bluuebunny/crossref_metadata_2025 huggingface dataset:
New π‐conjugated polyaryleneethynylenes containing a 1,3,5‐triazine unit in the main chain: Synthesis and optical and electrochemical properties
Authors: Fang Qiang , Ren Shijie , Xu Bing , Du Junping , Cao Amin
Published: April 2006

A series of new π‐conjugated poly(aryleneethynylene)s containing a 1,3,5‐triazine unit in the main chain were synthesized in yields higher than 70% by polycondensation between dibromophenyl‐1,3,5‐triazine monomers and alkyl‐substituted diethynylbenzene (or diethynylfluorene) comonomers with Pd(PPh3)4 and CuI as catalysts in the presence of triethylamine. The polymers had a number‐average molecular weight in the range of 5000–10,000 and showed good solubility in common organic solvents. The polymers were photoluminescent both in solutions and in the solid state. X‐ray diffraction patterns of the powders of the polymers revealed that the polymers were semicrystalline. Electrochemically, the polymers appeared to be reversible under reduction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3797–3806, 2006
The growth of compositionally stratified solid above a horizontal boundary
Authors: Woods Andrew W. , Huppert Herbert E.
Published: April 2006

The compositional stratification in solid formed by cooling a binary alloy from below is investigated theoretically and experimentally. It is shown that in order to grow composite solid the boundary temperature needs to be below the eutetic temperature. Two separate cases are considered. In the first, heavy fluid is released on solidification. The solid growth is then governed by the diffusive transport of heat and composition. The resultant solid is shown to have a fixed composition until the far-field conditions change. In the second case, light fluid is released on solidification. This generates turbulent compositional convection in the melt which significantly increases the transport of heat and composition across the solid/melt interface. As a result, the fraction of heavy component in the solid initially increases, but subsequently decreases to conserve mass. A simple theoretical model, using the approximation of a flat solid/melt interface is developed; this predicts differences in the thermal flux in saturated and undersaturated melts. Laboratory experiments involving aqueous solutions of sodium carbonate cooled from below which released light fluid displayed compositional convection and stratification of the solid as predicted.
Numerical simulation of the absolutely and convectively unstable wake
Authors: Hannemann K. , Jr H. Oertel
Published: April 2006

The development of the wake behind a flat plate at a supercritical Reynolds number (Re= 200, based on the plate thickness and free-stream velocity) is simulated numerically by solving the two-dimensional unsteady Navier-Stokes equations with a finite-difference Galerkin method. The intermediate quasi-steady state of the wake development is investigated with an Orr-Sommerfeld analysis for complex frequencies and wavenumbers. Based on this linear, local stability analysis it can be shown that the quasi-steady state can be divided into regions of local absolute and local convective instability. One goal of this work is to determine the validity of the linear, local stability theory by comparing the predictions of the Orr-Sommerfeld analysis to the results of a numerical wake simulation. Based on this comparison, for the investigated flow field, the frequency selection mechanisms recently proposed by several authors are discussed. Base bleed is applied in the numerical simulation of the wake as a control parameter, following the well-known experimental result that sufficient base bleed reduces the strength of the vortex street (see e.g. Wood 1964). It can be shown that from a critical base-bleed ratio, disturbances grow no longer in time but only in space, indicating a change of the global stability characteristics. In addition the linear, local stability analysis is used to investigate to what extent this global transition can be described.
Shock splitting in single-phase gases
Authors: Cramer M. S.
Published: April 2006

We consider single-phase gases in which the fundamental derivative is negative over a finite range of pressures and temperatures and show that inadmissible discontinuities give rise to shock splitting. The precise conditions under which splitting occurs are delineated and the formation of the split-shock configuration from smooth initial conditions is described. Specific numerical examples of shock splitting are also provided through use of exact inverse solutions.
Instabilities in channel flow with system rotation
Authors: Alfredsson P. Henrik , Persson Håkan
Published: April 2006

A flow visualization study of instabilities caused by Coriolis effects in plane rotating Poiseuille flow has been carried out. The primary instability takes the form of regularly spaced roll cells aligned in the flow direction. They may occur at Reynolds numbers as low as 100, i.e. almost two orders of magnitude lower than the critical Reynolds number for Tollmien-Schlichting waves in channel flow without rotation. The development of such roll cells was studied as a function of both the Reynolds number and the rotation rate and their properties compared with results from linear spatial stability theory. The theoretically obtained most unstable wavenumber agrees fairly well with the experimentally observed value. At high Reynolds number a secondary instability sets in, which is seen as a twisting of the roll cells. A wavytype disturbance is also seen at this stage which, if the rotational speed is increased, develops into large-scale ‘turbulence’ containing imbedded roll cells.
The propagation of two-dimensional and axisymmetric viscous gravity currents at a fluid interface
Authors: Lister John R. , Kerr Ross C.
Published: April 2006

