bluuebunny/crossref_metadata_2025 huggingface dataset:
Source-sink turbulence in a stratified fluid
Authors: Boubnov B. M. , Dalziel S. B. , Linden P. F.
Published: April 2006

A new method of generating turbulence in a stratified fluid is presented. The flow is forced by a symmetric array of sources and sinks placed around the perimeter of a tank containing stratified fluid. The sources and sinks are located in a horizontal plane and the flow from the sources is directed horizontally, so that fluid is withdrawn from and re-injected at its neutral density level with some horizontal momentum. The sources and sinks are arranged so that no net impulse or angular momentum is imparted to the flow. Measurements of the mixing produced by the turbulence are made using a conductivity probe to record the vertical density profile. The flow field is measured by tracking small neutrally buoyant particles which are placed within the fluid. The tracking of the particles and analysis of the flow fields are done automatically using DigImage, a recently developed suite of particle tracking software. The characteristics of the flow are found to depend on the forcing parameter F = V/Nd, where V is the mean velocity of the flow through the source orifices, d is the diameter of the sources and sinks and N is the buoyancy frequency of the stratification. At large F three-dimensional turbulence is produced within a mixed layer centred on the level of the sources and sinks. A comparison of mixing rates measured in this and more conventional experiments is made, and it is concluded that in terms of the local turbulence parameters the entrainment rates are similar. At low F, no significant mixing occurs and the flow is approximately two-dimensional with very small vertical velocities. Under these circumstances a qualitative change in the characteristics of the flow occurs after the experiment has been running for some hours. It is observed that the scale of the motion increases until there is an accumulation of the energy at the largest scale that can be accommodated within the tank. The structure of this large-scale circulation is analysed and it is found that a form of vorticity expulsion from the interior of the circulation has occurred. These results are compared with numerical simulations of two-dimensional turbulence, and some measurements of turbulent decay are discussed.
The motion generated by a slowly rising disk in an unbounded rotating fluid for arbitrary Taylor number
Authors: Vedensky D. , Ungarish M.
Published: April 2006

The motion of a disk rising steadily parallel to the axis of rotation in a uniformly rotating unbounded liquid is considered. In the limit of zero Rossby number the linear viscous equations of motion are reduced to a system of dual integral equations which renders an ‘exact’ solution for arbitrary values of the Taylor number, Ta. The investigation is focused on the drag and the flow field. In the limits of small and large Ta the asymptotic results of the present formulation agree with – and extend – previous investigations by different approaches.

A particular novel feature, for large Ta, is the contribution of the Ekman-layer flux to the outer motion. New insight into the structure of the Taylor column is gained; in particular, it is shown that the main part of the column is a ‘bubble’ of recirculating fluid, detached from the body and not communicating with the Ekman layer. However, it turns out that the essential discrepancy in drag between experiments (Maxworthy 1970) and previous theories cannot be attributed to the Ekman-layer suction effect.
Observations of purely elastic instabilities in the Taylor–Dean flow of a Boger fluid
Authors: Joo Yong Lak , Shaqfeh Eric S. G.
Published: April 2006

An experimental and theoretical investigation of the stability of the viscoelastic flow of a model Boger fluid between rotating cylinders with an applied pressure gradient is presented. In our theoretical study, a linear stability analysis based on the Oldroyd-B fluid model which predicts the critical conditions and the structure of the vortex flow at the onset of instability is developed. Our results reveal that certain non-axisymmetric modes are more unstable than the previously studied axisymmetric mode when the shearing by the cylinder rotation is the dominant flow-driving force. This is consistent with recent results presented by Beris & Avgousti (1992) on the stability of elastic Taylor–Couette flow. On the other hand, the axisymmetric mode is more unstable when the pressure gradient becomes dominant. Furthermore, we investigate the mechanism of purely elastic Taylor–Dean instability with respect to non-axisymmetric disturbances through an examination of the disturbance-energy equation. It is found that the mechanism of the elastic Taylor–Dean instability is associated with the coupling between the disturbance polymeric stresses due to the azimuthal variation of the disturbance flow and the base state velocity gradients. In our experimental study, evidence of non-inertial, cellular instabilities in the Taylor–Dean flow of a well-characterized polyisobutylene/polybutene Boger fluid is presented. A stationary, meridional obstruction is placed between independently rotating, concentric cylinders to generate an azimuthal pressure gradient in opposition to the shearing flow. Flow visualization experiments near the critical conditions show the transition from purely azimuthal flows to secondary vortex flows, and the development of evenly spaced, banded vortex structures. The critical wavenumber obtained from spectral image analysis of the visualizations, and the critical Deborah number are presented for various ratios of the pressure gradient to the shear driving force. Although there is a quantitative discrepancy between data and theory, the qualitative trends in the data are in agreement with our theoretical predictions. In addition, laser-Doppler velocimetry (LDV) measurements show that the instability is a stationary mode when the pressure gradient is the dominant flow-driving force, while it is an oscillatory instability when the shearing is dominant, again as predicted by the theory.
Active turbulence control for drag reduction in wall-bounded flows
Authors: Choi Haecheon , Moin Parviz , Kim John
Published: April 2006

