by means of Laplace transform and numerically solved for two-layer power-law nanofluid fluid flow. The transient mechanism of adopting conducting power-law nanofluid as a pumping force and that of pumping nonconducting power-law nanofluid are both discussed by presenting the two-layer velocity, flow rates, temperature, and Nusselt number at different power-law rheology, nanoparticle volume fraction, electrokinetic width and Brinkman number. The results demonstrate that shear thinning conducting nanofluid represents a promising tool to drive nonconducting samples, especially samples with shear thickening features. The increase in nanoparticle volume fraction promotes heat transfer performance, and the shear thickening feature of conducting nanofluid tends to suppress the effects of viscous dissipation and electrokinetic width on heat transfer.

Modeling Open Channel Flows of a Viscous Fluid: Critical Transition and Apparent Bottom

The Shallow Water model (SWM) provides a simplification of the Navier–Stokes model (NSM) for stratified flows over a topography when the depth of the fluid layer is small compared to the horizontal scale of the flow. Nevertheless, the application of SWM is limited to the case of slowly variable bottoms and fails in describing the fluid flow over steep obstacles. In this work, we propose to extend the applicability of SWM when the topography is no longer slowly variable with space, by replacing the topography with an “apparent bottom”. This methodology is tested for the laminar flow of a two-layer fluid over a semi-circular cylinder. Sixteen different steady configurations are investigated in order to assess the influence of the Froude number and the blocking factor corresponding to the ratio between the obstacle height and the fluid layer normal height. Here, the apparent bottom required for SWM is obtained by enforcing the liquid height profile to be the one obtained from full resolution (NSM).

Thermal effects of two immiscible fluids in a stenosed tube with nanoparticles in the core region

A mathematical model for the two-layered fluid flow with the presence of nanoparticles mixed with blood in the core region through an artery with having soft stenosis is considered for the study. The nanoparticle mixed with base blood in the core region is a non-Newtonian fluid and the fluid (blood without having nanoparticles) in the peripheral layer is a Newtonian fluid means only blood flow. Thermal effects on the blood flow characteristics in the presence of nanoparticles in the core region of the artery with mild stenosis have been examined and analysed. The analytical solutions i.e. the closed-form mathematical expressions for blood flow (two-fluid model) characteristics, namely, the velocities, temperature and concentration distribution are obtained to solve the governing equations using the Homotopy perturbation method (HPM). The effect of various physical characteristics of fluid flow on the resistance to the flow and wall shear stress are analysed graphically. A novel result is found that the resistance of fluid flow increases when the viscosity of the fluid in the peripheral layer enhances but the shear at the wall diminishes. The steam lines are drawn to explore the flow pattern and characteristics of momentum transfer.

Nonlinear simulation of mucociliary clearance: A three- dimensional study

In this study three-dimensional (3D) numerical simulation of mucociliary clearance from the lung has been studied. The major thrust of this investigation is 3D simulation of mucociliary clearance accounting for non-linear viscoelastic characteristics of the mucus layer which is one of the most complex fluids in our body. Using a numerical code, three-dimensional unsteady flow computations have been carried out to study ciliary motion in a two-layer fluid model of the (bronchial) airway surface liquid (ASL) consisting of a Newtonian lower periciliary layer (PCL) and a nonlinear viscoelastic upper mucus layer. The projection finite difference method is used to solve the governing and constitutive equations on a staggered Eulerian grid. The immersed boundary method (IBM) is also employed to study the effect of cilia propulsive force on the fluid flow. The 5-mode nonlinear Giesekus model has been used as the constitutive equation of mucus which is characterized by nonlinear (non-Newtonian viscosity) properties. Numerical results have been devoted to study the effect of various parameters such as cilia beat frequency, cilia length as well as PCL and mucus depth on mucociliary clearance. The present 3D model shows very good agreement with previous experimental studies, while ca. 2.5-fold larger clearance rates were found for 2D models. 3D results show that cilia beating frequency and cilia length are the most critical factors affecting mucociliary clearance, while PCL depth and mucus depth have little and intermediate effect on mucus flow and hence clearance rate respectively.