Viscous gravity currents resulting from the introduction of fluid between an upper layer of fluid of lesser density and a lower layer of greater density are analysed. The nonlinear equations governing the spread and shape of the intrusion are formulated for the cases of intrusion at low Reynolds number between deep ambient layers and of flow over a shallow layer of viscous fluid with a rigid lower boundary. Similarity solutions of these equations are obtained in both two-dimensional and axisymmetric geometries, under the assumption that the volume of intruding fluid increases with time like tα. The theoretical predictions are shown to be in reasonable agreement with experimental observations of the spreading of glucose syrups and of viscous hydrocarbons between fluid layers of differing densities. Scaling arguments are used to derive many new results for the rates of spread of intrusions in a wide variety of further situations. A compendium of spreading relations, including some previously isolated results, is derived within a coherent framework and tabulated.
Passage through the critical Froude number for shallow-water waves over a variable bottom
Authors: Kevorkian J. , Yu J.
Published: April 2006

We study the behaviour of shallow (of order δ [Lt ] 1) water waves excited by a small (of order ε [Lt ] 1) amplitude bottom disturbance in the presence of a uniform oncoming flow with either constant or slowly varying Froude number F. When F* ≡ |F − 1|ε−½ [Gt ] 1, the speed and free surface perturbations are of order ν = O(ε); these grow to become of order ε½ if F* = O(1). Therefore, the asymptotic expansions of the solution for ε → 0 depend on the order of F*. These expansions are constructed in a form which remains valid for times of order ν−1; they are then matched to provide results which are also valid for all F. The analytic results exhibit the interesting effects of weak nonlinearities including the steepening of waves and eventual formation of bores if δν−½ [Lt ] 1, the surface rippling due to dispersion if δν−½ = O(1), the strong interaction of waves and the periodic generation of upstreampropagating solitary waves if F* = O(1), etc. All these results are confirmed by numerical integration of the governing equations.
Some integral theorems relating to the oscillations of bubbles
Authors: Longuet-Higgins Michael S.
Published: April 2006

Two integral theorems are proved which are applicable to the motion of an incompressible fluid in three dimensions. From either of these theorems one can derive the monopole component of the pressure fluctuation at infinity when a bubble undergoes non-spherical oscillations. The results confirm and generalize some recent calculations of this effect (Longuet-Higgins 1989a). They also provide a basis for a physical discussion of the origin of the monopole terms.
Reverse flow in a channel with an obstruction at the entry
Authors: Gowda B. H. Lakshmana , Tulapurkara E. G.
Published: April 2006

In this study the flow through and around a parallel-walled channel with an obstruction (flat plate) placed at the channel inlet is investigated. Depending on the position of the obstruction, the flow inside the channel is in a direction opposite to that outside, stagnant or in the same direction as outside but with reduced magnitude. Flow visualization in water is used to examine the fluid motion, although some wind tunnel measurements have been made and are also reported. The parameters that have been varied are the gap between the obstruction and the entry to the channel, the length of the channel and the Reynolds number. The maximum value of the reverse flow velocity is found to be about 20% of that of the flow outside. The maximum forward velocity inside the channel (when it occurs) is only about 65% of the outside velocity even for very large gaps between the obstruction and the channel entrance. A tentative explanation is offered for the observed features.
The flow downstream of screens and its influence on the flow in the stagnation region of cylindrical bodies
Authors: Böttcher J. , Wedemeyer E.
Published: April 2006

Screens used in settling chamber of wind tunnels are known to introduce non-uniformities into the flow which, in turn, may influence the flow in the working section. A thorough investigation was made, using a flow visualization technique, of the development of non-uniformities generated by screens and their influence on the flow in the stagnation region of circular cylinders placed normal to the flow. A theoretical model of the flow downstream of screens is presented that is consistent with the experimental findings.
The influence of initial deformation on drop breakup in subcritical time-dependent flows at low Reynolds numbers
Authors: Stone H. A. , Leal L. G.
Published: April 2006

Transient effects associated with the deformation and breakup of a drop following a step change from critical to suberitical flow conditions are studied experimentally and numerically. In the experiments, we consider step changes in both the shear rate and flow type for two-dimensional linear flows generated in a four-roll mill. Numerically we consider step changes in shear rate only for a uniaxial extensional flow. Depending upon the degree of deformation prior to the change in flow conditions, the drop may either return to a steady deformed shape, or continue to stretch at a reduced rate, or, for intermediate cases, the drop may break without large-scale stretching. This behaviour is a consequence of the complicated interaction between changes of shape due to interfacial tension and changes of shape due to the motion of the suspending fluid. This mode of breakup is most pronounced for high viscosity ratios, because very large extensions are necessary to guarantee breakup if the flow is stopped abruptly. For drops that are not too deformed, the sudden addition of vorticity to the external flow is characterized by rapid rotation of the drop to a new steady orientation followed by deformation and/or breakup according to the effective flow conditions at the new orientation. Finally, for viscous drops in flows with vorticity, it is demonstrated experimentally that breakup can be achieved if the initial shape is sufficiently non-spherical even though the same drop could not be made to break in the same flow at any capillary number when beginning with a near-spherical shape.
Turbulent oscillatory boundary layers at high Reynolds numbers
Authors: Jensen B. L. , Sumer B. M. , Fredsøe J.
Published: April 2006