The objective of this study is to explore concepts for active control of turbulent boundary layers leading to skin-friction reduction using the direct numerical simulation technique. Significant drag reduction is achieved when the surface boundary condition is modified to suppress the dynamically significant coherent structures present in the wall region. The drag reduction is accompanied by significant reduction in the intensity of the wall-layer structures and reductions in the magnitude of Reynolds shear stress throughout the flow. The apparent outward shift of turbulence statistics in the controlled flows indicates a displaced virtual origin of the boundary layer and a thickened sublayer. Time sequences of the flow fields show that there are essentially two drag-reduction mechanisms. Firstly, within a short time after the control is applied, drag is reduced mainly by deterring the sweep motion without modifying the primary streamwise vortices above the wall. Consequently, the high-shear-rate regions on the wall are moved to the interior of the channel by the control schemes. Secondly, the active control changes the evolution of the wall vorticity layer by stabilizing and preventing lifting of the spanwise vorticity near the wall, which may suppress a source of new streamwise vortices above the wall.
Compositional convection in the solidification of binary alloys
Authors: Emms P. W. , Fowler A. C.
Published: April 2006

When a binary alloy is directionally solidified, a two-phase mushy dendritic zone is often formed. Interdendritic convection of the melt may occur, and is coupled with compositional convection of the residual melt. If fluid flow velocities are high enough, local melt-back of the dendrites may occur, leading to channel formation, and thus preferred flow paths. In order to predict the onset of convection, a coupled liquid/mush model is proposed, which includes most of the known physics. An elaborate scaling procedure leads to certain conclusions concerning the nature of convection, and points to a much simplified model, which can essentially be solved analytically. Predictions of the theory are compared quantitatively with experiments.
The influence of drift flow turbulence on surface gravity wave propagation
Authors: Fabrikant A. L. , Raevsky M. A.
Published: April 2006

The theory of surface gravity waves scattering at vortex flows in the ocean is developed in this paper. A scattering amplitude is found in the Born approximation as a function of vorticity which appears very convenient for investigation of scattering at simple localized flows. It is shown that the wave scattering cross-section is determined by the vertical component of vorticity. For a random (turbulent) vortex field the scattering cross-section per unit voume is determined by a vorticity correlation function. The damping of the coherent wave component and the angular spectrum widening are calculated for multiple scattering by vortex turbulence of drift flows. The spectrum angular width evolution for waves scattered at self-similar vortices of the logarithmic boundary layer is determined only by its dynamical speed and the wave vector. The latter result may be used for a remote sensing of oceanic turbulent drift flows based on observations of surface waves.
Dynamics of large-amplitude geostrophic flows: the case of ‘strong’ beta-effect
Authors: Benilov E. S.
Published: April 2006

This paper examines the dynamics of geostrophic flows with large displacement of isopycnal surfaces. The β-effect is assumed strong i.e. the parameter (Rd cot θ)/Re (where θ is the latitude, Rd is the deformation radius, Re is the Earth's radius) is of the order of, or greater than, the Rossby number. A system of asymptotic equations is derived, with the help of which the stability of an arbitrary zonal flow with both vertical and horizontal shear is proven. It is demonstrated that the horizontal and vertical spatial variables in the asymptotic system are separable, which yields a ‘horizontal’ set of evolutionary equations for the amplitudes of the barotropic and baroclinic modes (the vertical profile of the latter is arbitrary).
Drop formation in a one-dimensional approximation of the Navier–Stokes equation
Authors: Eggers Jens , Dupont Todd F.
Published: April 2006

We consider the viscous motion of a thin axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier–Strokes equation. We compare our results with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.
Pressure fluctuations and their effect on cavitation inception within water jets
Authors: Ran Bing , Katz Joseph
Published: April 2006