Mitigation of Hydroelastic Responses in a Very Large Floating Structure by a Connected Vertical Porous Flexible Barrier

The hydroelastic response of an elastic thin plate combined with a vertical porous flexible plate floating on a single- or a two-layer fluid is analyzed in the two-dimensional Cartesian coordinate system. The vertical and the horizontal plates are placed in an inverted-L shape and rigidly connected together. The problem is studied with the aid of the method of matched eigenfunction expansions within the framework of linear potential flow theory. The fluid is assumed to be inviscid and incompressible, and the motion is assumed to be irrotational. Time–harmonic incident waves of the traveling mode with a given angular frequency are considered. Then, the least-squares approximation method and the inner product are used to obtain the expansion coefficients of the velocity potentials. Graphical results show the interaction between the water waves and the structure. The effects of several physical parameters, including the length and the complex porous-effect parameter of the vertical plate, on the wave reflection and transmission are discussed. The results show that a vertical plate can effectively eliminate the hydroelastic response of the very large floating structure. The longer a vertical plate is, the more waves are reflected by the vertical plate. With the increase in the porous-effect parameter, the deflection of vertical plate decreases. Besides the effects of the flexural rigidity, the lateral stress, the mooring line angle, the fluid density ratio, and the position of interface on the wave reflection and transmission are discussed. Numerical results show the significant mitigation effect due to the presence of the additional vertical plate.

Weakly nonlinear waves in stratified shear flows

<p style='text-indent:20px;'>We develop a Korteweg–De Vries (KdV) theory for weakly nonlinear waves in discontinuously stratified two-layer fluids with a generally prescribed rotational steady current. With the help of a classical asymptotic power series approach, these models are directly derived from the divergence-free incompressible Euler equations for unidirectional free surface and internal waves over a flat bed. Moreover, we derive a Burns condition for the determination of wave propagation speeds. Several examples of currents are given; explicit calculations of the corresponding propagation speeds and KdV coefficients are provided as well.</p>

Hydrodynamic behavior of a circular floating solar pond with an entrapped two-layer fluid

The resonant behavior in a moonpool of a floating circular solar pond, with an entrapped two-layer fluid, is studied. The problem is solved by applying a domain-decomposition method using eigenfunction matching. The surface- and internal-wave elevations and the hydrodynamic coefficients of a typical floating solar pond under forced heave or surge motion are computed. The effects of density stratification on surface-wave elevation, added mass, and damping coefficients are analyzed. A collection of resonance frequencies of surface and internal waves is examined, together with the corresponding variations of modal shapes. For heave resonance, the surface and internal waves are characterized by axisymmetric sloshing modes, as opposed to antisymmetric sloshing modes under surge resonances. A frozen-mode approximation method that treats the moonpool fluid as a density-stratified solid is developed to estimate piston-mode frequencies. Non-dimensional resonance frequencies corresponding to antisymmetric and axisymmetric sloshing modes are estimated based on the standing-wave approximation and reciprocity relations between surface and internal wavenumbers. Satisfactory agreement between the estimated resonance frequencies and those computed by eigenfunction matching method is achieved. It is found that the first resonance of the internal wave, rather than higher-order resonances, is more likely to affect the surface-wave behavior, whereas resonances of the surface-wave modes have significant effects on the internal waves. Parametric analyses are performed to study the effects of geometry configurations of the pond. It is found that the resonance frequencies of internal waves under forced heave or surge motion decrease with an increasing density ratio.

The joint influence of normal vibrations and electric field on the stability of a two-layer fluid system