This study deals with turbulent oscillatory boundary-layer flows over both smooth and rough beds. The free-stream flow is a purely oscillating flow with sinusoidal velocity variation. Mean and turbulence properties were measured mainly in two directions, namely in the streamwise direction and in the direction perpendicular to the bed. Some measurements were made also in the transverse direction. The measurements were carried out up toRe= 6 × 106over a mirror-shine smooth bed and over rough beds with various values of the parametera/kscovering the range from approximately 400 to 3700,abeing the amplitude of the oscillatory free-stream flow andksthe Nikuradse's equivalent sand roughness. For smooth-bed boundary-layer flows, the effect ofReis discussed in greater detail. It is demonstrated that the boundary-layer properties change markedly withRe. For rough-bed boundary-layer flows, the effect of the parametera/ksis examined, at large values (O(103)) in combination with largeRe.
Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below
Authors: Chen Falin , Chen C. F.
Published: April 2006

Experiments have been carried out in a horizontal superposed fluid and porous layer contained in a test box 24 cm × 12 cm × 4 cm high. The porous layer consisted of 3 mm diameter glass beads, and the fluids used were water, 60% and 90% glycerin-water solutions, and 100% glycerin. The depth ratio ď, which is the ratio of the thickness of the fluid layer to that of the porous layer, varied from 0 to 1.0. Fluids of increasingly higher viscosity were used for cases with larger ď in order to keep the temperature difference across the tank within reasonable limits. The top and bottom walls were kept at different constant temperatures. Onset of convection was detected by a change of slope in the heat flux curve. The size of the convection cells was inferred from temperature measurements made with embedded thermocouples and from temperature distributions at the top of the layer by use of liquid crystal film. The experimental results showed (i) a precipitous decrease in the critical Rayleigh number as the depth of the fluid layer was increased from zero, and (ii) an eightfold decrease in the critical wavelength between ď = 0.1 and 0.2. Both of these results were predicted by the linear stability theory reported earlier (Chen & Chen 1988).
Removing the irregular frequencies from integral equations in wave-body interactions
Authors: Lee C.-H. , Sclavounos P. D.
Published: April 2006

The paper presents a method that removes the effects of all irregular frequencies in boundary-integral equations governing the interaction of regular waves with floating bodies of general geometry. A modified integral equation is obtained by the linear superposition of the classical Green equation and its normal derivative with respect to the field point. The selection of a purely imaginary constant of proportionality ensures the removal of all irregular frequencies in the continuous problem and the appropriate selection of its magnitude eliminates their undesirable effects in its numerical implementation. Computations are presented of the added-mass and damping coefficients and exciting forces on a sphere and a truncated vertical cylinder, illustrating the effectiveness of the method.
Slow spreading of a sheet of Bingham fluid on an inclined plane
Authors: Liu Ko Fei , Mei Chiang C.
Published: April 2006

To study the dynamics of fluid mud with a high concentration of cohesive clay particles, we present a theory for a thin sheet of Bingham-plastic fluid flowing slowly on an inclined plane. The physics is discussed on the approximate basis of the lubrication theory. Because of the yield stress, the free surface need not be horizontal when the Bingham fluid is in static equilibrium, nor parallel to the plane bed when in steady flow. We then show that there is a variety of gravity currents that can advance at a constant speed and with the same profile. Experimental confirmation of one type is presented. By solving a nonlinear partial differential equation, transient flows due either to a steady upstream discharge or to the sudden release of a finite fluid mass on another fluid layer are studied. In the first case there is a mud front which ultimately propagates as a constant speed as a steady gravity current. In the second case, when the ambient layer is sufficiently shallow that there is no initial motion, the flow induced by the new fluid can terminate after the disturbance has travelled a finite distance. The extent of the final spread is examined. Disturbances due to an external pressure travelling parallel to the free surface are also examined. It is found in particular that a travelling localized pulse of pressure gradient not only generates a localized mud disturbance which travels along with the forcing pressure, but further leaves behind a permanent footprint.
Nonlinear compressible magnetoconvection Part 1. Travelling waves and oscillations
Authors: Hurlburt N. E. , Proctor M. R. E. , Weiss N. O. , Brownjohn D. P.
Published: April 2006