Instantaneous and phase averaged pressure distributions in the near field of a jet, and their effects on the conditions for the onset of cavitation are studied in detail. The measurements are performed by using microscopic bubbles as pressure sensors, and holography as a means of detecting them. Experiments are performed at Red exceeding 4 × 105, with and without acoustic excitation. The results show that the highest negative pressure peaks (–0.97) and the resulting cavitation inception occur because of vortex pairing. Prior to pairing the negative peaks are between –0.8 and –0.9. Weak acoustic excitation changes the entire flow structure and the spatial distributions of bubbles, but has little effect on the onset of cavitation. Downstream of the potential core the highest pressure peaks (∼ –0.6) are considerably smaller, in agreement with the occurrence of cavitation there. It is also shown that although the r.m.s. values of pressure fluctuations do not vary with the jet speed, the probability distribution changes significantly, causing a reduction in the inception index with increasing velocity. The probability of cavitation inception is estimated from the distributions of bubbles and pressure peaks. It is shown that the actual, non-uniform bubble distribution increases the probability of inception owning to migration of the bubbles to the low pressure regions.
Convection in a rotating cylinder. Part 2. Linear theory for low Prandtl numbers
Authors: Goldstein H. F. , Knobloch E. , Mercader I. , Net M.
Published: April 2006

The onset of convection in a low-Prandtl-number fluid confined in a uniformly rotating vertical cylinder heated from below is studied. The linear stability problem is solved for perfectly conducting stress-free or rigid boundary conditions at the top and bottom; the sidewalls are taken to be insulating and rigid. For these Prandtl numbers axisymmetric overstability leads to an oscillating concentric pattern of rolls. When the instability breaks axisymmetry the resulting pattern must in addition precess. The relationship between these two types of oscillatory behaviour is explored in detail. The complex interaction between different types of neutrally stable modes is traced out as a function of the Prandtl and Taylor numbers, as well as the aspect ratio. A qualitative explanation is provided for the multiplicity of modes of a given azimuthal wavenumber and its dependence on the parameters. Specific predictions are made for the Prandtl numbers 0.025, 0.49 and 0.78, corresponding to mercury, liquid helium 4 and compressed carbon dioxide gas.
On the high-Rayleigh-number structure of steady laminar natural-convection flow in a square enclosure
Authors: Ravi M. R. , Henkes R. A. W. M. , Hoogendoorn C. J.
Published: April 2006

Natural-convection flow in an enclosure with adiabatic horizontal walls and isothermal vertical walls maintained at a fixed temperature difference has been investigated. At high values of the natural-convection parameter, the Rayleigh number, a recirculating pocket appears near the corners downstream of the vertical walls, and the flow separates and reattaches at the horizontal walls in the vicinity of this recirculation. There is also a considerable thickening of the horizontal layer. In some previous studies by different authors, this corner flow was considered to be caused by an internal hydraulic jump, and the jump theory was used to predict bifurcation of the steady flow into periodic flow. The present work examines the corner phenomenon closely to decide if it is indeed caused by a hydraulic jump. The results of the analysis reveal the oversimplification of the problem made in the previous studies: there is no connection of the corner phenomenon with a hydraulic jump. The separation of flow at the ceiling is not a feature of hydraulic jumps, and the essential energy loss associated with hydraulic jumps is not observed in the corner flow. It is shown that the corner structure is caused by thermal effects. Owing to the temperature undershoots in vertical boundary layer, which are known to be caused by the stable thermal stratification of the core, relatively cold fluid reaches the upper corner. This cold fluid detaches from the ceiling like a plume at high Rayleigh numbers, and causes the separation and recirculation.
Wavenumber selection and irregularity of spatially developing nonlinear Dean and Görtler vortices
Authors: Guo Y. , Finlay W. H.
Published: April 2006

Spatially developing vortices found in curved channels (Dean vortices) and in a concave boundary layer (Görtler vortices) asre studied numerically using Legendre spectral-element methods. The linear instability of these vortices with respect to spanwise perturbations (Eckhaus instability) is examined using parabolized spatial stability analysis. The nonlinear evolution of this instability is studied by solving the parabolized Navier–Stokes equations. When the energy level of Dean and Görtler vortices in the flow is low, the spatial growth of the vortices is governed by primary instability (Dean or Görtler instability). At this stage, vortices with different wavelengths can develop at the same time and do not interact with each other significantly. When certain vortices reach the nonlinear stage first and become the dominant wavelength, spatial Eckhaus instability sets in. For all cases studied, spatially developing Dean and Görtler vortices are found to be most unstable to spanwise disturbances with wavelength twice or $\frac{3}{2}$ times that of the dominant one. The nonlinear growth of these perturbations generates a small vortex pair in between two pairs of vortices with long wavelength, but forces two pairs of vortices with short wavelength to develop into one pair. For Görtler vortices, this is manifested mostly by irregular and deformed vortex structures. For Dean vortices, this is manifested by vortex splitting and merging, and spatial Eckhaus instability plays an important role in the wavenumber selection process.
Electrophoretic motion of an arbitrary prolate body of revolution toward an infinite conducting wall
Authors: Feng Jian-Jun , WU Wang-YI
Published: April 2006