The article focuses on the joint influence of normal vibrations and normal electric field on the stability of a system consisting of two flat horizontal fluid layers. Two cases are considered. In the first one, the system is formed by two layers of dielectric fluids (both layers have the same thickness) and, in the second, the system includes a dielectric fluid layer and an ideal electrically conductive fluid layer. The results obtained for these two cases are qualitatively similar. We study two approximations: the low-viscosity approximation and high-frequency vibrations. For the low-viscosity approximation, the so-called electric instability mode and the resonant mode are analyzed. In this case, the short-wavelength and long-wavelength instability modes are considered. In the low viscosity approximation, there occurs a viscous boundary layer, which is analyzed using a fast coordinate. The problem is studied by applying a multiscale method. It is demonstrated that vibrations increase the critical value of the electric field strength for short-wave instability in the presence of an electric mode. In the case of the long-wave instability, vibrations increase the curvature of the neutral curve near the zero value of the wave number. As for the influence of the electric field on resonant modes, it can lead to the splitting of the first resonance into two or three modes, depending on the values of the Weber number. When splitting is absent, the electric field reduces the critical amplitude of the first resonant mode. Otherwise, the effect of the electric field is more complex. In the high-frequency limit, the expressions describing the critical value of the electric field strength are similar to those for the electric mode considered in the low-viscosity approximation for finite vibration frequencies, and no resonant perturbations occur in this case.

Investigation on Dynamic Pressure Characteristics Induced by an Internal Solitary Wave in a Two-Layer Fluid of Finite Depth

In this paper, the dynamic pressure characteristics induced by an internal solitary wave (ISW) in a two-layer fluid of finite depth are studied. A method for detecting ISWs by dynamic pressure is proposed. First, an accurate controllable ISW numerical flume is established based on the applicability conditions of three kinds of ISW theories. Then the relationship between the maximum dynamic pressure and the amplitude of the ISW under four density stratifications is studied. The results show that the dynamic pressure variation induced by the ISW is synchronous with that of interface displacement. Under the same density stratification, the maximum dynamic pressure has a strong linear relationship with the corresponding amplitude. Furthermore, the nonlinear error is less than 7 %, and the relationship is not affected by the ocean structure. According to the above characteristics of dynamic pressure, a series of dynamic pressure measurement experiments were carried out in a large internal wave flume (IWF) using a very low frequency (VLF) piezoelectric sensor. The experimental results show that the dynamic pressure measurement results are in good agreement with the numerical simulation results. Last, the Miyata-Choi-Camassa (MCC) theory is used to invert the measured maximum dynamic pressure to the amplitude of ISW, and compared with the measured amplitude, the maximum error is less than 6 %, which verifies the feasibility of the inversion method of ISW amplitude by using dynamic pressure measurement proposed in this paper, and provides a new method and idea for detecting ISW at sea in the future.

ВЛАСНІ ЧАСТОТИ КОЛИВАНЬ ПЛАСТИНИ, ЯКА ПОДІЛЯЄ ДВОШАРОВУ ІДЕАЛЬНУ РІДИНУ З ВІЛЬНОЮ ПОВЕРХНЕЮ У ПРЯМОКУТНОМУ КАНАЛІ

The frequency spectrum of plane vibrations of an elastic plate separating a two-layer ideal fluid with a free surface in a rectangular channel is investigated analytically and numerically. For an arbitrary fixing of the contours of a rectangular plate, it is shown that the frequency spectrum of the problem under consideration consists of two sets of frequencies describing the vibrations of the free surface of the liquid and the elastic plate. The equations of coupled vibrations of the plate and the fluid are presented using a system of integro-differential equations with the boundary conditions for fixing the contours of the plate and the condition for the conservation of the volume of the fluid. When solving a boundary value problem for eigenvalues, the shape of the plate deflection is represented by the sum of the fundamental solutions of a homogeneous equation for a loose plate and a partial solution of an inhomogeneous equation by expanding in terms of eigenfunctions of oscillations of an ideal fluid in a rectangular channel. The frequency equation of free compatible vibrations of a plate and a liquid is obtained in the form of a fourth-order determinant. In the case of a clamped plate, its simplification is made and detailed numerical studies of the first and second sets of frequencies from the main mechanical parameters of the system are carried out. A weak interaction of plate vibrations on vibrations of the free surface and vice versa is noted. It is shown that with a decrease in the mass of the plate, the frequencies of the second set increase and take the greatest value for inertialess plates or membranes. A decrease in the frequencies of the second set occurs with an increase in the filling depth of the upper liquid or a decrease in the filling depth of the lower liquid. Taking into account two terms of the series in the frequency equation, approximate formulas for the second set of frequencies are obtained and their efficiency is shown. With an increase in the number of terms in the series of the frequency equation, the previous roots of the first and second sets are refined and new ones appear.

