Lev Shemer

On Modifications of the Zakharov Equation for Surface Gravity Waves.

The Zakharov integral equation for surface gravity waves is modified to include higher-order (quintet) interactions, for water of constant (finite or infinite) depth. This new equation is used to study some aspects of class I (4-wave) and class II (5-wave) instabilities of a Stokes wave.

The relation between the Taylor bubble motion and the velocity field ahead of it

Abstract The motion of a single elongated (Taylor) bubble propagating in a transparent vertical pipe is studied experimentally in stagnant liquid, as well as in upward and downward liquid flow. Digital image processing of a sequence of video images serves as the main experimental method for the study of the Taylor bubble motion. In addition, the distribution of the velocities in front of the bubble and in the liquid film is measured using Particle Image Velocimetry. The relation between the Taylor bubble motion and the velocity field in front of it is discussed.

Pulsating flow in a pipe

Turbulent and laminar pulsating flows in a straight smooth pipe are compared at identical frequencies and Reynolds numbers. Most measurements were made at a mean Reynolds number of 4000, but the influence of Re was checked for 2900 < Re < 7500. The period of forcing ranged from 0.5 to 5 s, with corresponding change in the non-dimensional frequency parameter α = R √(ω/ν) from 4.5 to 15. The amplitude of the imposed oscillations did not exceed 35% of the mean in order to avoid flow reversal or relaminarization. Velocities at the exit plane of the pipe and pressure drop along the pipe were measured simultaneously; velocity measurements were made with arrays of normal hot wires. The introduction of the periodic surging had no significant effect on the time-averaged quantities, regardless of the flow regime (i.e. in both laminar and turbulent flows). The time-dependent components at the forcing frequency, represented by a radial distribution of amplitudes and phases, are qualitatively different in laminar and turbulent flows. The ensemble-averaged turbulent quantities may also be represented by an amplitude and a phase; however, the non-harmonic content of these intensities increases with increasing amplitude of the imposed oscillations. A normalization procedure is proposed which relates phase-locked turbulent flow parameters in unsteady flow to similar time-averaged quantities. An integral momentum equation in a time-dependent flow requires that a triad of forces (pressure, inertia and shear) will be in equilibrium at any instant of time. All the terms in the force-balance equation were measured independently, providing a good check of data. The analysis of the experimental results suggests that turbulence adjusts rather slowly to the local mean-flow conditions. A simple eddy-viscosity model described by a complex function can account for ‘memory’ of turbulence and explain the different phase distribution in laminar and turbulent flows.

Evolution of statistical parameters of gas-liquid slug flow along vertical pipes

Abstract The evolution of hydrodynamic and statistical parameters along the pipe was studied experimentally in gas–liquid slug flow for various flow conditions and two pipe diameters. The measuring modules comprise a set of three adjacent optical fiber probes and could be easily transferred to various positions along the pipes. The probes detect the passage of the gas–liquid interface. This technique enables one to measure the instantaneous velocities of nose and tail of elongated (Taylor) bubbles simultaneously with the slug length ahead of each bubble. The liquid slug and Taylor bubble length distributions along the pipe, together with the dependence of the Taylor bubble velocity on the liquid slug length ahead of it, are presented at various locations along the pipe. Empirical correlations relating the Taylor bubble velocity with the bubble separation distance are suggested. These correlations are used as an input to a model for slug length distribution. The model results are compared with the experiments.

Experimental Investigation of the Velocity Field Induced by a Taylor Bubble Rising in Stagnant Water

An experimental investigation of the flow field around a single Taylor bubble rising in a vertical pipe filled with stagnant water is presented. The Reynolds number of the flow based on the Taylor bubble rise velocity and the pipe diameter is 4350. The velocity field around the bubble was determined by Particle Image Velocimetry (PIV). The mean velocity fields in front of the bubble, in the liquid film, and in the wake region were calculated by ensemble-averaging the instantaneous velocity fields measured around 100 different bubbles. Ensemble-averaged velocities become negligible at 0.5D from the bubble nose and at � 12 D from the bubble tail. However, notable instantaneous velocity fluctuations were found to exist up to 50D from the Taylor bubble tail. These residual vortices may influence the shape and the propagation velocity of the trailing bubble even at large separation distances. 2002 Elsevier Science Ltd. All rights reserved.

Translational velocities of elongated bubbles in continuous slug flow

The translational velocities of elongated bubbles in continuous slug flow were measured for various flow rates, pipe inclinations and pipe diameters. Measurements were carried out by cross-correlating the output signals of consecutive optical fiber probes and by image processing technique. In addition, the velocities of single elongated bubbles in a stagnant and in a flowing liquid were measured by the same techniques. For all cases the measured velocities were compared to appropriate correlations. The measured velocities of single elongated bubbles were in all cases predicted quite well by the correlations while the velocities in continuous slug flow, for certain cases, were considerably underpredicted. This discrepancy is ascribed to the influence of the dispersed bubbles in the liquid slug region. A simplified model is proposed to calculate the translational velocity in continuous slug flow. The results of the model compare well with the measured translational velocities of elongated bubbles in continuous slug flow. 2002 Elsevier Science Ltd. All rights reserved.

An experimental study of spatial evolution of statistical parameters in a unidirectional narrow-banded random wavefield

[1] Unidirectional random waves generated by a wavemaker in a 300-m-long wave tank are investigated experimentally. Spatial evolution of numerous statistical wavefield parameters is studied. Three series of experiments are carried out for different values of the nonlinear parameter e. It is found that the frequency spectrum of the wavefield undergoes significant variation in the course of the wavefield evolution along the tank. The initially narrow Gaussian spectrum becomes wider at the early stages of the evolution and then narrower again, although it still remains wider than the initial spectrum at the most distant measuring location. It is found that the values of all the statistical wave parameters are strongly related to the local spectral width. The deviations of various statistical parameters from the Gaussian statistics increase with the width of the spectrum so that the probability of extremely large (the so-called freak) waves is highest when the local spectral width attains maximum. The deviations from the Rayleigh distribution also become more pronounced when the nonlinearity parameter e is higher. It is found that the Tayfun and Fedele 3rd order random wavefield model provides an appropriate description of the observed phenomena. An attempt is made to relate the spatial variations of the wavefield statistics reported here to the wavefield recurrence, as suggested recently.

Evolution of a nonlinear wave field along a tank: experiments and numerical simulations based on the spatial Zakharov equation

Evolution of a nonlinear wave eld along a laboratory tank is studied experimentally and numerically. The numerical study is based on the Zakharov nonlinear equation, which is modied to describe slow spatial evolution of unidirectional waves as they move along the tank. Groups with various initial shapes, amplitudes and spectral contents are studied. It is demonstrated that the applied theoretical model, which does not impose any constraints on the spectral width, is capable of describing accurately, both qualitatively and quantitatively, the slow spatial variation of the group envelopes. The theoretical model also describes accurately the variation along the tank of the spectral shapes, including free wave components and the bound waves.

Energy density directional spectra of a nearshore wave field measured by interferometric synthetic aperture radar

The nearshore wave field within Monterey Bay, California, is studied using remote sensing imaging by an interferometric synthetic aperture radar (INSAR) and simultaneous ground-based measurements. It is shown that INSAR imagery of the ocean surface offers some advantages over conventional synthetic aperture radar. Because of the direct imaging mechanism of INSAR, quantitative information about the complicated wave field can be obtained. The INSAR-derived directional energy density spectra and the corresponding ground-based spectra compare well.

Evolution of hydrodynamic and statistical parameters of gas–liquid slug flow along inclined pipes

The development of slug