Two-dimensional compressible convection in a polytropic layer with an imposed vertical magnetic field is studied in a series of numerical experiments. We consider a shallow layer, spanning only a fraction of a scale height in density, and increase the ratio (β−1) of the magnetic to the thermal pressure in a regime where convection sets in at an oscillatory bifurcation. Initially there are stable periodic oscillations (standing wave solutions). For moderate values of β the only deviations from Boussinesq behaviour are where the field is locally intense but as β is decreased magnetic pressure fluctuations become increasingly important. When β is of order unity at the top of the layer standing waves become unstable at higher Rayleigh numbers and travelling waves are preferred. This is an essentially compressible effect in which magnetic pressure plays a crucial role. The associated bifurcation structure is investigated in some detail.
Near-wall structure of a turbulent boundary layer with riblets
Authors: Choi Kwing-So
Published: April 2006

A detailed wind tunnel study has been carried out on the near-wall turbulence structure over smooth and riblet wall surfaces under zero pressure gradient. Time-average quantities as ‘well as conditionally sampled profiles were obtained using hotwire/film anemometry, along with a simultaneous flow visualization using the smoke-wire technique and a sheet of laser light. The experimental results indicated a significant change of the structure in the turbulent boundary layer near the riblet surface. The change was confined within a small volume of the flow close to the wall surface. A conceptual model for the sequence of the bursts was then proposed based on an extensive study of the flow visualization, and was supported by the results of conditionally sampled velocity fields. A possible mechanism of turbulent drag reduction by riblets is discussed.
Dendritic growth of an elliptical paraboloid with forced convection in the melt
Authors: Ananth Ramagopal , Gill William N.
Published: April 2006

All experimental observations of the growth of fully developed dendritic ice crystals indicate that the shape of the tip region is an elliptical paraboloid. Therefore, moving-boundary solutions of the three-dimensional Navier-Stokes and energy equations are obtained here for the shape-preserving growth of isothermal elliptical paraboloids by using the Oseen approximation which is valid for the low-Reynolds-number viscous flows which prevail in dendritic growth. Explicit expressions for the flow and the temperature fields are derived in a simple way using Ivantsov's method. It is shown that the growth Péclet number,PG, is a function of the aspect ratioA, the Stefan numberSt, the Reynolds numberRe, and the Prandtl numberPr. As the Reynolds number increasesPGbecomes linear inSt, less dependent onAand ultimately varies roughly asRe½.

A comparison between the exact solutions given here and the experiments of Kallungal (1974) indicate thatAdecreases asReincreases. This result agrees qualitatively with the experiments of Kallungal (1974) and Chang (1985). The differences between theory and experiments forRe> 10−3may be due to attachment kinetic resistance to growth along thec-axis and capillary effects at the tip which make ice dendrites non-isothermal and create conduction in the solid phase. However, more accurate simultaneous measurements ofR1andR2are needed to determine definitively the mechanisms responsible for these deviations between theory and experiment.
Resonant growth of three-dimensional modes in trnsitioning Blasius boundary layers
Authors: Corke T. C. , Mangano R. A.
Published: April 2006

By carefully controlled phase-coupled input of simultaneous two- and three-dimensional disturbances, the nonlinear evolution and breakdown of the laminar flow in a boundary layer was examined. This involved the generation of plane Tollmien–Schlichting waves and pairs of oblique waves so as to promote nearresonance conditions which have been theoretically shown to lead to the rapid development of three-dimensionality in unstble boundary layers. Special emphasis is placed on the two prominent mechanisms, namely resonant-triads of Orr–Sommerfeld modes and the secondary instability of the streamwise periodic flow to spanwise periodic three-dimensional disturbances. The sensitivity of these mechanisms on the amplitudes and wavenumbers of the input disturbances was of special focus.

The simultaneous two- and three-dimensional wave generation was accomplished using a spanwise array of line heaters suspended just above the wall at the approximate height of the critical layer in the laminar boundary layer. These were operated to produce, through local heating, time-periodic spanwise-phase-varying velocity perturbations. Of primary emphasis in this paper are conditions obtained by the combined forcing of fundamental plane waves with wavenumbers (α, 0) and pairs of subharmonic oblique waves (½α, ± β). The reslults document resonant growth of energy in the subharmonic modes, the formation of staggered lambda vortex patterns with a cross-stream scale commensurate with the seeded ± β condition, and their subsequet transition to turbulence. Complete documentation of the flow field at these various stages is presented using smoke-wire flow visualization and through phase-conditioned hot-wire surveys measuring all three velocity components in three space dimensions.
Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows
Authors: Prasad Rahul R. , Sreenivasan K. R.
Published: April 2006