The electrophoretic motion of an arbitrary prolate body of revolution perpendicular to an infinite conducting planar wall is investigated by a combined analytical–numerical method. The electric field is exerted normal to the conducting planar wall and parallel to the axis of revolution of the particle. The governing equations and boundary conditions are obtained under the assumption of electric double layer thin compared to the local particle curvature radius and the spacing between the particle and the boundary. The axisymmetrical electrostatic and hydrodynamic equations are solved by the method of distribution of singularities along a certain line segment on the axis of revolution inside the particle. The analytical expressions for fundamental singularities both of electrostatic and hydrodynamic equations in the presence of the infinite planar wall are derived. Employing a piecewise parabolic approximation for the density function and applying the boundary collocation method to satisfy the boundary conditions on the surface of the particle, a system of linear algebraic equations is obtained which can be solved by matrix reduction technique.

Solutions for the electrophoretic velocity of the colloidal prolate spheroid are presented for various values ofa/banda/d, whereaandbare the major and minor axes of the particle respectively anddis the distance between the centre and the wall. Numerical tests show that convergence to at least four digits can be achieved. For the limiting cases ofa=bord→ ∞, our results agree quite well with the exact solutions of electrophoresis of a sphere moving perpendicularly to an infinite planar wall or of a prolate spheroid in an unbounded fluid. As expected, owing to the effect of the wall, the electrophoretic mobility of the particle decreases monotonically for a given spheroid as it gets closer to the wall. Another important feature is that the wall effect on electrophoresis will reduce with the increase of slenderness ratio of the prolate spheroid at the same value ofa/d. The boundary effect on the particle mobility and flow pattern in electrophoresis differ significantly from those of the corresponding sedimentation problem and the wall effect on the electrophoresis is much weaker than that on the sedimentation. In order to demonstrate the generality of the proposed method, the convergent results for prolate Cassini ovals are also given in the present paper.
A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake
Authors: Dušek Jan , Gal Patrice Le , Fraunié Philippe
Published: April 2006

The first Hopf bifurcation of the infinite cylinder wake is analysed theoretically and by direct simulation. It is shown that a decomposition into a series of harmonics is a convenient theoretical and practical tool for this investigation. Two basic properties of the instability allowing the use and truncation of the series of harmonics are identified: the lock-in of frequencies in the flow and separation of the rapid timescale of the periodicity from the slow timescale of the non-periodic behaviour. The Landau model is investigated under weak assumptions allowing strong nonlinearities and transition to saturation of amplitudes. It is found to be rather well satisfied locally at a fixed position of the flow until saturation. It is shown, however, that no truncated expansion into a series of powers of amplitude can account correctly for this fact. The validity of the local Landau model is found to be related to the variation of the form of the unstable mode substantially slower than its amplification. Physically relevant characteristics of the Hopf bifurcation under the assumption of separation of three timescales – those of the periodicity, amplification and deformation of the mode – are suggested.
Streamwise vortices and transition to turbulence
Authors: Hamilton James M. , Abernathy Frederick H.
Published: April 2006

A series of experiments was conducted to determine the conditions under which streamwise vortices can cause transition to turbulence in shear flows. A specially designed obstacle was used to produce a single vortex in a water-table flow, and the design of this obstacle is discussed. Laser-Doppler velocimetry measurements of the streamwise and crossflow velocity fields were made in transitional and non-transitional flows, and flow visualization was also used. It was found that strong vortices (vortices with large circulation) lead to turbulence while weaker vortices do not. Determination of a critical value of vortex strength for transition, however, was complicated by ambiguities in calculating the vortex circulation. The profiles of streamwise velocity were found to be inflexional for both transitional and non-transitional flows. Transition in single-vortex and multi-vortex flows was compared, and no qualitative differences were observed, suggesting no significant vortex interactions affecting transition.
Direct numerical simulation of passive control of three-dimensional phenomena in boundary-layer transition using wall heating
Authors: Kral L. D. , Fasel H. F.
Published: April 2006

A numerical model is presented for investigating control of the three-dimensional boundary-layer transition process. Control of a periodically forced, spatially evolving boundary layer in water is studied using surface heating techniques. The Navier–Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. The Navier–Stokes equations are used in vorticity–velocity form and are coupled with the energy equation through the viscosity dependence on temperature. Passive control of small amplitude two-dimensional waves and three-dimensional oblique waves is numerically simulated with either uniform or non-uniform wall heating applied. Both amplitude levels and amplification rates are strongly reduced with heating applied. Comparison is made with parallel and non-parallel linear stability theory and experiments. Control of the early stages of the nonlinear breakdown process is also investigated using uniform wall heating. Both control of the fundamental and subharmonic routes to turbulence are investigated. For both breakdown processes, a strong reduction in amplitude levels and growth rates results. In particular, the high three-dimensional growth rates that are characteristic of the secondary instability process are significantly reduced below the uncontrolled levels.
Interaction of oblique instability waves with a nonlinear plane wave
Authors: Wundrow David W. , Hultgren Lennart S. , Goldstein M. E.
Published: April 2006

