Liquid Surface Waves Research Articles

Highly directional liquid surface wave source based on resonant cavity

By placing a point source inside a resonant cavity structure, we present a method to realize a highly directional liquid surface wave source. The resonant cavity is surrounded by two slabs of different thickness, with each slab consisting of a finite square array of rigid cylinders standing vertically in the liquid. It is shown that more than 68% of the total energy is emitted out along the normal directions of the cavity within a very narrow angular range. At the resonant frequency, narrow emission pattern with half-power angular width of only several degrees is obtained.

Liquid surface waves in parabolic tanks

Surface waves in cylindrical tanks with parabolic cross section formed by two confocal parabolas are studied. Exact general solutions for the inviscid gravity-capillary waves as function of the parabolic curvatures are presented, and the symmetry of the eigensolutions for the velocity potential modes is also investigated. For a complete characterization of the velocity potential and of the amplitude of the liquid surface, their analytic expressions in terms of hypergeometric functions are given. It is shown that for the particular case of two confocal parabolas with the same curvature, the velocity potential is described by the cylindrical functions. The evolution of the nodal structure for gravity-capillary waves for variable excitation, and in terms of the parabolic tank curvature, is analyzed.

Hamiltonian Formulation for Nonlinear Sloshing in Layered Two Immiscible Fluids

This paper deals with a nonlinear surface and interface sloshing in layered two immiscible fluids of different desities. Scientific interest in surface and interface sloshing includes the need to quantify allowance loads on separators or agitators in chemical plants and so on. We propose the analytical method for nonlinear sloshing in this problem by using Hamiltonian formulation. In theoretical analysis, the governing equations and canonical form (Hamiltonian equations) of a system of two fluids with a dynamic free surface and interface are given by applying Hamilton's principle. Moreover, the nonlinear ordinary differential system which governs liquid surface and interfacial wave motions is derived by using Dirichlet-Neumann operators and the generalized Fourier series expansion. Solving these ordinary differential system yields the time histories and the transitions of surface and interfacial wave motions in a rectangular tank. The validly of the theoretical analysis is verified through the experiments.

Hamiltonian Formulation of Free Surface and Interface Motions in a Tank(N-Wave Resonant Interaction Caused by Nonlinearity of System)

This paper deals with nonlinear liquid surface and interfacial wave motions in a tank containing two incompressible irrotational fluids of different densities. In order to investigate time history responses and nonlinear characteristics, we apply canonical equations (Hamiltonian equations) to this problem. The time histories and the transitions of surface and interfacial wave motions are given by solving the canonical equations of this system. This study is intended to clarify the nonlinear coupling characteristics for this system. We have focused on the N-Wave Resonant Interaction (NWRI) and investigated occurrence conditions of the NWRI. In particular, the time history responses on the resonant state caused by the Three-Wave Resonant Interaction (3WRI) are discussed for the rectangular and the circular cylindrical tanks. On the other hand, the validly of the theoretical analysis is verified through the experiments. These results are in good agreement with each other.

Hamiltonian Formulation of the Free Surface and Interface Motions in a Tank (3rd Report, N-Wave Resonant Interaction Caused by Nonlinearity of System)

This paper deals with nonlinear liquid surface and interfacial wave motions in a tank containing two incompressible irrotational fluids of different densities. In theoretical analysis, we employ Hamiltonian formulation to derive a canonical equation of this system. The time histories and the transitions of surface and interfacial wave motions in a rectangular tank and circular cylindrical tank are given by solving the canonical equation of this system. Moreover, we have focused in particular on the N-Wave Resonant Interaction (NWRI) and investigated occurrence conditions of the NWRI. On the other hand, The validly of the theoretical analysis is verified through the experiments. These results are in good agreement with each other.

Nonlinear Time History Response Analysis of Sloshing in a Tank by Using Dirichlet-Neumann Operators

This paper deals with nonlinear liquid surface wave motion in a tank subjected to horizontally and vertically excitation. In theoretical analysis, the fluid is assumed to be incompressible, inviscid, and irrotational. The governing equations of liquid surface wave motion are given by applying the variational principle. In addition, we derive nonlinear an ordinary differential system which govern liquid surface wave motions by using Dirichlet-Neumann operators and the generalized Fourier series expansion. The time histories of surface wave motion are obtained by solving the ordinary differential system. Moreover, the frequency components are observed by applying the discrete Fourier Transform to the theoretical results and the experimental results. The validly of the theoretical result by using Dirichlet-Neumann operators is verified through the experiments.