The three-dimensional turbulent field of a passive scalar has been mapped quantitatively by obtaining, effectively instantaneously, several closely spaced parallel two-dimensional images; the two-dimensional images themselves have been obtained by laser-induced fluorescence. Turbulent jets and wakes at moderate Reynolds numbers are used as examples. The working fluid is water. The spatial resolution of the measurements is about four Kolmogorov scales. The first contribution of this work concerns the three-dimensional nature of the boundary of the scalar-marked regions (the ‘scalar interface’). It is concluded that interface regions detached from the main body are exceptional occurrences (if at all), and that in spite of the large structure, the randomness associated with small-scale convolutions of the interface are strong enough that any two intersections of it by parallel planes are essentially uncorrelated even if the separation distances are no more than a few Kolmogorov scales. The fractal dimension of the interface is determined directly by box-counting in three dimensions, and the value of 2.35 ± 0.04 is shown to be in good agreement with that previously inferred from two-dimensional sections. This justifies the use of the method of intersections. The second contribution involves the joint statistics of the scalar field and the quantity χ* (or its components), χ* being the appropriate approximation to the scalar ‘dissipation’ field in the inertial–convective range of scales. The third aspect relates to the multifractal scaling properties of the spatial intermittency of χ*; since all three components of χ* have been obtained effectively simultaneously, inferences concerning the scaling properties of the individual components and their sum have been possible. The usefulness of the multifractal approach for describing highly intermittent distributions of χ* and its components is explored by measuring the so-called singularity spectrum (or the f(α)-curve) which quantifies the spatial distribution of various strengths of χ*. Also obtained is a time sequence of two-dimensional images with the temporal resolution on the order of a few Batchelor timescales; this enables us to infer features of temporal intermittency in turbulent flows, and qualitatively the propagation speeds of the scalar interface. Finally, a few issues relating to the resolution effects have been addressed briefly by making point measurements with the spatial and temporal resolutions comparable with the Batchelor lengthscale and the corresponding timescale.
Calculation of linear detonation instability: one-dimensional instability of plane detonation
Authors: Lee H. I. , Stewart D. S.
Published: April 2006

The detonation stability problem is studied by a normal mode approach which greatly simplifies the calculation of linear instability of detonation in contrast to the Laplace transform procedure used by Erpenbeck. The method of solution, for an arbitrary parameter set, is a shooting method which can be automated to generate easily the required information about instability. The condition on the perturbations applied at the end of the reaction zone is shown to be interpreted as either a boundedness condition or an acoustic radiation condition. Continuous and numerically exact neutral stability curves and boundaries are given as well as growth rates and eigenfunctions which are calculated for the first time. Our calculations include the Chapman–Jouguet (CJ) case which presents no special difficulty. We give representative results for our detonation model and summarize the one-dimensional stability behaviour in parameter space. Comparison with previous results for the neutral stability boundaries and approximations to the unstable discrete spectrum are given. Parametric studies of the unstable, discrete spectrum's dependence on the activation energy and the overdrive factor are given with the implications for interpreting the physical mechanism of instability observed in experiments. This first paper is restricted to the case of one-dimensional linear instability. Extensions to transverse disturbances will be treated in a sequel.
Diffraction of sea waves by a slender body. Part 2. Water of finite depth
Authors: Aranha J. A. P. , Martins C. A.
Published: April 2006

A uniformly valid theory (all wavelengths and angles of incidence) for the diffraction of sea waves by a slender body, correct to second order in the slenderness parameter, has been derived for the shallow-water limit. This theory is now extended to the finite water depth case, with the same results and accuracy.
An airfoil theory of bifurcating laminar separation from thin obstacles
Authors: Lee C. J. , Cheng H. K.
Published: April 2006

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.
Natural convection in porous media: effect of weak dispersion on bifurcation
Authors: He Xiaowei S. , Georgiadis John G.
Published: April 2006

We use weakly nonlinear analysis via a two-parameter expansion to study bifurcation of conduction into cellular convection of an internally heated fluid in a porous medium that forms a horizontal layer between two isothermal walls. The Darcy–Boussinesq model of convection is enhanced by including two nonlinear terms: (i) quadratic (Forchheimer) drag; and (ii) hydrodynamic dispersion enhancement of the thermal conductivity described by a weak linear relationship between effective conductivity and local amplitude of filtration velocity. The impact of the second term on the shape of the bifurcation curve for two-dimensional rolls is profound in the presence of uniform volumetric heating. The resulting bifurcation structure is unlike any pitchfork bifurcations typical of the classical Bénard problem. Although direct experimental validation of the novel bifurcation is not available, we would like to register it as an alternative or a supplement to models of small imperfections, and as an attempt to account for the scatter of observed critical values for the first bifurcation.
Separation of a boundary jet in a rotating fluid
Authors: Stern Melvin E. , Whitehead J. A.
Published: April 2006

