bluuebunny/crossref_metadata_2025 huggingface dataset:
The boundary layer on a fixed sphere on the axis of an unbounded rotating fluid
Authors: Dennis S. C. R. , Ingham D. B.
Published: April 2006

The problem of determining both the steady and unsteady axially symmetrical motion of a viscous incompressible fluid outside a fixed sphere when the fluid at large distances rotates as a solid body is considered. It is assumed that the Reynolds number for the motion is so large that the boundary-layer equations may be assumed to hold. The steady-state boundary-layer equations are solved using backward- forward differencing and the terminal solutions at the equator and the pole of the sphere are generatedas part ofthe numerical procedure. To check that this steady-state solution can be approached from an unsteady situation, the case of a sphere that is initially rotating with the same constant angular velocity as the fluid and is then impulsively brought to rest is investigated. I n this case the motion is governed by a coupled set of three nonlinear time-dependent partial differential equations, which are solved by employing the semi-analytical method of series truncation to reduce the number of independent variables by one and then solving by numerical methods a finite set of partial differential equations in one space variable and time. The physical properties of the flow are calculated as functions of the time and compared with the known solution at small times and the steady-state solution.
Nonlinear self-excited acoustic oscillations within fixed boundaries
Authors: Keller Jakob J.
Published: April 2006

In §1 a brief discussion of the general problem of self-excited acoustic oscillations within fixed boundaries is given. I n §2 a second-order analysis is developed for the special case of rectangular cavities. A nonlinear wave equation is derived for essentially arbitrary boundary conditions. The analysis can be extended to other cavity geometries provided that the first-order solutions can be expressed in closed form. Various applications of the analysis are discussed in §3. It turns out that two-dimensional problems of self-excited oscillations generally lead to nonlinear equations containing terms with a time lag. It is anticipated that the time lag (rather than viscous effects or sound radiation) represents the key to a fundamental understanding of the character of the oscillations and the variety of modes appearing in self-excited resonators.
Flow separation in a rotating annulus with bottom topography
Authors: Page M. A.
Published: April 2006

The flow in a rotating annular cylinder, of finite depth, is examined when the Rossby number Ro is O(E½), where E is the Ekman number, and when there is a topography of height O(E½) on the base of the container. The flow, relative to the rigid axial rotation, is forced by differential rotation of the lid and as it moves over the topography the streamlines are deflected parallel to the bottom surface. This induces O(1) velocity variations near the axial walls of the annulus to which the boundary layers there, of thickness O(E¼), respond. For sufficiently large values of a parameter γ ∝Ro/E½ the skin friction can vanish within these layers, with some similaritits to boundary-layer separation in a non-rotating fluid. In this study the interior flow, with horizontal viscous diffusion neglected, is calculated and used to provide a boundary condition for the, E¼ layer flow. Once λ exceeds a finite critical value a singularity is encountered in the boundary layer corresponding to flow separation from the wall. This demonstrates that E¼ layers in a rotating fluid, which for Ro = 0 have little direct influence on the interior flow, can modify the gross properties of the flow for non-zero Rossby numbers, a conclusion also reached by Walker & Stewartson (1972) in a different context.
Comparison of conditional sampling and averaging techniques in a turbulent boundary layer
Authors: Subramanian C. S. , Rajagopalan S. , Antonia R. A. , Chambers A. J.
Published: April 2006

Visual examination of simultaneous temperature traces from a rake of cold wires placed across a turbulent boundary layer had enabled the identification of coherent temperature fronts. An X-wirelcold-wire arrangement was used simultaneously with the rake to provide measurements of the velocity fluctuations u (longitudinal) and v (normal) and the temperature fluctuation θ. Conditional averages of u, v, θ and products uv, uθ, vθ were obtained by application of conditional techniques based on the detection of the temperature fronts using information obtained at only one point in space. These averages, obtained at various positions across the layer, have been compared with those obtained when the rake was used to detect the fronts. The comparison has indicated that none of the one-point detection techniques is in good quantitative agreement with the rake detection technique, the largest correspondence between the rake technique and any ofthe other one-point techniques being only 51 yo. With the exception of the hole technique used in conjunction with the quadrant decomposition analysis, conditional averages obtained from one-point techniques are in reasonable qualitative agreement with those deduced using the rake.
A vortex-street model of the flow in the similarity region of a two-dimensional free turbulent jet
Authors: Oler J. W. , Goldschmidt V. W.
Published: April 2006

The mean-velocity profiles and entrainment rates in the similarity region of a two-dimensional jet are generated by a simple superposition of Rankine vortices arranged to represent a vortex street. The spacings between the vortex centres, their two-dimensional offsets from the centreline, as well as the core radii and circulation strengths, are all governed by similarity relationships and based upon experimental data.