This paper is concerned with the downstream evolution of a resonant triad of initially non-interacting linear instability waves in a boundary layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude oblique modes that form a subharmonic standing wave in the spanwise direction. The growth rates are small and there is a well-defined common critical layer for these waves. As in Goldstein & Lee (1992), the wave interaction takes place entirely within this critical layer and is initially of the parametric-resonance type. This enhances the spatial growth rate of the subharmonic but does not affect that of the fundamental. However, in contrast to Goldstein & Lee (1992), the initial subharmonic amplitude is assumed to be small enough so that the fundamental can become nonlinear within its own critical layer before it is affected by the subharmonic. The subharmonic evolution is then dominated by the parametric-resonance effects and occurs on a much shorter streamwise scale than that of the fundamental. The subharmonic amplitude continues to increase during this parametric-resonance stage – even as the growth rate of the fundamental approaches zero – and the subharmonic eventually becomes large enough to influence the fundamental which causes both waves to evolve on the same shorter streamwise scale.
The spin-up of fluid in a rectangular container with sloping bottom
Authors: Heijst G. J. F. Van , Maas L. R. M. , Williams C. W. M.
Published: April 2006

The spin-up from rest of a homogeneous free-surface fluid contained in a rectangular tank with an inclined bottom has been studied in the laboratory. As in the case of a tank without bottom topography, it is found that in the spin-up process leading to the ultimate state of rigid-body rotation a number of stages can be distinguished, these being (i) the starting flow, characterized by zero absolute vorticity, (ii) the viscous generation of cyclonic vorticity at the lateral tank walls, leading to flow separation, and (iii) the formation of cyclonic and anticyclonic flow cells, which show a complicated interaction. When the topography steepness is small, these cells become organized in a regular array similar to what is observed in the non-sloping bottom case. For steeper topography, however, no organization into a regular cellular pattern is observed, and the relative fluid motion remains unsteady and irregular until eventually it has decayed owing to the spin-ip/spin-down mechanism provided by the Ekman layer at the tank bottom. During the first stage of the adjustment process the starting flow takes on the appearance of a large anticyclonic cell that fills the fluid domain entirely. Depending on the ratio of the horizontal and vertical lengthscales of the tank this cell is either symmetric or asymmetric, with a higher density of streamlines in the deeper part of the tank. The coupled vorticity equation, governing the depth-independent part of the starting flow, and the potential equation describing its depth-dependent part have been solved analytically, and the comparison between these results and observational data is generally good.
Transport of kinetically sorbing solute by steady random velocity in heterogeneous porous formations
Authors: Cvetkovic Vladimir , Dagan Gedeon
Published: April 2006

A Lagrangian framework is used for analysing reactive solute transport by a steady random velocity field, which is associated with flow through a heterogeneous porous formation. The reaction considered is kinetically controlled sorption–desorption. Transport is quantified by the expected values of spatial and temporal moments that are derived as functions of the non-reactive moments and a distribution function which characterizes sorption kinetics. Thus the results of this study generalize the previously obtained results for transport of non-reactive solutes in heterogeneous formations (Dagan 1984; Dagan et al. 1992). The results are illustrated for first-order linear sorption reactions. The general effect of sorption is to retard the solute movement. For short time, the transport process coincides with a non-reactive case, whereas for large time sorption is in equilibrium and solute is simply retarded by a factor R = 1+Kd, where Kd is the partitioning coefficient. Within these limits, the interaction between the heterogeniety and kinetics yields characteristic nonlinearities in the first three spatial moments. Asymmetry in the spatial solute distribution is a typical kinetic effect. Critical parameters that control sorptive transport asymptotically are the ratio εr between a typical reaction length and the longitudinal effective (non-reactive) dispersivity, and Kd. The asymptotic effective dispersivity for equilibrium conditions is derived as a function of parameters εr and Kd. A qualitative agreement with field data is illustrated for the zero- and first-order spatial moments.
Stability of inviscid conducting liquid columns subjected to a.c. axial magnetic fields
Authors: Castellanos Antonio , GonzÁalez Heliodoro
Published: April 2006

