bluuebunny/crossref_metadata_2025 huggingface dataset:
Low-frequency sound propagation in a quasi-one-dimensional flow
Authors: Mani R.
Published: April 2006

A systematic low-frequency theory is developed for the propagation of one-dimensional sound waves in a variable-area duct. The mean flow in the duct is assumed to be isentropic, compressible, and one-dimensional. Two applications are made of the theory. One concerns the reflexion coefficient from a pipe-nozzle combination, in which case comparisons are also made with some experimental data. In the second application, we consider the case of a sonic throat separating subsonic and supersonic flow. In this case, if the mean Mach number distribution in addition to being unity at the throat is also stationary at the throat, there is an axial ‘boundary-layer’ region in which the impedance of the sound wave changes from a fundamentally unsteady (reflexion-free) value at the sonic throat to the quasi-steady value away from the throat.
A Fourier approximation method for steady water waves
Authors: Rienecker M. M. , Fenton J. D.
Published: April 2006

A method for the numerical solution of steadily progressing periodic waves on irrotational flow over a horizontal bed is presented. No analytical approximations are made. A finite Fourier series, similar to Dean's stream function series, is used to give a set of nonlinear equations which can be solved using Newton's method. Application to laboratory and field situations is emphasized throughout. When compared with known results for wave speed, results from the method agree closely. Results for fluid velocities are compared with experiment and agreement found to be good, unlike results from analytical theories for high waves.

The problem of shoaling waves can conveniently be studied using the present method because of its validity for all wavelengths except the solitary wave limit, using the conventional first-order approximation that on a sloping bottom the waves at any depth act as if the bed were horizontal. Wave period, energy flux and mass flux are conserved. Comparisons with experimental results show good agreement.
The absorption of wave energy by a three-dimensional submerged duct
Authors: Thomas J. R.
Published: April 2006

It has been shown (Evans 1976) that the power absorbed by a general, axisymmetric body depends solely upon the added-mass and damping coefficients. These coefficients are fundamental properties of the body, representing the component of the force on the body proportional to the acceleration and velocity of the body respectively in the radiation problem, where the body is forced to oscillate in the absence of incoming waves.

In the present paper these coefficients are determined by solution of the radiation problem, for a mouth-upward cylindrical duct situated on the sea bed and fitted with a piston undergoing forced oscillations. The added-mass and damping coefficients are then used to study the power absorption properties of the duct when the power take-off is modelled by a linear-spring–dashpot system attached to the piston. Curves of the added mass, damping coefficients and absorption length (a measure of the power absorbed) as functions of wavenumber are presented, for different duct diameters and different depths of submergence.
Spectral modelling of homogeneous non-isotropic turbulence
Authors: Cambon C. , Jeandel D. , Mathieu J.
Published: April 2006

The paper describes a method to calculate homogeneous anisotropic turbulent fields associated with a constant mean velocity gradient. The equations governing the Fourier transform of the triple velocity correlations are closed by using an extended eddy-damped quasi-normal approximation. An angular parametrization of the second-order spectral tensor is introduced in order to integrate analytically all the directional terms over a spherical shell. Numerical solutions of the model are presented for typical homogeneous anisotropic flows.
The extended Rayleigh theory of the oscillation of liquid droplets
Authors: Morrison C. A. , Leavitt R. P. , Wortman D. E.
Published: April 2006

The Rayleigh theory of oscillation of liquid drops is extended to include the effects of viscosity and a uniform external electric field. The resonant frequencies of the modes of the drop are shown to be shifted by the electric field. The magnitude and sign of the frequency shift depends on the dielectric constant of the drop. The condition for instability of drops in large electric fields is given and found to differ from that given by previous workers. This difference is attributed to the assumption by previous workers that the drops, under the influence of an electric field, distort into ellipsoids of revolution about the field direction. The dynamical equations are derived and the solution for small oscillations is given in an oscillating field and in an amplitude-modulated optical field.
Fully developed MHD turbulence near critical magnetic Reynolds number
Authors: Léorat J. , Pouquet A. , Frisch U.
Published: April 2006

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.

This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.

We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.