Major details of the mean flow field such as the axial and lateral mean-velocity components and the magnitude of the Reynolds stress are properly determined by the model. The sign of the Reynolds stress is, however, not properly predicted.
Some aspects of the fluid dynamics of laser welding
Authors: Dowden John , Davis Michael , Kapadia Phiroze
Published: April 2006

When a laser beam is used as the energy source for welding two pieces of metal together, a hole is formed perpendicular to the plane of the workpiece. The latter is moved relative to the laser and metal is transferred from the front to the rear by fluid flow round the hole. The equations governing the process are set out and the conditions at the two boundaries in the problem (one between the hole and the molten metal, and the other between the liquid and the solid states of the metal) are considered.

Approximate solutions of the problem for low welding speeds are obtained for four different models. The first is one in which the viscosity is taken to be constant. In the second, the viscosity is allowed to depend linearly on temperature. The third model divides the liquid into a region in which the cooler part is taken to be viscous and the hotter part inviscid; the fourth model is then constructed as a limit, with the liquid motion considered as wholly inviscid. It is found that the motion is not irrotational in this last model. The models all display a downstream displacement of the boundary between the solid and liquid states, in agreement with observations. An expression for the minimum power of the laser is calculated.
An algorithmic approach to the linear stability of the Ekman layer
Authors: Melander Mogens V.
Published: April 2006

The linear stability of the stationary Ekman-layer flow near a plane boundary is considered. Analytical formulas for the eigenfunctions are derived by a spectral analysis. Standard optimization algorithms are used to calculate critical points, maximum growth rates and neutral-stability curves. The near approach provides a better basis for both a linear and a nonlinear stability analysis than the well-known methods have done. The method may also be applied to other boundary-layer problems.
Stokes flow past bubbles and drops partially coated with thin films. Part 2. Thin films with internal circulation – a perturbation solution
Authors: Johnson Robert E. , Sadhal S. S.
Published: April 2006

In the present study we examine the steady axisymmetric creeping flow due to the motion of a liquid drop or a bubble which is partially covered by a thin immiscible fluid layer or film. The analysis is based on the assumption that surface-tension forces are large compared with viscous forces which deform the drop, and that the circulation in the film is weak. The latter assumption is satisfied provided that the film-fluid viscosity is not too small. A perturbation scheme based on the thinness of the fluid layer is used to construct the solution.

One of the principal results is an expression for the drag force on the complex drop. We also find that the extent to which the drop or bubble is covered the film has a maximum value depending on the magnitude of the driving force on the film. In addition, we find the rather interesting result that when the ratio of the primary drop viscosity and bulk fluid viscosity is greater than ½, the circulation within the film may have a double-cell structure.
A spanwise structure in the plane shear layer
Authors: Jimenez Javier
Published: April 2006

We study experimentally the spanwise structure of the mean flow field of a plane shear layer. The field is dominated by a lateral undulation that persists downstream to form long longitudinal structures. Both the amplitude and spacing of these structures vary in such a way as to suggest that they are due to a secondary instability of the flow field. Some models for this instability are discussed and compared with the experimental results.
Flow past a liquid drop with a large non-uniform radial velocity
Authors: Sadhal S. S. , Ayyaswamy P. S.
Published: April 2006

In this analysis, the translation of a liquid drop experiencing a strong non-uniform radial velocity has been investigated. The situation arises when a moving liquid drop experiences condensation, evaporation or material decomposition at the surface. By simultaneously treating the flow fields inside and outside the drop, we have obtained physical results relevant to the problem. The magnitude of the radial velocity is allowed to be very large, but the drop motion is restricted to slow translation. The solution to the problem has been developed by considering a uniform radial flow with the translatory motion introduced as a perturbation. The role played by the inertial terms due to the strong radial field has been clearly delineated. The study has revealed several interesting features. An inward normal velocity on a slowly moving drop increases the drag. An increasing outward normal velocity decreases the drag up to a minimum beyond which it increases. The total drag force not only consists of contributions from the viscous and the form drags but also from the momentum transport at the interface. Since the liquid drop admits a non-zero tangential velocity, the tangential momentum convected by the radial velocity forms a part of this drag force. The circulation inside the drop decreases (increases) with an outward (inward) normal velocity. A sufficiently large non-uniform outward velocity causes the circulation to reverse.

In the limit of the internal viscosity becoming infinite, our analysis collapses to the simple case of a translating rigid sphere experiencing a large non-uniform radial velocity. By letting the radial velocity become vanishingly small the Stokes-flow solution is recovered.