The natural frequencies and stability criterion for cylinderical inviscid conducting liquid bridges and jets subjected to axial alternating magnetic fields in the absence of gravity are obtained. For typical conducting materials a frequency greater than 100 Hz is enough for a quasi-steady approximation to be valid. On the other hand, for frequencies greater than 105 Hz an inviscid model may not be justified owing to competition between viscous and magnetic forces in the vicinity of the free surface. The stability is governed by two independent parameters. One is the magnetic Bond number, which measures the relative influence of magnetic and capillary forces, and the other is the relative penetration length, which is given by the ratio of the penetration length of the magnetic field to the radius. The magnetic Bond number is proportional to the squared amplitude of the magnetic field and inversely proportional to the surface tension. The relative penetration length is inversely proportional to square root of the product of the frequency of the applied field and the electrical conductivity of the liquid. It is shown in this work that stability is enhanced by either increasing the magnetic Bond number or decreasing the relative penetration length.
Axisymmetric unsteady stokes flow past an oscillating finite-length cylinder
Authors: Loewenberg Michael
Published: April 2006

The flow field generated by axial oscillations of a finite-length cylinder in an incompressible viscous fluid is described by the unsteady Stokes equations and computed with a first-kind boundary-integral formulation. Numerical calculations were conducted for particle oscillation periods comparable with the viscous relaxation time and the results are contrasted to those for an oscillating sphere and spheroid. For high-frequency oscillations, a two-term boundary-layer solution is formulated that involves two, sequentially solved, second-kind integral equations. Good agreement is obtained between the boundary-layer solution and fully numerical calculations at moderate oscillation frequencies. The flow field and traction on the cylinder surface display several features that are qualitatively distinct from those found for smooth particles. At the edges, where the base joins the side of the cylinder, the traction on the cylinder surface exhibits a singular behaviour, characteristic of steady two-dimensional viscous flow. The singular traction is manifested by a sharply varying pressure profile in a near-field region. Instantaneous streamline patterns show the formation of three viscous eddies during the decelerating portion of the oscillation cycle that are attached to the side and bases of the cylinder. As deceleration proceeds, the eddies grow, coalesce at the edges of the particle, and thus form a single eddy that encloses the entire particle. Subsequent instantaneous streamline patterns for the remainder of the oscillation cycle are insensitive to particle geometry: the eddy diffuses outwards and vanishes upon particle reversal; a simple streaming flow pattern occurs during particle acceleration. The evolution of the viscous eddies is most apparent at moderate oscillation frequencies. Qualitative results are obtained for the oscillatory flow field past an arbitrary particle. For moderate oscillation frequencies, pathlines are elliptical orbits that are insensitive to particle geometry; pathlines reduce to streamline segments in constant-phase regions close to and far from the particle surface.
The observation of the simultaneous development of a long- and a short-wave instability mode on a vortex pair
Authors: Thomas P. J. , Auerbach D.
Published: April 2006

Experiments on the stability of vortex pairs are described. The vortices (ratio of length to core diameter L/c of up to 300) were generated at the edge of a flat plate rotating about a horizontal axis in water. The vortex pairs were found to be unstable, displaying two distinct modes of instability. For the first time, as far as it is known to the authors, a long-wave as well as a short-wave mode of instability were observed to develop simultaneously on such a vortex pair. Experiments involving single vortices show that these do not develop any instability whatsoever. The wavelengths of the developing instability modes on the investigated vortex pairs are compared to theoretical predictions. Observed long wavelengths are in good agreement with the classic symmetric long-wave bending mode identified by Crow (1970). The developing short waves, on the other hand, appear to be less accurately described by the theoretical results predicted, for example, by Windnall, Bliss & Tsai (1974).
Distortions of inertia waves in a rotating fluid cylinder forced near its fundamental mode resonance
Authors: Manasseh Richard
Published: April 2006

A series of experimental observations is presented of a flow in which inertial oscillations are excited. The homogeneous fluid is contained in a completely filled right circular cylinder. The cylinder is spun about its axis of symmetry and a small ‘forced precession’ (or coning motion) is impulsively started. The flow is visualized by an electrolytic dyeline method. The mathematical problem for linear inviscid inertial oscillations in this system, although ill-posed in general, admits a solution in terms of wave modes for the specific boundary conditions considered here. The experiments show that while this linear inviscid theory provides some facility for predicting the flow structure at early times, the flow rapidly and irreversibly distorts away from the predicted form. This behaviour is seen as a precursor to some of the more dramatic breakdowns described by previous authors, and it may be pertinent to an understanding of the breakdowns reported in experiments on elliptical flow instabilities.
An experimental investigation of concentrated suspension flows in a rectangular channel
Authors: Koh Christopher J. , Hookham Philip , Leal L. G.
Published: April 2006

An experimental adaptation of the well-known laser-Doppler anemometry technique is developed for measuring the velocity and concentration profiles in concentrated suspension flows. To circumvent the problem of optical turbidity, the refractive indices of the solid and liquid phases are closely matched. The residual turbidity, owing to small mismatches of the refractive indices, as well as impurities in the particles, allows a Doppler signal to be detected when a particle passes through the scattering volume. By counting the number of Doppler signals in a period of time, the local volume fraction is also measured.