We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).
On the mechanism of wall turbulence
Authors: Perry A. E. , Chong M. S.
Published: April 2006

In this paper an attempt is made to formulate a model for the mechanism of wall turbulence that links recent flow-visualization observations with the various quantitative measurements and scaling laws established from anemometry studies. Various mechanisms are proposed, all of which use the concept of the horse-shoe, hairpin or ‘A’ vortex. It is shown that these models give a connection between the mean-velocity distribution, the broad-band turbulence-intensity distributions and the turbulence spectra. Temperature distributions above a heated surface are also considered. Although this aspect of the work is not yet complete, the analysis for this shows promise.
Motion of a particle generated by chemical gradients Part 1. Non-electrolytes
Authors: Anderson J. L. , Lowell M. E. , Prieve D. C.
Published: April 2006

When a particle is placed in a fluid in which there is a non-uniform concentration of solute, it will move toward higher or lower concentration depending on whether the solute is attracted to or repelled from the particle surface. A quantitative understanding of this phenomenon requires that the equations representing conservation of mass and momentum within the fluid in the vicinity of the particle are solved. This is accomplished using a method of matched asymptotic expansions in a small parameter L/a, where a is the particle radius and L is the length scale characteristic of the physical interaction between solute and particle surface. This analysis yields an expression for particle velocity, valid in the limit L/a → 0, that agrees with the expression obtained by previous researchers. The result is cast into a more useful algebraic form by relating various integrals involving the solute/particle interaction energy to a measurable thermodynamic property, the Gibbs surface excess of solute Γ. An important result is that the correction for finite L/a is actually O(Γ/C∞a), where C∞ is the bulk concentration of solute, and could be O(1) even when L/a is orders of magnitude smaller.
On the extrication of large objects from the ocean bottom (the breakout phenomenon)
Authors: Foda Mostafa A.
Published: April 2006

An analytical theory is developed to describe how negative pressure, (or ‘mud suction’, as it is sometimes referred to) develops underneath a body as it detaches itself from the ocean bottom. Biot's quasistatic equations of poro-elasticity are used to model the ocean bottom, and a general three-dimensional time-dependent analysis of the problem is worked out first using the boundary-layer approximation recently proposed by Mei and Foda. Then, explicit leading-order analytical solutions are presented for the problems of extrication of slender bodies as well as axisymmetric bodies from the ocean bottom.
Flow of fluid of non-uniform viscosity in converging and diverging channels
Authors: Hooper Alison , Duffy B. R. , Moffatt H. K.
Published: April 2006

It is shown that the well-known Jeffery–Hamel solution of the Navier–Stokes equations admits generalization to the case in which the viscosity μ and density ρ are arbitrary functions of the angular co-ordinate θ. When |Rα| [Lt ] 1, where R is the Reynolds number and 2α the angle of divergence of the planes, lubrication theory is applicable; this limit is first treated in the context of flow in a channel of slowly varying width. The Jeffery–Hamel problem proper is treated in §§ 3–6, and the effect of varying the viscosity ratio λ in a two-fluid situation is studied. In § 5, results already familiar in the single-fluid context are recapitulated and reformulated in a manner that admits immediate adaptation to the two-fluid situation, and in § 6 it is shown that the singlefluid limit (λ → 1) is in a certain sense degenerate. The necessarily discontinuous behaviour of the velocity profile as the Reynolds number (based on volume flux) increases is elucidated. Finally, in § 7, some comments are made about the realizability of these flows and about instabilities to which they may be subject.
Quasilinear approximation for the spectrum of wind-generated water waves
Authors: Janssen Peter A. E. M.
Published: April 2006

According to Miles’ theory of wind-wave generation, water waves grow if the curvature of the wind profile at the critical height is negative. As a result, the wind profile changes in time owing to the transfer of energy to the waves. In the quasilinear approximation (where the interaction of the waves with one another is neglected) equations for the coupled air–water system are obtained by means of a multiple-time-scale analysis. In this way the validity of Miles’ calculations is extended, thereby allowing a study of the large-time behaviour.

While the water waves grow owing to the energy transfer from the air flow, the waves in turn modify the flow in such a way that for large times the curvature of the velocity profile vanishes. The amplitude of the waves is then limited because the energy transfer is quenched.

In the high-frequency range the asymptotic wave spectrum is given by a ‘–4’ law in the frequency domain rather than the ‘classical’ ‘–5’ law.
Theory for electric charging in turbulent pipe flow
Authors: Abedian Behrouz , Sonin Ain A.
Published: April 2006

Basec on somewhat simplified profiles of turbulent eddy diffusivity and mean vcLacity in turbulent flow, an expression is derived for the convection current in a pipe where electrification occurs at the wall. The expression is in explicit analytic form, and applies for all turbulent Reynolds numbers and all fluid conductivities, from conditions where the Debye length is small compared with the diffusion sublayer (typical aqueous solutions) to conditions where the Debye length is large compared with the sublayer (typical liquid hydrocarbons).
On the spreading of a turbulent spot in the absence of a pressure gradient
Authors: Wygnanski I. , Zilberman M. , Haritonidis Joseph H.
Published: April 2006

We derive a path-integral representation for the effective diffusion function of a passive scalar field. We use it to calculate the long-time effective diffusivity in Gaussian turbulence in the near-Markovian limit. Our results confirm the negative effect of vorticity predicted by previous discussions. They also demonstrate that the helicity of the turbulence when present may be as important an influence as the vorticity.
Turbulent Couette flow between concentric cylinders at large Taylor numbers
Authors: Smith G. P. , Townsend A. A.
Published: April 2006