A semi-infinite jet flows along a vertical wall in a rotating fluid, with the nose of the intrusion approaching a corner where the wall turns through an obtuse angle θ + 180°. The jet separates at the corner and flows into the interior if θ exceeds a critical θc, otherwise part of the jet continues around the corner and flows along the downstream segment of the wall. The separation criterion is computed using an inviscid and piecewise-uniform-vorticity model, with s denoting the ratio of the maximum ‘offshore’ to ‘inshore’ vorticity. The separation effect is demonstrated by a laboratory experiment in which a two-dimensional jet flows along the wall from a source. Average velocities are used to estimate s, and to make semi-quantitative comparisons of experimental and theoretical θc. This suggests that the separation mechanism is independent of local viscous forces, although the cumulative effect of lateral eddy stresses in the jet is important in establishing the value of s immediately upstream from the corner. We suggest that our barotropic separation mechanism is relevant to mesoscale oceanic coastal currents.
The spectrum of a turbulent passive scalar in the viscous–convective range
Authors: Qian J.
Published: April 2006

The closed equations of isotropic turbulence, obtained by the method of non-equilibrium statistical mechanics and a perturbation-variation approach (Qian 1983, 1985, 1988), are applied to the study of the spectrum dynamics of a turbulent passive scalar in the viscous–convective range. Batchelor's k−1 spectrum is further confirmed. Moreover the effective average value of the least principal rate of strain γ in Batchelor's spectrum function is theoretically evaluated and it is found that γ−1 = C(ν/ε)½ with C = 2√5. Here ν is the kinematic viscosity, and ε is the energy dissipation rate. This prediction is in agreement with experimental data reported by Grant et al. (1968) and Williams & Paulson (1977).
Laminar secondary flows in curved rectangular ducts
Authors: Thangam S. , Hur N.
Published: April 2006

The occurrence of secondary flow in curved ducts due to the centrifugal forces can often significantly influence the flow rate. In the present work, the secondary flow of an incompressible viscous fluid in a curved duct is studied by using a finite-volume method. It is shown that as the Dean number is increased the secondary flow structure evolves into a double vortex pair for low-aspect-ratio ducts and roll cells for ducts of high aspect ratio. A stability diagram is obtained in the domain of curvature ratio and Reynolds number. It is found that for ducts of high curvature the onset of transition from single vortex pair to double vortex pair or roll cells depends on the Dean number and the curvature ratio, while for ducts of small curvature the onset can be characterized by the Dean number alone. A comparison with the available theoretical and experimental results indicates good agreement. A correlation for the friction factor as a function of the Dean number and aspect ratio is developed and is found to be in good agreement with the available experimental and computational results for a wide range of parameters.
Marangoni effects of trace impurities on the motion of long gas bubbles in capillaries
Authors: Ratulowski J. , Chang H.-C.
Published: April 2006

When a viscous liquid is displaced by a long air bubble in a capillary, it leaves behind a wetting liquid film. A lubrication analysis by Bretherton (1961), which assumes a mobile surface, underpredicts the film thickness at low bubble speeds. In this investigation, the Marangoni effect of small amounts of impurities is shown to be capable of explaining this discrepancy. We carry out an asymptotic analysis for different convective, diffusive and kinetic timescales and show that, if transport in the film is mass-transfer limited such that a bulk concentration gradient exists in the film, the film thickness increases by a maximum factor of 4 2/3; over Bretherton's mobile result at low bubble speeds. Moreover, at large bubble speeds, Bretherton's mobile prediction is approached for all ranges of timescales. For intermediate bubble speeds, the film thickness varies with respect to the bubble speed with an exponent smaller than 2/3 of the mobile theory. These results are favourably compared to literature data on film thickness.
Stability of the flow past a sphere
Authors: Kim Inchul , Pearlstein Arne J.
Published: April 2006

Experiment shows that the steady axisymmetric flow past a sphere becomes unstable in the range 120 < Re < 300. The resulting time-dependent non-axi-symmetric flow gives rise to non-axisymmetric vortex shedding at higher Reynolds numbers. The present work reports a computational investigation of the linear stability of the steady axisymmetric base flow. We use a spectral technique to represent the base flow. We then perform a linear stability analysis with respect to axisymmetric and non-axisymmetric disturbances. A spectral technique similar to that employed in the base-flow calculation is used to solve the linear-disturbance equations in stream-function form (for axisymmetric disturbances), and in a modified primitive variables form (for non-axisymmetric disturbances). The analysis shows that the axisymmetric base flow undergoes a Hopf bifurcation at Re = 175.1, with the critical disturbance having azimuthal wavenumber m = 1, and dimensionless frequency (non-dimensionalized as a Strouhal number, St) 0.0955. The critical Re, azimuthal mode number, and St are favourably compared to previous experimental work.
A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low Stokes numbers
Authors: Tatsuno M. , Bearman P. W.
Published: April 2006