This new technique is utilized to study concentrated suspension flows in a rectangular channel. The general behavior of the suspension is that the velocity profile is blunted while the concentration profile has a maximum near the centre. Comparisons are made with theoretical predictions based on the shear-induced particle migration theory.
A computational investigation of inviscid hypervelocity flow of a dissociating gas past a cone at incidence
Authors: Macrossan M. N. , Pullin D. I.
Published: April 2006

Calculations have been performed for the inviscid hypervelocity flow of nitrogen past a 15° semi-angle sharp cone at an incidence of 30°, at an enthalpy sufficiently high to produce dissociation/recombination chemistry downstream of the bow shock wave. A spatially second-order-accurate scheme for the numerical solution of the inviscid Euler equations was used combined with the Lighthill–Freeman model of the non-equilibrium ideal dissociating gas. The computational method has been used as a ‘numerical wind tunnel’ in order to gain understanding of the interaction between the gas dynamics and the finite-rate gas chemistry. Inviscid flow has been considered to ensure that the only physical lengthscales in the flow are those associated with the chemical reactions. It was found that a chemical lengthscale Ls based on the local dissociation length behind the shock on the windward plane of symmetry is an important governing parameter of the flow. However, as the flow lengthscale becomes large and the flow approaches the limiting case of equilibrium chemistry, Ls is not the dominant chemical lengthscale. This is particularly true of the leeward flow, which contains a shock–vortex structure. A simple modelling technique has been used to determine a more appropriate lengthscale, Lr, t, for the leeward flow as the equilibrium limit is approached. This lengthscale is based on the expected equilibrium conditions behind the cross-flow shock.
Mass transport under partially reflected waves in a rectangular channel
Authors: Wen Jiangang , Liu Philip L.-F.
Published: April 2006

Mass transport under partially reflected waves in a rectangular channel is studied. The effects of sidewalls on the mass transport velocity pattern are the focus of this paper. The mass transport velocity is governed by a nonlinear transport equation for the second-order mean vorticity and the continuity equation of the Eulerian mean velocity. The wave slope, ka, and the Stokes boundary-layer thickness, k (ν/σ)½, are assumed to be of the same order of magnitude. Therefore convection and diffusion are equally important. For the three-dimensional problem, the generation of second-order vorticity due to stretching and rotation of a vorticity line is also included. With appropriate boundary conditions derived from the Stokes boundary layers adjacent to the free surface, the sidewalls and the bottom, the boundary value problem is solved by a vorticity-vector potential formulation; the mass transport is, in gneral, represented by the sum of the gradient of a scalar potential and the curl of a vector potential. In the present case, however, the scalar potential is trivial and is set equal to zero. Because the physical problem is periodic in the streamwise direction (the direction of wave propagation), a Fourier spectral method is used to solve for the vorticity, the scalar potential and the vector potential. Numerical solutions are obtained for different reflection coefficients, wave slopes, and channel cross-sectional geometry.
On one-dimensional flow of a conducting gas between electrodes – with application to MHD thrusters
Authors: Cowley M. D. , Horlock J. H.
Published: April 2006

Inviscid, adiabatic, one-dimensional flow of a conducting gas in the presence of crossed electric and magnetic fields is investigated for the case where the magnetic field is generated by the current being supplied to the gas. The electrode geometry and the connections to the electrical power supply are such that the magnetic field falls to zero at the downstream end of the MHD duct. The analysis allows for magnetic Reynolds number rm to be anywhere in the range 0 to ∞ The main part of the investigation is restricted to consideration of ducts with constant spacing between electrodes.

The way in which the density of the gas varies along the duct with the changing magnetic field is analysed generally and the results are then applied to the case where gas is fed to the MHD duct from high pressure in a plenum chamber and where the duct exhausts to a region of negligible pressure. If the flow is choked by the converging entry to the duct and the magnetic Reynolds number is moderate to high, the main electromagnetic effect is for the j × B forces to accelerate the gas to supersonic speeds. As rm is reduced, ohmic heating becomes more important, and it may cause the flow to be choked at exit from the duct, giving rise to a reduction in mass flow. For certain ranges of rm and ratio of initial magnetic pressure to plenum-chamber pressure the flow may choke at a sonic point within the duct itself, while accelerating from subsonic to supersonic through the point.