Measurements have been made of the Couette flow in the annular space between concentric cylinders with a radius ratio of 1.5, the outer cylinder being held stationary and the inner one rotated at speeds to give Taylor numbers in the range 1.0 × 104−2.3 × l06 times the critical value for first instability of the steady viscous flow. Mean velocities have been measured both with Pitot tubes and with linearized hot-wire anemometers, and turbulent intensities and stresses, frequency spectra and space-time correlations have been obtained using single hot-wire anemometers of X-form and linear arrays of eight single-wire anemometers. For Taylor-number ratios to the critical number less than 3 × l05, the most prominent feature of the flow is a system of toroidal eddies, encircling the inner cylinder and uniformly spaced in the axial direction with nearly the separation of the Taylor vortices of the viscous instability. They are superimposed on a background of irregular motion and, except within the thin wall layers, the toroidal eddies contribute more to the total intensity. With increase of rotation speed, the toroidal eddies lose their regularity, and they cannot be clearly distinguished at Taylor-number ratios beyond 5 × l05.

The change of flow type from quasi-regular toroidal to fully irregular turbulent takes place over an extensive range of Taylor-number ratio centred near 3 × l05, and it may be linked with changes in the thin wall layers that separate the flow boundaries from the central region of nearly constant circulation. For ratios over 5 × l05, an appreciable part of the wall layers is comparatively unaffected by flow curvature and has a logarithmic distribution of mean velocity similar to that found in channel flows. It is suggested that the motion in the wall layers changes from a set of Gortler vortices characteristic of curved-wall flow to the more irregular motion found on plane walls, causing the toroidal eddies to break into sections of length ranging from a considerable fraction of the flow perimeter to nearly the separation of the cylinders. Changes in the frequency spectra of the radial and azimuthal velocit'y fluctuations are consistent with such a change.
Generalized vortex methods for free-surface flow problems
Authors: Baker Gregory R. , Meiron Daniel I. , Orszag Steven A.
Published: April 2006

The motion of free surfaces in incompressible, irrotational, inviscid layered flows is studied by evolution equations for the position of the free surfaces and appropriate dipole (vortex) and source strengths. The resulting Fredholm integral equations of the second kind may be solved efficiently in both storage and work by iteration in both two and three dimensions. Applications to breaking water waves over finite-bottom topography and interacting triads of surface and interfacial waves are given.
Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film – exact solution
Authors: Sadhal S. S. , Johnson Robert E.
Published: April 2006

In this investigation the creeping flow due to the motion of a liquid drop or a bubble in another immiscible fluid is examined when the interface is partially covered by a stagnant layer of surfactant. The associated boundary-value problem involves mixed boundary conditions at the interface, which lead to a set of dual series equations. An inversion of these equations yields the exact solution to the stagnant cap problem.

Several useful results are obtained in closed form. Among these are the expressions for the drag force, the difference between the maximum and the minimum interfacial tensions, and the amount of adsorbed surfactant. A shifting of the centre of the internal vortex is observed.
Oscillating-grid turbulence including effects of rotation
Authors: Dickinson Stuart C. , Long Robert R.
Published: April 2006

Experiments were performed to investigate some aspects of turbulence in rotating and non-rotating fluid systems where the turbulence was induced by a horizontal grid oscillating vertically. An earlier theory by the second author made use of a planar source of energy, which appeared to be similar to the energy source of the grid, in determining the characteristics of the turbulence at points some distance away. The simplicity of the theory was in the parameterization of the grid ‘action’ by a single quantity K, with dimensions and characteristics of eddy viscosity.

The experimental results provide additional confirmation of the theory in the non-rotating case, and indicate the usefulness of the idealized energy source in the rotating case. In the latter, we measured the propagation of the front separating disturbed and undisturbed fluid, moving along the axis of rotation. The thickness d(t) of the disturbed region increases at first as (Kt)½, as in a non-rotating fluid, until the Rossby number K/Ωd2k becomes of order unity.

Beyond this the disturbances are wavelike and rotationally dominated, and the thickness now increases linearly with time, yielding a speed of propagation for the front proportional to the wave speed (KΩ)½. Finally, the disturbances reach the bottom and the vessel is in statistical steady state. Then a region of thickness dk independent of time is found, and it contains motion that resembles ordinary, three-dimensional turbulence. dk ∼ (K/Ω)½ is analogous to the depth of the turbulent Ekman layer H ∼ (K/Ω)½, where K is taken as an eddy viscosity.