An important contribution of the present study is the identification of a new singularity in the flow description. It accounts for both the inertial and the viscous forces and displays Stokeslet-like characteristics at infinity.
Long-time behaviour of a random inhomogeneous field of weakly nonlinear surface gravity waves
Authors: Janssen Peter A. E. M.
Published: April 2006

In this paper we investigate nonlinear interactions of narrowband, Gaussian-random, inhomogeneous wavetrains. Alber studied the stability of a homogeneous wave spectrum as a function of the width σ of the spectrum. For vanishing bandwidth the deterministic results of Benjamin & Feir on the instability of a uniform wavetrain were rediscovered whereas a homogeneous wave spectrum was found to be stable if the bandwidth is sufficiently large. Clearly, a threshold for instability is present, and in this paper we intend to study the long-time behaviour of a slightly unstable modulation by means of a multiple-timescale technique. Two interesting cases are found. For small but finite bandwidth – the amplitude of the unstable modulation shows initially an overshoot, followed by an oscillation around the time-asymptotic value of the amplitude. This oscillation damps owing to phase mixing except for vanishing bandwidth because then the well-known Fermi–Pasta–Ulam recurrence is found. For large bandwidth, however, no overshoot is found since the damping is overwhelming. In both cases the instability is quenched because of a broadening of the spectrum.
Fluid-property effects on flow-generated waves on a compliant surface
Authors: Hansen R. J. , Hunston D. L.
Published: April 2006

An experimental study of the influence of liquid viscosity and viscoelasticity on flow-generated waves on a compliant surface has been conducted in a rotating-disk geometry. Over the entire range of liquid properties studied, each test gave a well-defined critical onset flow velocity above which waves were present and below which no waves were observed. This onset velocity increased with increasing fluid viscosity, and for sufficiently high viscosities the onset occurred when the flow on the disk was laminar rather than turbulent. The effects of liquid viscoelasticity were examined in the turbulent flow using dilute solutions of high-molecular-weight polymers. This type of viscoelasticity had little influence on the onset flow velocity in these circumstances, but did make the wave structure on the surface more regular in appearance than when the liquid was Newtonian. In all cases the wave structure produced a dramatic increase in drag similar to that expected for a rough surface. For the viscoelastic fluid, however, the increase in drag was much less than for a viscous fluid of the same viscosity.
The lift on an aerofoil in starting flow
Authors: Graham J. M. R.
Published: April 2006

An analysis is given of the initial development of the lift on an aerofoil in inviscid starting flow. It is shown that because of the spiral shape of the vortex sheet shed initially from the trailing edge the lift and drag are both singular at the start of impulsive motion. This result is in contrast with the prediction of finite forces by methods that assume the vortex sheet to be initially planar. The effect of a steady rate of change of incidence following the sudden onset of transverse (heaving) motion of an aerofoil in a steady stream is also discussed.
Initial-value problems for Rossby waves in a shear flow with critical level
Authors: Tung Ka Kit
Published: April 2006

The time-dependent evolution of sheared Rossby waves starting from an initial disturbance is studied for the simple case in which the shear is uniform. The uniform-shear assumption allows explicit solutions to be obtained which are useful in addressing the issue of the long-time asymptotic approach to normal modes and in assessing the relative importance of viscosity, nonlinearity and time-dependence in the evolution of Rossby waves in the presence of critical layers.
Boundary-layer transition and the behaviour of spiral vortices on rotating spheres
Authors: Kohama Y. , Kobayashi R.
Published: April 2006

The mechanism of boundary-layer transition and the behaviour of spiral vortices on spheres rotating in otherwise undisturbed fluid were investigated experimentally. Critical and transition Reynolds numbers which determine the laminar-turbulent transition regime on the sphere surface were measured. In addition the number of spiral vortices on the sphere and the direction of the vortex axis were clarified.
Numerical investigation of supercritical Taylor-vortex flow for a wide gap
Authors: Fasel H. , Booz O.
Published: April 2006