Some illustrative examples of how properties vary with distance along the duct have been computed and the consequences of the analysis for MHD thrusters are explored. The magnetic forces will augment thrust per unit cross-sectional area, the essential measure of this being the drop in magnetic pressure along the duct, but there is an upper limit on the ratio of magnetic pressure to plenum-chamber pressure for flows to be possible. Flow at low magnetic Reynolds number is favoured if the object is to increase specific thrust by reducing mass flow through the duct.
Bifurcation and chaos in shape and volume oscillations of a periodically driven bubble with two-to-one internal resonance
Authors: Feng Z. C. , Leal L. G.
Published: April 2006

We study the dynamic sof gas or vapour bubbles when the volume mode of oscillation is coupled with one of the shape modes through quadratic resonance. In particular, the frequency ratio of the volume mode and the shape mode is assumed to be close to two-to-one. The analysis is based upon the use of a two-timescale asymptotic approximation, combined with domain perturbation theory. The viscous effect of the fluid is included by using a rigorous treatment of weak viscosity. Through solvability conditions, amplitude equations governing the slow-timescale dynamics of the resonant modes are obtained. Bifurcation analysis of these amplitude equations reveals interesting phenomena. When volume oscillations are forced by oscillations of the external pressure, we find that the volume mode may lose stability for sufficiently large amplitudes of oscillation, and this instability may lead to chaotic oscillations of both the volume and the shape modes. However, we find that for chaos to occur, a critical degree of detuning is required between the shape and volume modes, in the sense that their natural frequencies must differ by more than a critical value. When a shape mode is forced by oscillations of anisotropic components of the external pressure, we find that chaos can occur even for exact resonance of the two modes. The physical significance of this result is also given.
Solitons, solitary waves, and voidage disturbances in gas-fluidized beds
Authors: Harris S. E. , Crighton D. G.
Published: April 2006

In this paper, we consider the evolution of an initially small voidage disturbance in a gas-fluidized bed. Using a one-dimensional model proposed by Needham & Merkin (1983), Crighton (1991) has shown that weakly nonlinear waves of voidage propagate according to the Korteweg–de Vries equation with perturbation terms which can be either amplifying or dissipative, depending on the sign of a coefficient. Here, we investigate the unstable side of the threshold and examine the growth of a single KdV voidage soliton, following its development through several different regimes. As the size of the soliton increases, KdV remains the leading-order equation for some time, but the perturbation terms change, thereby altering the dependence of the amplitude on time. Eventually the disturbance attains a finite amplitude and corresponds to a fully nonlinear solitary wave solution. This matches back directly onto the KdV soliton and tends exponentially to a limiting size. We interpret the series of large-amplitude localized pulses of voidage formed in this way from initial disturbances as corresponding to the ‘voidage slugs’ observed in gas fluidization in narrow tubes.
Evolution of long water waves in variable channels
Authors: Teng Michelle H. , Wu Theodore Y.
Published: April 2006

This paper applies two theoretical wave models, namely the generalized channel Boussinesq (gcB) and the channel Korteweg–de Vries (cKdV) models (Teng & Wu 1992) to investigate the evolution, transmission and reflection of long water waves propagating in a convergent–divergent channel of arbitrary cross-section. A new simplified version of the gcB model is introduced based on neglecting the higher-order derivatives of channel variations. This simplification preserves the mass conservation property of the original gcB model, yet greatly facilitates applications and clarifies the effect of channel cross-section. A critical comparative study between the gcB and cKdV models is then pursued for predicting the evolution of long waves in variable channels. Regarding the integral properties, the gcB model is shown to conserve mass exactly whereas the cKdV model, being limited to unidirectional waves only, violates the mass conservation law by a significant margin and bears no waves which are reflected due to changes in channel cross-sectional area. Although theoretically both models imply adiabatic invariance for the wave energy, the gcB model exhibits numerically a greater accuracy than the cKdV model in conserving wave energy. In general, the gcB model is found to have excellent conservation properties and can be applied to predict both transmitted and reflected waves simultaneously. It also broadly agrees well with the experiments. A result of basic interest is that in spite of the weakness in conserving total mass and energy, the cKdV model is found to predict the transmitted waves in good agreement with the gcB model and with the experimental data available.
Energetics of oscillating lifting surfaces by the use of integral conservation laws
Authors: Ahmadi Ali R. , Windnall Sheila E.
Published: April 2006

The energetics of oscillating lifting surfaces in two and three dimensions is calculated by the use of integral conservation laws in inviscid incompressible flow for general and harmonic transverse oscillations. Wing deformations are prescribed as a function of time and total thrust is calculated from the momentum theorem, and energy loss rate due to vortex shedding in the wake is calculated from the principle of conservation of mechanical energy. Total power required to maintain the oscillations and hydro-dynamic efficiency are also determined. In two dimensions, the results are obtained in closed form. In three dimensions, the distribution of vorticity on the lifting surface is also required as input to the calculations. Therefore, unsteady lifting-surface theory must be used as well. The analysis is applicable to oscillating lifting surfaces of arbitrary planform, aspect ratio and reduced frequency and does not require calculation of the leading-edge thrust.