McEwan constructed a similar rotating experiment, although with a different energy source, and observed vortices parallel to the axis of rotation, provided that the Rossby number was less than a critical value. Our observations and theory indicate that the disappearance of the vortices corresponds to h < dk, where h is the total depth of the fluid. At that point, the whole tank is filled with three-dimensional turbulence.
Interfacial stability of binary mixtures evaporating at reduced pressure
Authors: Bose Arijit , Palmer Harvey J.
Published: April 2006

When a liquid evaporates under vacuum, its free surface is potentially unstable to local variations in evaporative flux, surface depressions being produced by the recoil force of the departing vapour and sustained convection in the liquid being driven by the shearing action of the vapour on the distorted liquid surface. For a binary mixture, local variations in evaporative flux may be produced by fluctuations in both surface concentration and temperature. With the aid of linear hydrodynamic-stability theory, this paper examines the extents to which key mass-transfer properties affect the interfacial stability of the system. The mass-transfer aspects that distinguish this problem from its heat-transfer analogue centre on the dependence of relative volatility on temperature and composition as well as the importance of the bulk-flow term in Fick's law. Results indicate that the stability criteria for interfacial convection are extremely sensitive to the difference in volatility between the two components, that the destabilizing effects of surface concentration and temperature on evaporative flux are additive in determining stability limits, and that for certain operating pressures spontaneous convection can only be induced by adverse concentration gradients. Attention is limited to low-surface-tension mixtures for which there are no concentration effects on surface tension (Marangoni instability).
The meniscus on a needle – a lesson in matching
Authors: Lo Lilian L.
Published: April 2006

We reconsider the second approximation for the height of the meniscus on a slender vertical cylinder, which has been calculated by James using the method of matched asymptotic expansions. Fraenkel has warned that the asymptotic matching principle may fail in certain cases, and we confirm that failure here. This meniscus problem is used to discuss the kind of failures that may occur if Fraenkel's restricted form of the matching principle is not used. A less restricted matching principle is also suggested in this paper. With this matching principle, we show that the last known term of order Re3 In Re in the drag on a sphere in low-Reynolds-number flow is correct, even though it was found in a way that violates Fraenkel's warning.
The primary electroviscous effect in a suspension of spheres with thin double layers
Authors: Hinch E. J. , Sherwood J. D.
Published: April 2006

We study the primary electroviscous effect in a suspension of spheres when the double layer thickness κ−1 is small compared with the particle radius a. The case of a 1–1 symmetric electrolyte is examined using the methods of Dukhin & coworkers (1974), whilst the asymmetric electrolyte is studied along lines similar to those of O'Brien (1983). Sherwood's (1980) asymptotic results for high surface potentials and high Hartmann numbers are extended and complemented.
The laminar unsteady flow of a viscous fluid away from a plane stagnation point
Authors: Hommel Mark J.
Published: April 2006

The development with time of the impulsively started laminar flow of a viscous fluid away from a stagnation point is investigated. A series expansion in time is formulated for the shear stress and displacement thickness. This series expansion is obtained from a numerical solution of the full Navier–Stokes equations, and 44 terms are computed for the shear-stress series. The series is analysed and series-improvement techniques are employed to improve its convergence properties. The final series that results converges even for infinite time, and acceptable agreement with the Proudman & Johnson calculations of shear stress for steady-state flow at a stagnation point is obtained. Only 17 terms in the displacement-thickness series are reported, owing to numerical difficulties which are considerably more of an obstacle than in the shear-stress calculation. However, it is observed that the displacement thickness grows exponentially with time. Acceptable agreement with calculations of Proudman & Johnson is obtained for small time. For dimensionless time greater than 2.5, it is concluded that not enough terms are known to extrapolate the displacement-thickness series further.
The reflection of obliquely incident tsunamis
Authors: Carrier George F. , Noiseux Claude F.
Published: April 2006

When a tsunami is incident on a plane shelf, the waveform and amplitude of the reflected wave differ significantly from those of the incident wave, and, when the shelf has the extremely irregular character of real continental shelves, the contrast between the two amplitudes is even greater. Here we quantify these statements and we also give an account of the manner in which the run-up depends on the obliquity and on other parameters characterizing the incident wave.
Attenuated wave-induced drift in a viscous rotating ocean
Authors: Weber Jan Erik
Published: April 2006

Mean drift currents due to spatially periodic surface waves in a viscous rotating fluid are investigated theoretically. The analysis is based on the Lagrangian description of motion. The fluid is homogeneous, the depth is infinite, and there is no continuous energy input at the surface. Owing to viscosity the wave field and the associated mass transport will attenuate in time. For the non-rotating case the present approach yields the time-decaying Stokes drift in a slightly viscous ocean. The analysis shows that the drift velocities are finite everywhere. In a rotating fluid it is found that the effect of viscosity implies a non-zero net mass transport associated with the waves, as opposed to the result of no net transport obtained from inviscid theory (Ursell 1950).
Generalized energy methods in electrohydrodynamic stability theory
Authors: Deo B. J. S. , Richardson A. T.
Published: April 2006