Elastic Bottom Effects on Ocean Water Wave Scattering by a Composite Caisson-Type Breakwater Placed Upon a Rock Foundation in a Two-Layer Fluid

The association of oblique surface gravity waves with a caisson-type multi-chamber porous breakwater fitted with a perforated front wall in a two-layer fluid is studied in finite ocean depth with an elastic bottom. This study focuses on the influence of porous parameters of the interface-piercing structure on wave attenuation in surface and interfacial modes. The flexural gravity wave motion establishes the influence of the elastic bottom. The reflection coefficients for waves in both modes are evaluated to show their effects on the free surface and interface elevations and the waveloads. Consequently, the appropriateness of various configurations of the structure on the wave scattering is studied. Due to wave dissipation by the structure, less waveload is detected on the stiff wall and less elevation is noticed in the porous zone. The structure’s multi-chamber division allows it to have more dissipative and reflective properties. Adjustment of the structure’s height, breadth, and porous parameter leads to achieving good amount of wave reflection and maximum energy dissipation. An optimal width can be determined for a suitable configuration of the structure so that a breakwater can be built with an acceptable level of reflection and dissipation characteristics. The shear force and bottom deflection show how elastic parameters of the sea-floor affect wave scattering.

Water wave scattering by a submerged horizontal semi-circular barrier in a two-layer fluid

This paper studies water wave scattering by a submerged horizontal bottom-mounted semi-circular barrier in a two-layer fluid based on the linear potential flow theory. Two cases, i.e., the barrier completely located in the lower fluid and the barrier intersecting the internal interface of two fluids, are considered independently. In the former case, an analytical solution for the wave scattering problem is derived by using the method of multipole expansions, whereas in the latter case, a numerical solution is developed by employing the multi-domain boundary element method (BEM). The conservation relations of wave energy for incident waves in surface and internal modes are derived, and the reflection and transmission energy coefficients as well as the wave forces acting on the barrier are calculated. Comparisons of calculated results between the analytical solution and the BEM numerical solution are conducted. Calculation examples are presented to examine the effects of various physical parameters (angular frequency, interface position, density ratio of two fluids and incident angle) on wave forces acting on the barrier and the energy transformation between two wave modes. It is found that there is a noticeable difference in the energy transformation between the barrier intersecting the fluid interface or not.

Peristaltic Flow of Two-Layered Fluids in an Elastic Tube

Peristaltic Flow of Two-Layered Fluids in an Elastic Tube

Rogue and lump waves for the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a liquid or lattice

Two-layer fluid models are used to depict some nonlinear phenomena in fluid mechanics, medical science and thermodynamics. In this paper, we investigate a (3[Formula: see text]1)-dimensional Yu-Toda-Sasa-Fukuyama equation for the interfacial waves in a two-layer liquid or elastic quasiplane waves in a lattice. Via the Kadomtsev-Petviashvili hierarchy reduction, we derive the rational solutions in the determinant forms and semi-rational solutions. The [Formula: see text]th-order lump waves and multi-lump waves are obtained, where [Formula: see text] is a positive integer. We observe the second-order lump waves: Two-lump waves interact with each other and separate into two new lump waves. Two-lump waves are observed: Overtaking interaction takes place between the two-lump waves; After the interaction, the two-lump waves propagate with their original velocities and amplitudes. Studying the semi-rational solutions, we show the fusion between a lump wave and a bell-type soliton and fission of a bell-type soliton. Interaction between a line rogue wave and a bell-type soliton is shown.

Ultra Low Frequency Wave Produced by Underwater Oscillating Sphere and Its Measurement

When an underwater target moves in viscous fluid, it may cause the periodic movement of the surrounding fluid and generate ultra-low-frequency (ULF) gravity waves. The initial domain of the gravitational surface wave propagating above the moving target is named circular wave. This article studies the ULF circular wave generated by underwater oscillating sphere, which will provide basis for underwater long-range target detection. Firstly, the circular wave caused by the sphere oscillation in a finite deep fluid is studied based on the theory of linear potential flow. Meanwhile, the multipole expansion theory is established to solve the circular wave field. Secondly, the interface wave generated by the target oscillation in a two-layer fluid are numerically analyzed by comparison with the free surface fluctuation of a single-layer fluid. The results show that the amplitude of the internal interface displacement (AIID) is smaller than that of the free surface (AFSD). When the sphere is in the lower layer, the layering effect of the fluid has significant influences on the AFSD. Finally, the results of the pool experiment verified that the wave generated by the oscillating sphere is the surface gravity wave. Furthermore, the change trend of the test result is consistent with the simulation result.

