Stability of Three-Dimensional Interfacial Waves Under Subharmonic Disturbances

This study examines the stability regimes of three-dimensional interfacial gravity waves.The numerical results of the linear stability analysis extend the three-dimensional surface waves results of Ioualalen and Kharif(1994)to three-dimensional interfacial waves.An approach of the collocation type has been developed for this purpose.The equations of motion are reduced to an eigenvalue problem where the perturbations are spectrally decomposed into normal modes.The results obtained showed that the density ratio plays a stabilizing factor.In addition,the dominant instability is of three-dimensional structure,and it belongs to class I for all values of density ratio.

Validity ranges of interfacial wave theories in a two-layer fluid system

In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness dl, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehaute＇s plot for free surface waves if water depth ratio r= d1/d2 approaches to infinity and the upper layer water density p1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ=（P2 - Pl）/P2 → 1.0 and r 〉 1.0. In the end, several figures of the validity ranges for various interfacial wavetheories in the two-layer fluid are given and compared with the results for surface waves.

Second-Order Solutions for Random Interfacial Waves Under Steady Uniform Currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a fiat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. （2004. Science in China, Ser. D, 47（12）： 1147-1154） for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth＇s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.

Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids

The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schr6dinger equations （1-NLS） with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoret- ically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.

Three-dimensional interfacial wave theory of dendritic growth: (Ⅰ). multiple variables expansion solutions

Dendritic pattern formation at the interface between liquid and solid is a commonly observed phenomenon in crystal growth and solidification process. The theoretical investigation of dendritic growth is one of the most profound and highly challenging subjects in the broad areas of interfacial pattern formation, condensed matter physics and materials science, preoccupying many researchers from various areas. Some longstanding key issues on this subject finally gained a breakthrough in the late of last century, via the ＇Interracial Wave （IFW） Theory＇ on the ground of systematical global stability analysis of the basic state of dendritic growth. The original form of the IFW theory mainly focus on the investigation of various axi-symmetric unsteady perturbed modes solutions around the axi-symmetrie basic state of system of dendritic growth. In reality, the system may allow various non-axi-symmetric, unsteady perturbed states. Whether or not the system of dendritic growth allows some growing non-axi-symmetric modes？ Will the stationary dendritic pattern be destroyed by some of such non-axi- symmetric modes？ Or, in one word, what is the stability property of the system, once the non-axi-symmetric modes can be evoked？ The answers for these questions are important for the solid foundation of IFW theory. The present work attempts to settle down these issues and develop a three-dimensional （3D） interfacial wave theory of dendritic growth. Our investigations verify that dendritic growth indeed allows a discrete set of non-axi-symmetric unstable global wave modes, which gives rise to a set of multiple arms spiral waves propagating along the Ivantsov＇s paraboloid.

Preliminary study of impaction mechanism of interfacial wave in explosive welding

The characteristics of both the detonation and explosive loading are studied comparatively. The width of the detonation reaction zone is from 0. 1 to 1 mm approximately, and it about equals the wavelength of interfacial wave in explosive welding. Both of them increase with the increasing of the thickness and detonation velocity of the explosive. The pressure of the detonation reaction zone is also wavy. The amplitude of the interfacial wave is decided by the detonation loading and the rate of the strength of the base and drive plate materials, and the wavelength is equal to the width of detonation reaction zone. So, a new impaction mechanism of pressure and inlaying due to wavy loading is put forward.

Numerical investigation on characteristics of interfacial wave of liquid film in gas-liquid two-phase flow using OpenFOAM