Measurement of the damping of liquid surface wave by diffraction method

A simple method for measuring the damping of the liquid surface wave (LSW) based on the diffraction method was proposed in this paper. In the experiment, the phenomenon was observed that the intensity distribution of the diffraction patterns from the LSW varies with the position of the incident spot. By theoretical analysis of the relationship between the intensity distribution and the LSW amplitude, the damping constant was obtained. In addition, the viscosity of the liquid can be calculated with this method, too.

Surface wave propagation in a fluid saturated incompressible porous half-space lying under two layers of different liquids

Abstract A study of surface wave propagation in a fluid saturated incompressible porous half-space lying under a double-layer consisting of non-homogeneous and homogeneous liquids is presented. The frequency equation connecting the phase velocity with wave number is derived. Special cases as: (i) Rayleigh type surface waves in an incompressible poro-elastic half-space lying under a uniform layer of a homogeneous liquid, (ii) Rayleigh type surface waves in an incompressible poro-elastic half-space lying under a uniform layer of a non-homogeneous liquid and (iii) Rayleigh type surface waves propagating along the free surface of a fluid saturated incompressible porous elastic half-space, are investigated. Numerical results with graphical presentations of the variations of phase velocity with wave number for different cases are also included.

Hamiltonian Formulation of the Free Surface and Interface Motions in a Tank (2nd Report, Nonlinear Time History Response Analysis)

This paper deals with nonlinear liquid surface and interfacial wave motions in a tank containing two incompressible irrotational fluids of different densities. In theoretical analysis, the governing equations and canonical form of a system of two fluids with a dynamic free surface and interface are given by applying Hamilton's principle. Moreover, the nonlinear ordinary differential system which governs liquid surface and interfacial wave motions is derived by using Dirichlet-Neumann operators and the generalized Fourier series expansion. Solving these ordinary differential system yields the time histories and the transitions of surface and interfacial wave motions in a rectangular tank. The validly of the theoretical analysis is verified through the experiments. The theoretical results are shown to be in good agreement with the experimental results.

Unusual distribution of the diffraction patterns from liquid surface waves

Light diffraction from liquid surface acoustic wave at low frequency was experimentally realized. In the experiment, steady and visible diffraction patterns were obtained, and obvious asymmetry of patterns was observed. The approximate conditions of the surface wave diffraction and the damped wave model were theoretically analyzed, and the corresponding analytic expression of the displacement of the nth-order diffraction component to the center of the patterns was derived. This explained the asymmetrical distribution well. The theoretical and experimental results are in good agreement.

Probing liquid surface waves, liquid properties and liquid films with light diffraction

Surface waves on liquids act as a dynamical phase grating for incident light. In this paper, we revisit the classical method of probing such waves (wavelengths of the order of mm) as well as inherent properties of liquids and liquid films on liquids, using optical diffraction. A combination of simulation and experiment is proposed to trace out the surface wave profiles in various situations (e.g. for one or more vertical, slightly immersed, electrically driven exciters). Subsequently, the surface tension and the spatial damping coefficient (related to viscosity) of a variety of liquids are measured carefully in order to gauge the efficiency of measuring liquid properties using this optical probe. The final set of results deal with liquid films where dispersion relations, surface and interface modes, interfacial tension and related issues are investigated in some detail, both theoretically and experimentally. On the whole, our observations and analysis seem to support the claim that this simple, low cost apparatus is capable of providing a wealth of information on liquids and liquid surface waves in a non-destructive way.

Omnidirectional total reflection for liquid surface waves propagating over a bottom with one-dimensional periodic undulations

We study theoretically the propagation of liquid surface waves over a bottom with one-dimensional (1D) periodic undulations. We find a general criterion for omnidirectional total reflection in such a system. Numerical simulations based on a transfer matrix method demonstrate unambiguously the existence of omnidirectional total reflection for liquid surface waves propagating over a bottom with 1D periodic undulations.