A generalized energy stability analysis necessarily incorporating charge-diffusion effects is applied to an electrohydrodynamic equilibrium comprising a dielectric liquid confined between two planar electrodes and subjected to an injection of unipolar charge. Generalized energy, kinetic-charge and mixed-type functionals are considered. Using the physical constraint that the sign of space-charge density can never change, it is possible to bound the nonlinear terms in the functional evolution equations. Sufficient conditions to guarantee global monotonic stability in the mean are then derived. In the case of a strong injection of charge the mixed-type functional provides theoretical values of the stability parameter close to the experimental values. Sufficient conditional stability bounds are also obtained for the leading-order diffusion-free equilibrium.
Numerical analysis of the flow through a corrugated tube with application to arterial prostheses
Authors: Savvides C. N. , Gerrard J. H.
Published: April 2006

Steady and oscillating axisymmetric laminar flows are determined by a finite-difference solution of the vorticity and continuity equations for an incompressible fluid contained in a straight concertina-shaped tube far from its ends. In steady flow the size of the wall corrugations is varied as well as the Reynolds number of the flow. In unsteady flow one tube geometry is studied, and the parameters varied are the Reynolds number, the ratio of the mean volume flow rate to its amplitude, and the frequency of oscillation. The analysis produces streamlines, particle paths and the pressure difference across a length of the tube. The resistance to the flow is determined in terms of an equivalent cylindrical tube diameter.

In steady flow the onset of flow separation and the growth of the separated region of flow is determined. The equivalent diameter is found to be principally a function of the product of Reynolds number and the non-dimensional pressure difference. This product depends on the height of the wall corrugations and less strongly on Reynolds number and the length of the corrugations. Resistance increases with increasing height of the corrugations. Comparison is made with other computational and experimental values of the pressure difference.

In unsteady flow the mean velocity to amplitude ratio has little effect except on the particle paths. The flow pattern is found to be governed by the Stokes number (radius × (2π/(kinematic viscosity × period))½) and the Reynolds number. There is a region of quasi-steady flow at the time of zero acceleration at maximum flow, but unsteady flow in between. The mixing produced by radial convection is restricted to the outer parts of the tube where the wall is corrugated. In oscillating flow the resistance relative to a cylindrical tube decreases as frequency and Reynolds number increase.

In the medical application of the work the concern is whether sustained stagnant regions occur in the corrugations and whether there is a large change in resistance relative to a cylindrical tube. This part of the investigation was made with an arterial waveform which contained six harmonics. It is found that there are no regions of stagnant fluid in the range of parameters considered. The difference between the variation with the flow parameters of the resistance of the corrugated tube and of a cylindrical tube was found not to be large.
Turbulent gravity-stratified shear flows
Authors: Chu Vincent H. , Baddour Raouf E.
Published: April 2006

Two simple turbulent shear flows, namely a surface jet and a mixing layer, under the influence of stable gravity stratification, were investigated experimentally. The shear flows were generated in the laboratory by letting fresh water flow over saline water in a two-dimensional channel. Velocity and salinity measurements were made using a hot-film probe and a single-electrode conductivity probe. The experimental results for the two flows were correlated each using a different set of length and velocity scales. The initial development of the flows was relatively unaffected by the stable stratification. As the shear flows grew in thickness, they were observed to have a tendency to approach a ‘neutrally stable state’ in which the turbulent motion neither extracted energy from nor lost energy to the mean flow. The gradient Richardson number in this neutrally stable state was found to have the critical value predicted by linear inviscid stability theory. The decay of turbulent intensity in the longitudinal direction was observed to follow a power-law relationship similar to the one obtained by Comte-Bellot & Corrsin (1966) for the decay of grid-generated turbulence.
A turbulent-transport model for concentration fluctuations and fluxes
Authors: Sykes R. I. , Lewellen W. S. , Parker S. F.
Published: April 2006

A second-order closure model describing the diffusion of a passive scalar from a small source is presented. The model improves upon the earlier work of Lewellen & Teske (1976) by ensuring the early stage of the release, the so-called meander phase, is accurately described. In addition to the mean concentration and scalar fluxes, a model equation for the evolution of the scalar variance is proposed. The latter introduces a new lengthscale which represents the scale of the concentration fluctuations. The model predictions are compared with the recent experimental data of Fackrell & Robins (1982a, b).
Velocity characteristics in the turbulent near wakes of confined axisymmetric bluff bodies
Authors: Taylor A. M. K. P. , Whitelaw J. H.
Published: April 2006