For a wide gap (R1/R2= 0.5) and large aspect ratiosL/d, axisymmetric Taylor-vortex flow has been observed in experiments up to very high supercritical Taylor (or Reynolds) numbers. This axisymmetric Taylor-vortex flow was investigated numerically by solving the Navier–Stokes equations using a very accurate (fourth-order in space) implicit finite-difference method. The high-order accuracy of the numerical method, in combination with large numbers of grid points used in the calculations, yielded accurate and reliable results for large supercritical Taylor numbers of up to 100Tac(or 10Rec). Prior to this study numerical solutions were reported up to only 16Tac. The emphasis of the present paper is placed upon displaying and elaborating the details of the flow field for large supercritical Taylor numbers. The flow field undergoes drastic changes as the Taylor number is increased from just supercritical to 100Tac. Spectral analysis (with respect toz) of the flow variables indicates that the number of harmonics contributing substantially to the total solution increases sharply when the Taylor number is raised. The number of relevant harmonics is already unexpectedly high at moderate supercriticalTa. For larger Taylor numbers, the evolution of a jetlike or shocklike flow structure can be observed. In the axial plane, boundary layers develop along the inner and outer cylinder walls while the flow in the core region of the Taylor cells behaves in an increasingly inviscid manner.
Natural large-scale structures in the axisymmetric mixing layer
Authors: Zaman K. B. M. Q. , Hussain A. K. M. F.
Published: April 2006

This paper summarizes results of our investigations on: optimization of conditional sampling technique for eduction of naturally occurring large-scale structures in an axisymmetric mixing layer, comparison of the natural structure with that induced via controlled excitation, and the sensitivity of the educed structure to the excitation amplitude and of the natural coherent structure to Reynolds number and initial condition. Measurements include sectional-plane contours of various structure properties; however, coherent vorticity is the principal measure used in these considerations. All plausible alternative triggering criteria, based on reference velocity signals from fixed probes, were considered in order to arrive at the best practical eduction technique. It is shown that the simple criterion of triggering on the positive peaks of the longitudinal velocity signal derived from the high-speed edge of the mixing layer results in the optimum eduction. The characteristics of the natural structures, educed by the optimum detection criterion, are found to be independent ofReDover the measurement range 5.5 × 104−8 × 105. A mild dependence on the initial condition (viz laminarvs.turbulent) is observed, the structures being more disorganized for the initially laminar boundary-layer case. The educed natural structures agree well with those induced by controlled sinusoidal excitation at low excitation levels; higher levels, however, produce considerably stronger structures.
The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion
Authors: Corcos G. M. , Lin S. J.
Published: April 2006

Experimental evidence suggests that in the turbulent mixing layer the fundamental mechanism of growth is two-dimensional and little affected by the presence of vigorous three-dimensional motion. To quantify this apparent property and study the growth of streamwise vorticity, we write for the velocity field
\[
{\boldmath V}(x, t) = {\boldmath U}(x, z, t) + {\boldmath u}(x, y, z, t),
\]
where U is two-dimensional and u is three-dimensional. In a first version of the problem U is independent of u, while in the second U is the spanwise average of V. In both cases the equation for u is linearized around U. The equations for U and u are solved simultaneously by a finite-difference calculation starting with a slightly disturbed parallel shear layer.

The solutions provide a detailed description of the growth of the three-dimensional motion. They show that its characteristics are dictated by the distribution of spanwise vorticity which results from roll-up and pairing. Pairing inhibits its growth. The solutions also demonstrate that even when the three-dimensional flow attains large amplitudes it has a negligible effect on the interaction of spanwise vortices and thus on the growth of the layer.
Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield
Authors: Lun C. K. K. , Savage S. B. , Jeffrey D. J. , Chepurniy N.
Published: April 2006

The flow of an idealized granular material consisting of uniform smooth, but nelastic, spherical particles is studied using statistical methods analogous to those used in the kinetic theory of gases. Two theories are developed: one for the Couette flow of particles having arbitrary coefficients of restitution (inelastic particles) and a second for the general flow of particles with coefficients of restitution near 1 (slightly inelastic particles). The study of inelastic particles in Couette flow follows the method of Savage & Jeffrey (1981) and uses an ad hoc distribution function to describe the collisions between particles. The results of this first analysis are compared with other theories of granular flow, with the Chapman-Enskog dense-gas theory, and with experiments. The theory agrees moderately well with experimental data and it is found that the asymptotic analysis of Jenkins & Savage (1983), which was developed for slightly inelastic particles, surprisingly gives results similar to the first theory even for highly inelastic particles. Therefore the ‘nearly elastic’ approximation is pursued as a second theory using an approach that is closer to the established methods of Chapman-Enskog gas theory. The new approach which determines the collisional distribution functions by a rational approximation scheme, is applicable to general flowfields, not just simple shear. It incorporates kinetic as well as collisional contributions to the constitutive equations for stress and energy flux and is thus appropriate for dilute as well as dense concentrations of solids. When the collisional contributions are dominant, it predicts stresses similar to the first analysis for the simple shear case.
A Conditional-Sampling Study Of The Interaction Of Two Turbulent Wakes
Authors: Fabris G.
Published: April 2006