The structures of the flow induced by a circular cylinder performing sinusoidal oscillations in a fluid at rest are investigated by means of flow visualization. The experiments are carried out at Keulegan–Carpenter numbers between 1.6 and 15 and at Stokes numbers between 5 and 160. Above a certain value of Keulegan–Carpenter number, depending on the Stokes number, some asymmetry appears in the flow separation and the associated vortex development behind the cylinder. The two vortices that are developed in a half cycle differ in strength and may be convected in different directions. This results in a fascinating set of flow patterns. Eight different regimes of flow can be identified within the ranges of Keulegan–Carpenter number and Stokes number studied. Furthermore, most of the resulting flows show a three-dimensional instability along the axis of the cylinder. Measurements of the wavelength of these disturbances are presented.
Turbulent boundary layer relaxation from convex curvature
Authors: Alving Amy E. , Smits Alexander J. , Watmuff Jonathan H.
Published: April 2006

A study was undertaken to examine the flat plate relaxation behaviour of a turbulent boundary layer recovering from 90° of strong convex curvature (δ0/R = 0.08), for a length of ≈ 90δ0 after the end of curvature, where δ0 is the boundary layer thickness at the start of the curvature. The results show that the relaxation behaviour of the mean flow and the turbulence are quite different. The mean velocity profile and skin friction coefficient asymptotically approach the unperturbed state and at the last measuring station appear to be fully recovered. The turbulence relaxation, however, occurs in several stages over a much longer distance. In the first stage, a stress ‘bore’ (a region of elevated stress) is generated near the wall, and the bore thickens with distance downstream. Eventually it fills the whole boundary layer, but the stress levels continue to rise beyond their self-preserving values. Finally the stresses begin a gradual decline, but at the last measuring station they are still well above the unperturbed levels, and the ratios of the Reynolds stresses are distorted. These results imply a reorganization of the large-scale structure into a new quasi-stable state. The long-lasting effects of curvature highlight the sensitivity of a boundary layer to its condition of formation.
Homogeneous turbulence in the presence of rotation
Authors: Jacquin L. , Leuchter O. , Cambonxs C. , Mathieu J.
Published: April 2006

Turbulence in solid-body rotation is generated by a flow of air passing through a rotating cylinder containing a dense honeycomb structure and a turbulence-producing grid. The velocity field is probed downstream of this device by hot-wire probes. Using the statistical quantities characterizing the fluctuating field, we show that the rotation affects mainly the components normal to the rotation axis and that these effects are triggered when the Rossby numbers constructed from macroscopic turbulent quantities, are less than unity. These results are discussed in the framework of other available experimental results on the subject. A theoretical interpretation, chiefly based on spectral analysis, is then proposed to explain the trends of the observations.
The evolution of a localized disturbance in a laminar boundary layer. Part 1. Weak disturbances
Authors: Breuer Kenneth S. , Haritonidis Joseph H.
Published: April 2006

The evolution of a low-amplitude localized disturbance in a laminar boundary layer is considered. Linear inviscid theory illustrates that the disturbance may be divided into two parts: a dispersive wave part, represented by solutions to the Rayleigh equation which travel at their characteristic speeds, and a transient or advective part travelling at the local mean velocity. For a three-dimensional initial disturbance, calculations based on linear inviscid theory indicate that the transient portion of the disturbance does not decay and has the form of an inclined shear layer which elongates as the disturbance propagates downstream. The amplitude of the transient part exceeds by far that of the wave part of the disturbance. Experimental results are presented for a disturbance created by the impulsive motion of a small membrane flush-mounted at the wall. For small amplitudes, the initial evolution of the disturbance is found to be in good qualitative agreement with the inviscid calculations, showing the rapid formation of an inclined shear layer. Further downstream, the transient portion of the disturbance decays owing to viscous effects, leaving a linearly unstable dispersive wave packet. The evolutions of equal and opposite disturbances are compared and it is shown that, despite a weak nonlinearity that develops, the resultant wave packets are equal in structure but of opposite phase.
Instabilities of flow in a collapsed tube
Authors: Jensen O. E.
Published: April 2006

In a previous paper (Jensen & Pedley 1989) a model was analysed describing the effects of longitudinal wall tension and energy loss through flow separation on the existence and nature of steady flow in a finite length of externally pressurized, elastic-walled tube. The stability of these steady flows to small time-dependent perturbations is now determined. A linear analysis shows that the tube may be unstable to at least three different modes of oscillation, with frequencies in distinct bands, depending on the governing parameters; neutral stability curves for each mode are calculated. The motion of the separation point at a constriction in the tube appears to play an important role in the mechanism of these oscillations. A weakly nonlinear analysis is used to examine the instabilities in a neighbourhood of their neutral curves and to investigate mode interactions. The existence of multiple independent oscillations indicates that very complex dynamical behaviour may occur.
Response of a turbulent boundary layer to sinusoidal free-stream unsteadiness
Authors: Brereton G. J. , Reynolds W. C. , Jayaraman R.
Published: April 2006

