Liquid Surface Waves Research Articles

Continuum mechanics and its applications

Part 1 Mechanics of solids: the problem of Boussinesq and Cerruti, N.Sneddon nonlinear wave propagation in composites, M.McCarthy continuum thermodynamics of electrical hysteresis in ceramics, G.Maugin and E.Bassiouny. Part 2 Fluid mechanics: turbulent transport and the random occurrence of coherent events, A.Newell et al waves in shear-flows, S.Maslowe canonical equations of long wave, weakly non-linear asymptotics, R.Rosales dispersion and attenuation of surface waves in viscous liquids, P.Le Blond et al the Jeffrey paradox, S.Smith a numerical study of large bubble dynamics, R.Rowe and J.Bugg numerical approximation of the steady and unsteady euler equations of gas dynamics, K.Morton aspects of magnetic flow with non-equilibrium magnetization, R.Rosensweig and R.Johnston analysis of particles' aggregation phenomena in magnetic fluids, A.Satoh and S.Kamiyama solitons on a magnetic fluid, M.Shen the subscismic wave equation, M.Rochester vascular input impedance for arterial modes, T.Moodie and R.Gan. Part 3 Partial differential equations and foundations: continuous dependence on geometry with applications in continuum mechanics, L.Payne a new approach to PDE's with variable coefficients, B.Seymour and E.Varley.

The theory of internal and surface waves in a stratified liquid

The initial-boundary value problem for the equation of a stratified liquid in the Boussinesq approximation is considered. This models the oscillations of a stratified liquid under an ice-field that has a free surface section. A solution is constructed that is expresed explicitly in terms of the eigenfunctions of some operator V, and its behaviour at long times is investigated.

Central focusing of surface waves in shallow heavy liquid

Effects associated with the motion of circular surface waves in a liquid toward the center were considered in [1, 2]. In [3], a study was made of the generation and propagation of a wave from a bow front in the form of a circular arc. The difficulty of analytic description of these phenomena was noted. The present paper considers the results of numerical investigation of the formation and evolution of the focused long-wavelength radiation produced by an initial steady raised level of the following forms in plan: rectilinear, semicircular, circular, and regular pentagon inscribed in a circle. The obtained results are generalized to the case of a wave generator of any length, and the derived relationships make it possible to estimate the accumulation effect independently of the initial conditions if the amplitude at the crest of a radially converging wave at the moment when the motion of the free surface begins to proceed solely under the influence of gravity is determined in some manner or other. The simulation of such waves in hydraulic situations with pulsed, radially acting unsteady source is considered.

The surface tension of concentrated aqueous solutions of 1.1-electrolytes measured by means of Wilhelmy and laser light scattering methods

Surface tension measurements were made on concentrated (<4 moles/kg) aqueous solutions of the following 1.1-electrolytes: KF, KCl, KI, HCl, and HNO 3. Two different measurement techniques were used: the Wilhelmy slide method and a method based on the scattering of laser light by small amplitude liquid surface waves. The surface tension determined by the two methods agrees within ±0.5% and for each solution it is found to vary almost linearly with concentration. The shear viscosity was also measured for these solutions by means of the laser method and a standard flow viscosimeter. The measured values were found to agree within ±5%.

Surface waves and stability of free surface of a magnetizable liquid

Linear theory of surface waves in a magnetizable liquid is examined. A stability criterion for a plane-free surface of a magnetizable liquid is studied for an arbitrary magnetization law.

The evolution of a solitary wave in a nonhomogeneous medium

Using the example of surface waves in a heavy liquid, the article discusses the propagation of a solitary wave in a nonhomogeneous medium. Ananalysis is made of processes of the decomposition of a wave into solitary waves, as a function of differences in the depth.

Interaction between radiation and a superfluid liquid surface

The surface motion of a superfluid liquid due to ponderomotive effect of radiation on matter is discussed. In particular, the possibility of optical excitation of surface (capillary) waves in a superfluid liquid (He II) is considered. Under certain conditions this effect is shown to cause instability of surface waves, i.e., stimulated surface scattering of light in a superfluid liquid.

Surface Waves on Water with Depths Less than the Boundary-Layer Thickness

Equations are derived for the complex wavenumber for plane surface waves in liquids of low viscosity with depths from one-fifth to two-thirds of the boundary-layer thickness. For capillary waves, the values of the real wavenumber and of the spatial absorption coefficient are approximately proportional to (νσ)1/4, where ν is the kinematic coefficient of viscosity and σ is the real angular frequency. Numerical calculations agree with experimental values for a frequency of 20 Hz and a depth of one-half of the water boundary-layer thickness δ. For gravity waves with depths of about 14δ, the value of the real wavenumber equals that of the spatial absorption coefficient. Each is proportional to (νδ)1/2 but the coefficient is quite different from that of the main term for the absorption coefficient at intermediate depths.

Non-ohmic electron transport on liquid surfaces

A calculation of the electron distribution function and mobility is outlined for electrons on a liquid surface. Electrons are scattered by gas atoms and liquid surface waves. If surface wave scattering dominates, the mobility increases rapidly with increasing electric field in the non-ohmic region.

Moiré fringes for liquid surface wave measurement

A simple method is described for measurement of wavelength and decay of travelling waves on the surface of transparent liquids. Light transmitted through a fixed line grating is deviated by the wave-carrying surface, producing a distorted image of the grating. The moire fringes produced by projection of this optically distorted grating onto a second stationary grating permit visualisation and measurement of the waves as they travel across the surface. The wave slope can be measured at all points on the wave system, enabling decay to be calculated. The method is used to examine the effect of small additions of a polymer on surface wave properties.

Basic flows of a micropolar liquid

Steady plane shear flow, rotation flow, plane wave disturbances, oscillatory boundary layers, and free surface waves in a micropolar liquid are investigated.

Damping of surface waves in an incompressible liquid

The damping of surface waves of small amplitude in liquid contained in cylinders has been calculated. Viscous dissipation in an assumed laminar boundary layer was taken to be the primary cause of damping. Experimental results were obtained for the logarithmic decrement as a function of the ratio of liquid height to cylinder radius for several water-filled cylinders. Theory and experiment were found to be in good agreement.