Measurements were taken of a developing complex turbulent flow formed by the merging of two far turbulent wakes of equal cylinders. The lower wake only was slightly heated, permitting the use of the conditional-sampling technique to study the interaction of the two wakes in detail. A special four-wire probe (Fabris 1978) enabled simulataneous uncontaminated measurement of all three instantaneous velocity components and temperature. The single-wake data of Fabris (1979) served as a reference. The interaction of the two single turbulent wakes resulted in a striking enhancement of the lateral transfer of heat. Undulations of the thermal interface are significantly wider laterally, but shorter streamwise than in the basic single wake. Lateral velocities of the heated and the unheated intermittent lumps are amplified two- to threefold by the interaction process. Levels of all three components of the kinetic energy of turbulence reach their highest relative maxima in the heated zones as they cross the upper cold wake. These maxima are higher than appropriate conventional or conditional maxima in the single wake. In addition to physical insights into the phenomena of turbulent flow, the data should be useful in refining and validating predictive methods, possibly spurring their further development.
Wave propagation in a thin-walled liquid-filled initially stressed tube
Authors: Kuiken G. D. C.
Published: April 2006

Wave propagation through a thin-walled cylindrical orthotropic viscoelastic initially stressed tube filled with a Newtonian fluid is discussed. Special attention is drawn to the influence of the initial stretch on the wave propagation. It is shown that initial stretching of real arteries enhances the propagation of blood pressure pulses in mammalian arteries. The dispersion equation for the initial-value problem of a semi-infinite tube is also derived. It is shown that the speed of propagation and the attenuation vary with the distance from the support. The results obtained for the axial wave mode provide an explanation for the experimental observations, which is not possible with the results obtained for the infinite tube.
The application of laser-induced Rayleigh light scattering to the study of turbulent mixing
Authors: Pitts William M. , Kashiwagi Takashi
Published: April 2006

This work describes the development and characterization of an experimental system employing laser-induced Rayleigh light scattering with digital data acquisition as a time-resolved quantitative concentration probe in the turbulent flow field of a binary gas mixture. Equations for the expected signal and noise levels are given. Estimates of these parameters for the experimental system used here are in satisfactory agreement with experiment. It is demonstrated that the laser Rayleigh-light-scattering technique provides measurements having high spatial and temporal resolution for various locations within the concentration flow field. Measurements at various positions in the flow field of an axisymmetric methane jet issuing into a slow flow of air are reported and, where possible, compared with appropriate literature results. The statistical properties of the turbulent concentration fluctuations are found to be in good agreement with other independent measurements. Conditionally sampled measurements are also reported and shown to behave in the same manner as the limited number of similar measurements in the literature. The capability of calculating power spectra and correlation functions for the time behaviour of the methane concentration is also demonstrated. Raman and Rayleigh scattering techniques are compared as measurement techniques of scalar values in turbulent flow fields.
Analysis of the forced ventilation in containership holds
Authors: Baum Howard R. , Rockett John A.
Published: April 2006

An analysis of the fluid flow and mass transfer induced by ventilation systems in containership holds was carried out. The result of the work was used to support the U.S. position before a committee of the International Convention on Safety to Life at Sea. The analysis consists of a detailed calculation of the forced motion through an interconnected set of narrow, stably stratified, vertical air passages, which represent an idealized containership hold. The results of this calculation were then used to predict the vapour concentration of spilled volatile material assumed to lie at the bottom of the vertical air passages. The result is a set of formulae which determine the rate of extraction of volatile material as a function of hold geometry, ventilation parameters, and ambient stratification. A variety of computed results are presented. The results indicate the crucial importance of locating the extractor as close to the hold bottom as technically possible.
Particle trajectories in nonlinear capillary waves
Authors: Hogan S. J.
Published: April 2006

The particle trajectories of nonlinear capillary waves are derived. The properties of the surface and subsurface particles are presented in exact analytic form, up to and including the highest wave. It is found that the orbits of the steeper waves are neither circular nor closed. For the highest wave, a particle moves through a distance [X] equal to 7.99556 λ in one orbit, where λ is the wavelength. It moves with an average horizontal drift velocity U equal to 0.88883c, where c is the phase speed of the wave. In addition, the subsurface particles (at depths nearly three-quarters that of the wavelength) move at speeds up to one-tenth that of surface particles.
Organized structures in turbulent Taylor-Couette flow
Authors: Barcilon A. , Brindley J.
Published: April 2006

A simple mathematical model is constructed to describe the regime of flow, extending over a wide range of values of Taylor number, in which turbulent Taylor–Couette flow in the annular region between two coaxial circular cylinders is characterized by the coexistence of steady coherent motion on two widely separated scales. These scales of motion, corresponding to the gap width of the annular region and to a boundary-layer thickness, are each identified as the consequence of a centrifugal instability, and are described as Taylor vortices and Görtler vortices respectively.