In this paper, selected findings of a detailed experimental investigation are reported concerning the effects of forced free-stream unsteadiness on a turbulent boundary layer. The forced unsteadiness was sinusoidal and was superimposed locally on an otherwise-steady mainstream, beyond a turbulent boundary layer which had developed under constant-pressure conditions. Within the region over which free-stream unsteadiness was induced, the sinusoidal variation in pressure gradient was between extremes of zero and a positive value, with a positive average level. The local response of the boundary layer to these free-stream effects was studied through simultaneous measurements of the u- and v-components of the velocity field

Although extensive studies of unsteady, turbulent, fully-developed pipe and channel flow have been carried out, the problem of a developing turbulent boundary layer and its response to forced free-stream unsteadiness has received comparatively little attention. The present study is intended to redress this imbalance and, when contrasted with other studies of unsteady turbulent boundary layers, is unique in that: (i) it features an appreciable amplitude of mainstream modulation at a large number of frequencies of forced unsteadiness, (ii) its measurements are both detailed and of high spatial resolution, so that the near-wall behaviour of the flow can be discerned, and (iii) it allows local modulation of the mainstream beyond a turbulent boundary layer which has developed under the well-known conditions of steady, two-dimensional, constant-pressure flow

Results are reported which allow comparison of the behaviour of boundary layers under the same mean external conditions, but with different time dependence in their free-stream velocities. These time dependences correspond to: (i) steady flow, (ii) quasi-steadily varying flow, and (iii) unsteady flow at different frequencies of mainstream unsteadiness. Experimental results focus upon the time-averaged nature of the flow; they indicate that the mean structure of the turbulent boundary layer is sufficiently robust that the imposition of free-stream unsteadiness results only in minor differences relative to the mean character of the steady flow, even at frequencies for which the momentary condition of the flow departs substantially from its quasi-steady state. Mean levels of turbulence production are likewise unaffected by free-stream unsteadiness and temporal production of turbulence appears to result only from modulation of the motions which contribute to turbulence production as a time-averaged measure.
Experimental study of the Faraday instability
Authors: Douady S.
Published: April 2006

An experimental study of surface waves parametrically excited by vertical vibrations is presented. The shape of the eigenmodes in a closed vessel, and the importance of the free-surface boundary conditions, are discussed. Stability boundaries, wave amplitude, and perturbation characteristic time of decay are measured and found to be in agreement with an amplitude equation derived by symmetry. The measurement of the amplitude equation coefficients explains why the observed transition is always supercritical, and shows the effect of the edge constraint on the dissipation and eigen frequency of the various modes. The fluid surface tension is obtained from the dispersion relation measurement. Several visualization methods in large-aspect-ratio cells are presented.
Axisymmetric vortex breakdown Part 1. Confined swirling flow
Authors: Lopez J. M.
Published: April 2006

A comparison between the experimental visualization and numerical simulations of the occurrence of vortex breakdown in laminar swirling flows produced by a rotating endwall is presented. The experimental visualizations of Escudier (1984) were the first to detect the presence of multiple recirculation zones and the numerical model presented here, consisting of a numerical solution of the unsteady axisymmetric Navier-Stokes equations, faithfully reproduces these phenomena and all other observed characteristics of the flow. Further, the numerical calculations elucidate the onset of oscillatory flow, an aspect of the flow that was not clearly resolved by the flow visualization experiments. Part 2 of the paper examines the underlying physics of these vortex flows.
Two-dimensional flow of a viscous fluid in a channel with porous walls
Authors: Cox Stephen M.
Published: April 2006

We consider the flow of a viscous incompressible fluid in a parallel-walled channel, driven by steady uniform suction through the porous channel walls. A similarity transformation reduces the Navier-Stokes equations to a single partial differential equation (PDE) for the stream function, with two-point boundary conditions. We discuss the bifurcations of the steady solutions first, and show how a pitchfork bifurcation is unfolded when a symmetry of the problem is broken.

Then we describe time-dependent solutions of the governing PDE, which we calculate numerically. We analyse these unsteady solutions when there is a high rate of suction through one wall, and the other wall is impermeable: there is a limit cycle composed of an explosive phase of inviscid growth, and a slow viscous decay. The inviscid phase ‘almost’ has a finite-time singularity. We discuss whether solutions of the governing PDE, which are exact solutions of the Navier-Stokes equations, may develop mathematical singularities in a finite time.

When the rates of suction at the two walls are equal so that the problem is symmetrical, there is an abrupt transition to chaos, a ‘homoclinic explosion’, in the time-dependent solutions as the Reynolds number is increased. We unfold this transition by perturbing the symmetry, and compare direct numerical integrations of the governing PDE with a recent theory for ‘Lorenz-like’ dynamical systems. The chaos is found to be very sensitive to symmetry breaking.