Measurements of the velocity characteristics and wall pressure are reported for the axisymmetric turbulent flow downstream of three bluff bodies (disks of 25% and 50% area blockage and a cone of 25% blockage) confined by a long pipe. The dimensions of the recirculation regions were found from the mean-velocity components, which were determined by a laser-Doppler velocimeter: the corresponding components of Reynolds stress were also recorded. The lengths and maximum widths of the recirculation bubbles (in bluff-body diameters), recirculating mass-flow rates (normalized by the average velocity in the plane of the baffle, U0, and the baffle diameter) and maximum turbulent kinetic energy (normalized by U02) were as follows: cone 1.55, 0.55, 0.19, 0.11; disk (25% blockage) 1.75, 0.62, 0.31, 0.19; disk (50% blockage) 2.20, 0.55, 0.26, 0.16. The increase in recirculation length with blockage is opposite to the trend in unconfined, annular jets. The distribution of Reynolds stresses is strongly dependent on blockage: for the smaller blockage both the disk and the cone have the maximum value of kinetic energy near the rear stagnation point. It is proposed that this is because the generation of turbulence by normal stresses is more important in the flow consequent on the smaller blockage.

The measurements include profiles of the velocity characteristics at, as well as upstream of, the trailing edges of the baffles for use as boundary conditions in numerical solutions of the equations of motion.
LDV measurements of an air-solid two-phase flow in a vertical pipe
Authors: Tsuji Yutaka , Morikawa Yoshinobu , Shiomi Hiroshi
Published: April 2006

Measurements of air and solid-particle velocities were made in a vertical pipe two-phase flow by the use of a laser-Doppler velocimeter (LDV). Five kinds of plastic particles, diameters of which ranged from about 3 mm to 200 μm, were transported in a vertical pipe of 30 mm inner diameter. It was found that, the smaller the particle size, the flatter was the mean air velocity distribution for the same mass flow ratio of solids to air. Large particles increased air turbulence throughout the pipe section, while small particles reduced it. Both effects of promotion and suppression of turbulence were observed at the same time in the presence of particles of medium size, that is, the turbulence was increased around the pipe centre and reduced near the wall. The frequency spectrum of air turbulence normalized by the turbulence intensity was not changed by the large particles. In the presence of the small particles, the higher-frequency parts of the spectrum increased.
Turbulent flow over large-amplitude wavy surfaces
Authors: Buckles Jeffrey , Hanratty Thomas J. , Adrian Ronald J.
Published: April 2006

The laser-Doppler velocimeter is used to measure the mean and the fluctuating velocity for turbulent flow over a solid sinusoidal wave surface having a wavelength λ of 50.8 mm and a wave amplitude of 5.08 mm. For this flow, a large separated region exists, extending from x/λ = 0.14 to 0.69. From the mean velocity measurements, the time-averaged streamlines and therefore the extent of the separated region are calculated. Three flow elements are identified: the separated region, an attached boundary layer, and a free shear layer formed by the detachment of the boundary layer from the wave surface. The characteristics of these flow elements are discussed in terms of the properties of the mean and fluctuating velocity fields.
Cavitation phenomena within regions of flow separation
Authors: Katz Joseph
Published: April 2006

The phenomenon of cavitation inception was studied on four axisymmetric bodies whose boundary layers underwent a laminar separation and subsequent turbulent reattachment. The non-cavitating flow was studied by holographic and schlieren flow-visualization techniques. Surface distributions on the mean and the fluctuating pressures were also measured. The conditions for cavitation inception and desinence were determined and holograms were recorded just prior to and at the onset of cavitation. The population of microbubbles and the subsequent development of visible cavitation was determined from the reconstructed image. In every case the appearance of visible cavitation was preceded by a cluster of microscopic bubbles in a small portion of the flow field providing clear evidence that cavitation is initiated from small nuclei. The inception zone was located within the turbulent shear layer downstream of transition and upstream of the reattachment region of the bodies with large separation regions. The location and the shape of this cavitation suggested a relation to the mixing-layer eddy structure. The inception region on the body with the smallest separation zone, a hemisphere-cylinder body, was located in the reattachment region, but the cavities were still detached from the surface. Instantaneous minimum-surface-pressure measurements do not account for observed cavitation-inception indices except for the hemisphere body, where the correlation is satisfactory. The rate of cavitation events was estimated from measurements of nuclei population, and fluctuating-pressure statistics in the portion of the flow susceptable to cavitation. It was demonstrated for the hemisphere body that at least one such cavitation event could occur every second. These findings are consistent with what is observed visually at the onset of cavitation and support the location of inception determined holographically.
Two-phase displacement in Hele-Shaw cells: experiments on viscously driven instabilities
Authors: Park C.-W. , Gorell S. , Homsy G. M.
Published: April 2006