The assumption that both scales of motion are near marginal stability gives a closure to a pair of coupled eigenvalue problems, and the results of a linear analysis are shown to be in good agreement with many features of experimental observations.
Three-dimensional viscous flows with large secondary velocity
Authors: Briley W. R. , Mcdonald H.
Published: April 2006

A new system of approximating equations is derived for three-dimensional steady viscous compressible flows in which a primary flow direction is present, but in which both transverse velocity components can be large. If the transverse velocity vector which corrects a given potential flow is first decomposed into ‘potential’ and ‘rotational’ vector components, then a re-examination of three-dimensional boundary-layer theory shows that both components (vϕ, wϕ) of the potential-velocity vector may be assumed small, whereas both components (vψ, wψ) of the rotational-velocity vector and hence of the composite secondary flow (v, w) can remain of order unity. An assumption of small scalar potential then leads to a system of governing equations whose characteristic polynomial has a non-elliptic form for arbitrary Mach number, without introducing any direct approximation of either streamwise or transverse pressure gradient terms. These non-elliptic equations can be solved very economically as a well-posed initial/boundary-value problem. Computed results for laminar subsonic flow in a curved square duct confirm the small scalar-potential approximation for both large (R/d = 100) and small (R/d = 2) radius of curvature. Other computations for R/d = 2.3 are in good agreement with the measurements of Taylor, Whitelaw & Yianneskis (1980).
Theoretical study of the transonic flow past wedge profiles with detached shock waves
Authors: Abboud Michel
Published: April 2006

This report presents a numerical study of the two-dimensional, steady and inviscid flow of a perfect gas past wedge profiles with detached shock waves for free-stream Mach numbers between 1.05 and 1.44.

Utilizing the hodograph transformation, a boundary-value problem for the mixed flow is formulated in the hodograph plane and subsequently solved by a finite-difference scheme, iterating respectively between the elliptic and hyperbolic regions. The use of boundary-fitted coordinates and a graded lattice failed to achieve satisfactory results, owing to either convergence difficulties or numerical inaccuracies introduced through the coordinate generator. On the other hand, Cartesian coordinates presented no convergence problems and yielded accurate results.

After transforming the solution back to the physical plane, the flow field between the shock wave and the limiting Mach wave is determined. A comparison of the results with experiments and other theories shows a good agreement both for the pressure distribution on the wedge and for the shock stand-off distance.

Also of special interest is a quantitative comparison of the results with the small-disturbance theory (solution of the Tricomi equation) and the limiting case of the free-stream Mach number 1.

Moreover, an example of the flow past round-nosed wedges, with and without an angle of attack, is treated using the inverse method.
Mixing and combustion with low heat release in a turbulent shear layer
Authors: Mungal M. G. , Dimotakis P. E.
Published: April 2006

Turbulent mixing and combustion are investigated in a gaseous shear layer formed between two streams: one containing a low concentration of hydrogen in nitrogen and the other containing a low concentration of fluorine in nitrogen. The resulting temperature field is measured simultaneously at eight points across the width of the layer using fast-response cold-wire thermometry. The results show the presence of large, hot structures separated by tongues of cool fluid that enter the layer from either side. The usual bell-shaped mean-temperature profiles therefore result from a duty cycle whereby a fixed probe sees alternating hot and cool fluid, which results in the local mean. The adiabatic flame temperature is not achieved in the mean, at any location across the layer. For fixed velocities, it is found that, in general, two different mean-temperature profiles result from a given pair of reactant compositions if the sides of the layer on which they are carried are exchanged (‘flipped’). This finding is a direct consequence of the asymmetric entrainment of fluid into the layer. Results are compared with the predictions of Konrad and discussed in the context of the Broadwell–Breidenthal model. By comparison with the liquid result of Breidenthal, the amount of product formed in the layer at high Reynolds number is found to be dependent upon the Schmidt number. Results for a helium–nitrogen layer are discussed briefly.
Structure and mixing of a transverse jet in incompressible flow
Authors: Broadwell J. E. , Breidenthal R. E.
Published: April 2006

The flow field induced by a jet in incompressible cross-flow is analysed and the results compared with those obtained in a reacting water-jet experiment. It is argued that the axial vortex pair in the flow arises from the jet momentum normal to the free stream, the momentum flux being equivalent to a normal force, i.e. to a lift.
Some observations of the transition process on the windward face of a long yawed cylinder
Authors: Poll D. I. A.
Published: April 2006