Numerical Simulation for the Evolution of Internal Solitary Waves Propagating over Slope Topography

In this study, the propagation and evolution characteristics of internal solitary waves on slope topography in stratified fluids were investigated. A numerical model of internal solitary wave propagation based on the nonlinear potential flow theory using the multi-domain boundary element method was developed and validated. The numerical model was used to calculate the propagation process of internal solitary waves on the topography with different slope parameters, including height and angle, and the influence of slope parameters, initial amplitude, and densities jump of two-layer fluid on the evolution of internal solitary waves is discussed. It was found that the wave amplitude first increased while climbing the slope and then decreased after passing over the slope shoulder based on the calculation results, and the wave amplitude reached a maximum at the shoulder of the slope. A larger height and angle of the slope can induce larger maximum wave amplitude and more obvious tail wave characteristics. The wave amplitude gradually decreased, and a periodic tail wave was generated when propagating on the plateau after passing the slope. Both frequency and height of the tail wave were affected by the geometric parameters of the slope bottom; however, the initial amplitude of the internal solitary wave only affects the tail wave height, but not the frequency of the tail wave.

(2+1)-dimensional coupled Boussinesq equations for Rossby waves in two-layer cylindrical fluid* *Supported by the Nature Science Foundation of Shandong Province of China (ZR2018MA017).

In this paper, the existence and propagation characteristics of Rossby waves in a two-layer cylindrical fluid are studied. Firstly, based on the dimensionless baroclinic quasi-geostrophic vortex equations including exogenous and dissipative, we derive new (2+1)-dimensional coupled Boussinesq equations describing wave propagation in polar coordinates by employing a multiscale analysis and perturbation method. Then, the Lie symmetries and conservation laws of the coupled Boussinesq equations are analyzed. Subsequently, by using the -expansion method, the exact solutions of the (2+1)-dimensional coupled Boussinesq equations are obtained. Finally, the effects of coupling term coefficients on the propagation characteristics of Rossby waves are analyzed.

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear current. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive the modal equations from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (group speed, wave action conservation law) and to constructing more general ‘hybrid solutions’ consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. Detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions (i.e. eigenfunctions of the relevant spectral problems) for the surface waves in homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a large family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. Global and local measures of the deformation of wavefronts are introduced and evaluated.

Impact of solitons on the progression of initial lesion in aortic dissection

Aortic dissection (AD) is the most common catastrophic disease reported at cardiovascular emergency in hospitals. Herein, a tear in the tunica intima results into separation of layers of aortic wall leading to rupture and torrential bleed. Hypoxia and oxidative stress are associated with AD. The release of hypoxia inducible factor (HIF)-[Formula: see text] from the initial flap lesion in the tunica intima is the basis for aneurysmal prone factors. We framed a boundary value problem (BVP) to evaluate homeostatic saturation for oxygen dynamics using steady-state analysis. We prove uniqueness and existence of the solution of the BVP for gas exchange at capillary–tissue interface as a normal physiological function. Failure of homeostatic mechanism establishes hypoxia, a new quasi-steady-state in AD. We model permeation of two-layer fluid comprised of blood and HIF-[Formula: see text] through tunica media as a generalized [Formula: see text]-dimensional nonlinear evolution equation and solve it using Lie group of transformations method. We note that the two-layer fluid permeates the tunica media as solitary wave including solitons such as bright soliton, dark soliton, peregrine soliton, topological soliton, kink soliton, breather soliton and multi-soliton complex. Also, we introduce the main result and discuss the implications of soliton solution, using graphic interpretation, to describe the early stage of progression of AD.