Liquid film cooling as an advanced cooling technology is widely used in space vehicles.Stable operation of liquid film along the rocket combustion inner wall is crucial for thermal protection of rocket engines.The stability of liquid film is mainly determined by the characteristics of interfacial wave,which is rarely investigated right now.How to improve the stability of thin film has become a hot spot.In view of this,an advanced model based on the conventional Volume of Fluid(VOF)model is adopted to investigate the characteristics of interfacial wave in gas-liquid flow by using OpenFOAM,and the mechanism of formation and development of wave is revealed intuitively through numerical study.The effects from gas velocity,surface tension and dynamic viscosity of liquid(three factors)on the wave are studied respectively.It can be found that the gas velocity is critical to the formation and development of wave,and four modes of droplets generation are illustrated in this paper.Besides,a gas vortex near the gas-liquid interface can induce formation of wave easily,so changing the gas vortex state can regulate formation and development of wave.What’s more,the change rules of three factors influencing on the interfacial wave are obtained,and the surface tension has a negative effect on the formation and development of wave only when the surface tension coefficient is above the critical value,whereas the dynamic viscosity has a positive effect in this process.Lastly,the maximum height and maximum slope angle of wave will level off as the gas velocity increases.Meanwhile,the maximum slope angle of wave is usually no more than 38°,no matter what happens to the three factors.

UNSTEADY INTERFACIAL WAVES DUE TO SINGULARITIES IN TWO SEMI-INFINITE INVISCID FLUIDS

The generation of unsteady interfacial gravity waves by a singularity immersed in two semi-infinite fluids was analytically investigated in detail by the methods of integral transform and of stationary-phase analysis. The fluids were assumed to be initially stationary, immiscible, inviscid and incompressible. The disturbed flows, generated by an impulsive and oscillatory source/dipole immersed above or be neath the interface, were governed by the I.aplace equations. The kinematic and dynamic boundary conditions on the interface were linearized for the small-amplitude waves. By means of the stationary phase analysis on the exact integral form solutions, the asymptotic representations for the interracial waves were derived for large time with a fixed distance to time ratio. The relation between a submerged singularity and a sur face pressure point was discussed. It is found that the local wavelength and the local wave period of the interracial waves are elongated in comparison with those of free-surface waves for a single fluid.

Forces of fully nonlinear interfacial periodic waves on a cylindrical pile in a two-layer fluid with free-surface boundary conditions

In the frame of fully nonlinear potential flow theory,series solutions of interfacial periodic gravity waves in a two-layer fluid with free surface are obtained by the homotopy analysis method(HAM),and the related wave forces on a vertical cylinder are analyzed.The solution procedure of the HAM for the interfacial wave model with rigid upper surface is further developed to consider the free surface boundary.And forces of nonlinear interfacial periodic waves are estimated by both the classical and modified Mori-son equations.It is found that the estimated wave forces by the classical Morison equation are more conservative than those by the modified Morison’s formula,and the relative error between the total inertial forces calculated by these two kinds of Morison’s formulae remains over 25%for most cases unless the upper and lower layer depths are both large enough.It demonstrates that the convective acceleration neglected in the classical Morison equation is rather important for inertial force exerted by not only internal solitary waves but also interfacial periodic waves.All of these should further deepen our understanding of internal periodic wave forces on a vertical marine riser.

A Hydrodynamic Modei for Slug Frequency in Horizontal Gas-Liquid Two-Phase Flow

The prediction of slug frequency has important significance on gas-liquid two-phase flow. A hydrody-namic modei was put forward to evaluate slug frequency for horizontal two-phase flow, based on the dependence of slug frequency on the frequency of unstable interfacial wave. Using air and water, experimental verification of the modei was carried out in a large range of flow parameters. Six electrical probes were installed at different positions of a horizontal plexiglass pipe to detect slug frequency development. The pipe is 30m long and its inner diameter is 24 mm. It is observed experimentally that the interfacial wave frequency at the inlet is about l to 3 times the frequency of stable slug. The slug frequencies predicted by the modei fit well with Tronconi (1990) modei and the experimental data. The combination of the hydrodynamic modei and the experimental data results in a conclusion that the frequency of equilibrium liquid slug is approximately half the miniraum frequency of interfacial wave.

ON THE INSTABILITY IN GAS ATOMIZATION

The instability theory of fluid flow is applied in gas atomization and the results show that the instability of interfacial wave is the main cause of gas atomization. The size of the droplets and its change with parameters are also studied, the results are compatible with the experiments.