An experiment has been performed to determine the effect of yaw upon transition in the boundary layer formed on the windward face of a long cylinder. The china-clay-evaporation and surface-oil-flow techniques have been used to study the development of the fixed-wavelength stationary disturbances which are characteristic of cross-flow instability. It has been found that the boundary layer is also susceptible to time-dependent disturbances which grow to very large amplitudes prior to the onset of transition. These disturbances have been studied with a hot-wire anemometer. The conditions necessary for the onset and completion of transition have been determined by the use of surface Pitot tubes. Data from the experiment have been compared with the simple criteria for instability and transition which were proposed by Owen & Randall over thirty years ago. In general it has been found that these criteria are inadequate, and, where possible, improvements have been proposed. The raw data are presented in sufficient detail for them to be used to test, or calibrate, future theoretical models of the transition process in three-dimensional boundary-layer flows.
Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 2. Analysis
Authors: Dewey J. M. , Mcmillin D. J.
Published: April 2006

A non-stationary approach to the reflection of weak plane shocks is suggested as an alternative to the usual pseudo-stationary transformation. For regular reflection the non-stationary model produces results which are identical to those obtained using the pseudo-stationary assumption, but with simpler algebra. For weak Mach reflections, where the predictions of the pseudo-stationary model are in disagreement with experimental results, the non-stationary model predicts accurately the observed shapes and positions of the reflected and Mach stem shocks and the spatially varying flow properties behind these shocks. However, the non-stationary model predicts that the gas flows above and below the contact surface, relative to the triple point, are not quite parallel. Parallel flows could be obtained only in the limiting case of grazing incidence, when the reflected shock was sonic. The model is based on the experimental results presented in Part 1 of this paper.
An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow
Authors: Bach Poul , Hassager Ole
Published: April 2006

An algorithm is constructed for the use of the Lagrangian kinematic specification in Newtonian fluid mechanics. The algorithm is implemented with a finite-element method, and it is demonstrated that the method accurately describes free-surface flow, including the effects of surface tension, with the use of just bilinear isoparametric elements. Moving contact lines are modelled with a small amount of slip near the contact lines. The contact angle boundary condition is included in the form of a net interfacial force specified at the contact line. Simulations of measurements in a parallel-plate geometry show that the measured apparent contact angle is not the true angle, and that the true angle is always very close to the equilibrium value.
On flow visualization using reflective flakes
Authors: Savaş Ö.
Published: April 2006

An analysis of flow visualization using small reflective flakes is introduced. This rational analysis is based on a stochastic treatment of Jeffery's (1922) solution for the motion of ellipsoidal particles in a viscous fluid, wherein thin flakes tend to align with stream surfaces. The predicted light fields are confirmed by examples of parallel flows, the flow over a rotating disk, and the spinup from rest in a cylindrical cavity. The Tollmien–Schlichting wave packet trailing a turbulent spot is taken as an example to discuss the suitability of the technique for visualizing small-amplitude waves. Attenuation of light through a suspension is described.
Geodynamic thermal runaway with melting
Authors: Ockendon J. R. , Tayler A. B. , Emerman S. H. , Turcotte D. L.
Published: April 2006

We consider the penetration of a solid medium by a foreign body which is large enough for frictional heating to melt the medium and maintain a thin liquid layer ahead of the body. This study is motivated by the possibility of the Earth's core having been formed by liquid iron diapirs melting their way through the solid, deformable mantle. Our principal results are the existence of a critical size for the body for the motion to be maintained under gravity and the ease with which an immiscible liquid body can penetrate at constant velocity compared to a solid one.
Forces on cylinders in viscous oscillatory flow at low Keulegan-Carpenter numbers
Authors: Bearman P. W. , Downie M. J. , Graham J. M. R. , Obasaju E. D.
Published: April 2006

This paper presents a comparison between theory and experiment for the in-line forces on cylinders of general cross-section in planar oscillatory flows of small amplitude. The theoretical analysis evaluates corrections to the standard inviscid inertial force at low Keulegan-Carpenter numbers which arise from the presence of viscous laminar boundary layers and from the development of vortex shedding. The boundary-layer contribution due to both skin friction and displacement effects is calculated to first order in the Stokes parameter β−½. The contribution to the in-line force from separation and vortex shedding, for which the results presented only apply to sharp-edged bodies, is taken from previous work on vortex shedding from isolated edges using the discrete vortex modelling technique. The resulting force has components both in phase with the fluid acceleration (inertia) and in phase with the velocity (drag).