Surface and internal waves in a stratified layer of liquid and an analysis of the impedance boundary conditions

The surface and internal waves in a multilayered ideal liquid for specified displacements of the bottom are considered. The upper surface of the liquid is either free or displacements are specified on it. In the long-wave approximation, asymptotically accurate models of the waves propagating along the surface layers of an incompressible liquid are constructed both for intense stratification (the ratio of the densities of neighbouring layers are associated with a small parameter) and for weak stratification. The important case of this problem of the dynamic contact of rigid bodies through a layer of incompressible or compressible liquid is investigated. High-order impedance boundary conditions are constructed and the results of testing them using the exact solutions are presented.

301 Dirichlet-Neumann Operatorを用いた直方体容器内液面の非線形揺動

This paper deal with the time history of liquid surface wave motion in a rectangular tank which is oscillated horizontally. In theoretical analysis, the governing equations of liquid surface wave motion are derived by applying the variational principle. The nonlinear ordinary differential equations of time which govern liquid surface wave motion are derived by using Dirichlet-Neumann operators. An experiment was carried out using a model tank. The frequency components are observed by applying the discrete Fourier Transform to the theoretical results and the experimental results. The high-frequency components are observed at the both results. And, these results are in good agreement qualitatively.

Large band gaps of water waves through two-dimensional periodic topography

In this Letter, the band structures and band gaps of liquid surface waves propagating over two-dimensional periodic topography was investigated by plane-waves expansion method. The periodic topography drilled by square hollows with square lattice was considered. And the effects of the filling fraction and the orientation of bottom-hollows on the band gaps are investigated in detail.

Modulated interference of reflected light from a liquid surface wave at tens Hertz frequencies

An analytic intensity expression of the reflected light from a liquid surface with acoustic wave at a few tens Hertz was derived. The expression displays a distinct modulated oscillation. Meanwhile high visibility and modulated interference fringes were obtained experimentally. Line scans across the reflection patterns indicate that the theory predication is well consistent with the experimental data. Moreover, a practical technique can be developed, based on this study, to determine the wavelength and amplitude of the SAW at these frequencies as well as the dynamic surface tension.

A simple experiment on diffraction of light by interfering liquid surface waves

We describe a simple experiment on the diffraction of monochromatic light by interfering liquid surface waves. The surface wave profile, which acts as a reflection phase grating for incident light, is generated by electrically driven vertical oscillations of two or more slightly immersed exciters. The theoretical intensity of the diffracted light agrees well with observations. In particular, we show the relation between the intensity and the amplitude (height) of the surface wave. Although invisible to the naked eye, the interference of liquid surface waves can be optically detected from the characteristic features of the diffraction pattern. In addition, we can measure the amplitude, wavelength, and phase velocity of the surface wave that propagates along the line joining the exciters.

Self-collimation in liquid surface waves propagating over a bottom with periodically drilled holes

Liquid surface waves propagating over a bottom with periodically drilled holes are studied experimentally and theoretically. Point source waves are generated in the center of the array of the periodically drilled holes in order to observe the evolvements of these waves. We successfully observe the self-collimation phenomenon in liquid surface waves. Band structures and constant-frequency surfaces are calculated, which can give a satisfactory interpretation of the experimental observations.

(2 + 1) dimensional H?r?gus-Courcelle-Il?ichev model for the liquid surface waves in the presence of sea ice or surface tension: B�cklund transformation, exact solutions and possibly observable effects

The wave propagation on an ocean or water surface in the presence of sea ice or surface tension is of current importance. In this paper, we investigate the (2 + 1) dimensional 6th-order model proposed recently by Hărăgus-Courcelle and Il’ichev for such wave propagation. Firstly, we correct some errors in the original derivations of this model. With computerized symbolic computation and truncated Painleve expansion, we then obtain an auto-Backlund transformation and types of the solitonic and other exact analytic solutions to the model, with the solitary waves as a special case, able to be dealt with the powerful Wu method. Based on the results, we later propose some possibly observable effects for the future experiments, and in the end, provide a possible way to explain the regular structure of the open-sea ice break-up observations.

Superlensing effect in liquid surface waves.

We present experimental observations and numerical simulations of superlensing effect in liquid surface waves. We use rigid cylinders to create a two-dimensional periodic lattice, in which liquid surface waves propagate. Through the observation of a superlensing effect, we demonstrate the existence of negative refraction in surface waves. In addition, a complete band gap is found.