Experiments on the instability of the interface in two-phase displacements in Hele-Shaw cells were conducted using air and a viscous oil as the working fluids. The experiments had two objectives: (i) to provide quantitative measurements of the growth constants of the instability which occurs when a less-viscous fluid displaces a more-viscous one, and (ii) to compare the measured dispersion relations with the predictions of the recent theory of Park & Homsy (1984). The experiments were made by analysing the growth characteristics of between 10 and 20 Fourier modes describing the shape of the interface between displaced and displacing fluids, using still photography. For capillary numbers Ca = μU/γ less than approximately 4 × 10−3 the agreement is only fair, owing to substantial edge effects produced by a nearly static contact line near the lateral boundaries of the cell. For 4 × 10−3 < Ca < 1 × 10−2 theory and experiment agree to within the accuracy of the measurements. Location and verification of the behaviour of modes near the predicted cut-off wavenumber give partial verification of the theory of Park & Homsy.
Air flow and dispersion in rough terrain: a report on Euromech 173
Authors: Hunt J. C. R. , Lalas D. P. , Asimakopoulos D. N.
Published: April 2006

Euromech Colloquium 173 was held at Delphi from 13-16 September 1983. Thirty-six participants from eleven countries were present. Papers were presented on: (1) various approaches to calculating and computing air flow in rough terrain in the presence of changes in surface roughness, elevation and temperatures, including methods for interpolating, subject to certain physical constraints, the wind field from measurements at various fixed stations; (2) measurement and satellite photography of air flow in rough terrain near isolated mountains, near coastlines, over mountains, and over mountains near coastlines; (3) the applications of these studies to air-pollution dispersion and the exploitation of wind energy in rough terrain. The discussions led to agreement about how best to use and relate the various techniques for calculating air flows, the role of new techniques in remote sensing for improving understanding of flow in rough terrain, the factors determining air-pollution concentration that need particular study, and the special kinds of information about turbulence needed for estimating wind energy in rough terrain.
Shear dispersion and residence time for laminar flow in capillary tubes
Authors: Houseworth J. E.
Published: April 2006

The behaviour of passive tracer particles in capillary Poiseuille flow is investigated with regard to the residence time in short axial sections of length z, in which z/a < Va/D, where a is the capillary radius, V is the mean velocity and D the coefficient of molecular diffusion. While methods exist for calculating moments of the cross-sectionally averaged axial concentration distribution as a function of time (e.g. Smith 1982b), much less is known about the distribution of residence time as a function of axial distance. An approximate theoretical solution for point sources in high-Péclet-number flows reveals that the mean residence time 〈t(z)〉, which is asymptotic to z/V0 near the source, will then rise faster than z/V0 before converging to z/V for large z, provided the source is not at the capillary wall. V0 is the advective velocity at the point of release. The variance 〈t2(z)〉 is found to increase initially in proportion to z3 provided the source is not at the capillary wall or on the axis. A Monte Carlo method based on the solution to the diffusion equation in the capillary-tube cross-section is developed to compute particle trajectories which are used to analyse both axial and residence-time distributions. The residence-time distribution is found to display significant changes in character as a function of axial position, for both point sources and a uniform flux of particles along the tube.
Nonlinear convection in high vertical channels
Authors: Normand C.
Published: April 2006

Application of Landau's ideas to the theory of weakly nonlinear instabilities shows that the amplitude of the unstable modes behaves as the square root of the reduced control parameter ε, its critical value being ε = 0. When applied to cellular structures the theory has been improved by taking into account the slow spatial variations of the amplitude and phase of the unstable modes. Until now the case of thermo-convective instabilities in high vertical channels has not been studied using this approach. In high vertical structures the nonlinear terms disappear in the limit of an infinite height, and the supercritical behaviour requires a specific treatment. It differs from the standard analysis valid for the case of fluid layers of infinite horizontal extent, where the nonlinearities and the finite-size effects are disconnected. In the limit of high aspect ratios (height [Gt ] horizontal extent) we have derived an amplitude equation for convective systems where the nonlinear terms contain derivatives at the lowest order. As a consequence the amplitude equation cannot be put into a variational form and the stability of the stationary solutions cannot be deduced from an ordering in decreasing values of a Lyapunov functional.
Experiments on transient natural convection in a cavity
Authors: Ivey G. N.
Published: April 2006

A laboratory experiment is used to study the transient flow in an initially isothermal cavity at temperature T0 following the rapid change of the two vertical endwalls to temperatures T0 ± ΔT respectively. Individual temperature records are taken and the transient flow in the entire cavity is visualized with the aid of a tracer technique. It is shown that an oscillatory approach to final steady-state conditions exists for certain flow regimes, although the form of the oscillatory response is different to that suggested by previous work. It is argued that this oscillatory behaviour is due to the inertia of the flow entering the interior of the cavity from the sidewall boundary layers, which may lead to a form of internal hydraulic jump if the Rayleigh number is sufficiently large.
A unified description of two-layer flow over topography
Authors: Baines Peter G.
Published: April 2006