Analytical solutions for the interfacial viscous capillary-gravity waves due to an oscillating Stokeslet

The fundamental solutions of the Stokes/Oseen equations due to a point force in an unbounded viscous fluid are referred to as the Stokeslet/Oseenlet,for which a systematic derivation are analytically presented here in terms of a uniform expression.By means of integral transforms,the closed-form solutions are explicitly deduced in a formula which involves the Hamiltonian,Hessian,and Laplacian operators,and elementary functions.Secondly,interfacial viscous capillary-gravity waves between two semi-infinite fluids due to oscillating singularities,including a simple source in the upper inviscid fluid and a Stokeslet in the low viscous fluid,were analytically studied by the Laplace-Fourier integral transform and asymptotic analysis.The dynamics responses consist of the transient and steady-state components,which are dealt with by the method of stationary phase and the Cauchy residue theorem,respectively.The transient response is made up of one short capillarity・dominated and one long gravity-dominated wave with the former riding on the latter.The steady-state wave has the same frequency as that of oscillating singularities.Asymptotic solutions for the wave profiles and the exact solution for the wave number are analytically derived,which show the combined effects of fluid viscosity,surface capillarity and an upper layer fluid.

The Behavior and Characteristics of the InterfacialWaves in Gas-Liquid Two-Phase Separated FlowThrough Downward Inclined Rectangular Channel

An experimental investigation on the behavior and characteristics of interfacial waves in downward inclined rectangular channel was conducted. The interfacial waves were traced and measured by us-ing conductance technique. The wav patterns were distinguished and defined. The characteristics of the interfacial waves, such as time-averaged film thickness, wave height, wave propagation speed,wavlength and wave frequency, were systematically examined in terms of gas and liquid superficial volumetric fiuxes. The effect of the inclination and flow channel geometry of the test section on the interfacial wav was also investigated.

Morphology controllable urchin-shaped bimetallic nickel-cobalt oxide/carbon composites with enhanced electromagnetic wave absorption performance

The microscopic morphology of electromagnetic wave absorbers influences the multiple reflections of electromagnetic waves and impedance matching,determining the absorption properties.Herein,the urchin-shaped bimetallic nickel-cobalt oxide/carbon(NiCo_(2)O_(4)/C)composites are prepared via a hy-drothermal route,whose absorption properties are investigated by different morphologies regulated by changing calcination temperature.A minimum reflection loss(RL_(min))of-75.26 dB is achieved at a match-ing thickness of 1.5 mm,and the effective absorption bandwidth(EAB)of 8.96 GHz is achieved at 2 mm.Multi-advantages of the synthesized NiCo_(2)O_(4)/C composites contribute to satisfactory absorption proper-ties.First,the interweaving of the needle-like structures increases the opportunities for scattering and multiple reflections of incident electromagnetic waves,and builds up a conductive network to facilitate the enhancement of conductive losses.Second,the carbon component in the NiCo_(2)O_(4)/C composites en-hances the interfacial polarization and reduces the density of the absorber.Besides,generous oxygen va-cancy defects are introduced into the NiCo_(2)O_(4)/C composites,which induces defect polarization and dipole polarization.In summary,the ternary coordination of components,defects and morphology led to out-standing electromagnetic wave absorption,which lightened the path for improving the electromagnetic wave absorption property and enriching the family of NiCo_(2)O_(4) absorbers with excellent performance.

Oceanic internal solitary waves in three-layer fluids of great depth

This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth.The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified configuration.Based on the Ablowitz-Fokas-Musslimani formulation for irrotational flows,strongly nonlinear and weakly nonlinear models are developed for the“shallow-shallow-deep”and“deep-shallow-deep”scenarios.Internal solitary waves are computed using numerical iteration schemes,and their global bifurcation diagrams are obtained by a numerical continuation method and compared for different models.For the“shallow-shallow-deep”case,both mode-1 and mode-2 internal solitary waves can be found,and a pulse broad-ening phenomenon resulting in conjugate flows is observed in the mode-2 branch.While in the“deep-shallow-deep”situation,only mode-2 solitary waves can be obtained.The existence and stability of mode-2 internal solitary waves are confirmed by solving the primitive equations based on the MITgcm model.