Observations of the flow of a two-layer fluid resulting from the motion of a towed streamlined two-dimensional obstacle are described in some detail. The experiments were designed to further our understanding of the factors governing the nature and magnitude of upstream disturbances in the general flow of stratified fluid over two-dimensional topography, and predictions for arbitrary two-dimensional flows are made from the results of these experiments. In particular, the relationship between uniformly stratified flow and single-layer flow over topography is suggested. Most of the observed features of interest in these experiments are nonlinear in character. Relatively complete descriptions of the observed flows are presented over a wide range of parameter values, and the phenomena observed include upstream undular and turbulent bores, bores with zero energy loss, ‘rarefactions’ (in which the interface height changes monotonically over a transition region of continuously increasing length), and downstream hydraulic drops and jumps. Their properties are shown to be broadly consistent with predictions from a two-layer hydrostatic model based on continuity and momentum considerations, which employs jump criteria and rarefaction equations where appropriate. Bores occur because of nonlinear steepening when the layer containing the obstacle is thinner than the other, and rarefactions occur when this layer thickness is comparable with or greater than that of the other layer. The speed and amplitude of the upstream bores are governed by nonlinear effects, but their character is determined by a balance between nonlinear steepening, wave dispersion and interfacial friction when the bore is non-turbulent.

Experimental evidence is presented for two types of hysteresis or ‘multiple equilibria’ - situations where two different flow states may exist for the same external steady conditions. In the first of these hysteresis types, the upstream flow may be supercritical or consist of an upstream bore state. It is analogous to the type anticipated for single-layer flow by Baines & Davies (1980) and described numerically by Pratt (1983), but it is only found experimentally for part of the expected parameter range, apparently because of interfacial stress effects. The second hysteresis type is new, and involves the presence or absence of a downstream hydraulic drop and following jump.
A numerical study of vortex interaction
Authors: Bromilow I. G. , Clements R. R.
Published: April 2006

Flow visualization has shown that the interaction of line vortices is a combination of tearing, elongation and rotation, the extent of each depending upon the flow conditions. A discrete-vortex model is used to study the interaction of two and three growing line vortices of different strengths and to assess the suitability of the method for such simulation.

Many of the features observed in experimental studies of shear layers are reproduced. The controlled study shows the importance and rapidity of the tearing process under certain conditions.
Proximity-induced galloping of two interfering circular cylinders
Authors: Bokaian A. , Geoola F.
Published: April 2006

Experiments were conducted to investigate the response of a rigid two-dimensional elastically mounted smooth circular cylinder, with oscillations restricted to a plane normal to the incident flow, as influenced by the vicinity of an identical fixed body placed inside the wake. The static lift and drag coefficients, as well as the vibration amplitude and frequency of the upstream cylinder as functions of relative position of the pair of cylinders are given. Most measurements were carried out under two conditions of free-stream turbulence. Whilst turbulence decreased the magnitude of drag coefficients, it had no appreciable effect on lift coefficients. The forces on the upstream body were found to be influenced by the proximity to the downstream one in a significant way only when the streamwise spacing is less than two diameters.

In the dynamic tests, two kinds of instability, namely a vortex-resonance and galloping, were observed, with the latter only occurring when the downstream cylinder was well submerged in the near wake of the upstream one. The vortex-shedding frequency was always found to lock to oscillation frequency. Whereas the vibration characteristics remained essentially unaffected with changing turbulence intensity, the galloping amplitudes were observed to be sensitive to cylinders’ aspect ratio. A quasi-steady theory was developed to predict the galloping behaviour.
Laminar entrance flow in a curved pipe
Authors: Soh W. Y. , Berger S. A.
Published: April 2006

The full elliptic Navier–Stokes equations have been solved for entrance flow into a curved pipe using the artificial compressibility technique developed by Chorin (1967). The problem is formulated for arbitrary values of the curvature ratio and the Dean number. Calculations are carried out for two curvature ratios,a/R= 1/7 and 1/20, and for Dean number ranging from 108.2 to 680.3, in a computational mesh extending from the inlet immediately adjacent to the reservoir to the fully developed downstream region.

Secondary flow separation near the inner wall is observed in the developing region of the curved pipe. The separation and the magnitude of the secondary flow are found to be greatly influenced by the curvature ratio. As observed in the experiments of Agrawal, Talbot & Gong (1978) we find: (i) two-step plateau-like axial-velocity profiles for high Dean number, due to the secondary flow separation, and (ii) doubly peaked axial-velocity profiles along the lines parallel to the plane of symmetry, due to the highly distorted secondary-flow vortex structure.