The theoretical results are compared to measurements taken in a [xcup ]-tube water channel on a number of cylinders of different cross-section including circular cylinders and sharp-edged sections. The comparisons suggest that the theory is valid for Keulegan–Carpenter numbers below about 3 and for moderately high values of the β parameter.
Transient axisymmetric motion of a floating cylinder
Authors: Newman J. N.
Published: April 2006

A linear theory is developed in the time domain for vertical motions of an axisymmetric cylinder floating in the free surface. The velocity potential is obtained numerically from a discretized boundary-integral-equation on the body surface, using a Galerkin method. The solution proceeds in time steps, but the coefficient matrix is identical at each step and can be inverted at the outset.

Free-surface effects are absent in the limits of zero and infinite time. The added mass is determined in both cases for a broad range of cylinder depths. For a semi-infinite cylinder the added mass is obtained by extrapolation.

An impulse-response function is used to describe the free-surface effects in the time domain. An oscillatory error observed for small cylinder depths is related to the irregular frequencies of the solution in the frequency domain. Fourier transforms of the impulse-response function are compared with direct computations of the damping and added-mass coefficients in the frequency domain. The impulse-response function is also used to compute the free motion of an unrestrained cylinder, following an initial displacement or acceleration.
Bifurcation phenomena in flows between a rotating circular cylinder and a stationary square outer cylinder
Authors: Mullin T. , Lorenzen A.
Published: April 2006

The properties of steady cellular flows between a rotating cylinder and a stationary outer one of square cross-section have been investigated experimentally. Results for the primary-flow selection process, which involves four-cell and six-cell states, are intricate but bear a reassuring qualitative resemblance to those obtained previously for the standard Taylor–Couette model. In addition, the existence of anomalous modes disconnected from the primary flow has been demonstrated and their dependence upon the length of the flow domain studied. The phenomena are found to be in accord with the abstract theoretical framework that has been successfully used to interpret previous experimental observations on steady-flow problems with multiple solutions.
Influence of weak wall undulations on the structure of turbulent pipe flow: an experimental and numerical study
Authors: Chauve M. P. , Schiestel R.
Published: April 2006

The influence of weak periodic wall undulations on the structure of turbulent pipe flow has been studied in three ways: measurements in air flow using pressure probes and hot-wire techniques, visualizations in water flow and numerical predictions based on a turbulence (k-ε) model. The flows at Reynolds numbers of 30000 and 115000 have been particularly investigated. The flow characteristics proved to be very different from those observed in a straight pipe. Calculations and experiments agree well for the mean- and turbulent-energy fields; however the detailed behaviour of some local quantities such as anisotropy of the Reynolds stress is not well predicted particularly in the crest region. So the performances and the limitations of classical closure have been appraised. The existence of an unsteady reverse-flow region downstream of every crest suggested by measurements and calculations has been clearly confirmed by visualizations in water flow.
Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements
Authors: Loc Ta Phuoc , Bouard R.
Published: April 2006

Early stages of unsteady viscous flows around a circular cylinder at Reynolds numbers of 3 × 103 and 9.5 × 103 are analysed numerically by direct integration of the Navier–Stokes equations – a fourth-order finite-difference scheme is used for the resolution of the stream-function equation and a second-order one for the vorticity-transport equation. Evolution with time of the flow structure is studied in detail. Some new phenomena are revealed and confirmed by experiments.

The influence of the grid systems and the downstream boundary conditions on the flow structure and the velocity profiles is reported. The computed results are compared qualitatively and quantitatively with experimental visualization and measurements. The comparison is found to be satisfactory.
Countercurrent convection in a double-diffusive boundary layer
Authors: Nilson R. H.
Published: April 2006

Countercurrent flow may be induced by opposing buoyancy forces associated with compositional gradients and thermal gradients within a fluid. The occurrence and structure of such flows is investigated by solving the double-diffusive boundary-layer equations for steady laminar convection along a vertical wall of finite height. Non-similar solutions are derived using the method of matched asymptotic expansions, under the restriction that the Lewis and Prandtl numbers are both large. Two sets of asymptotic solutions are constructed, assuming dominance of one or the other of the buoyancy forces. The two sets overlap in the central region of the parameter space; each set matches up with neighbouring unidirectional similarity solutions at the respective borderlines of incipient counterflow.

Interaction between the buoyancy mechanisms is controlled by their relative strength R and their relative diffusivity Le. Flow in the outer thermal boundary layer deviates from single-diffusive thermal convection, depending upon the magnitude of the parameter RLe. Flow in the inner compositional boundary layer deviates from single-diffusive compositional convection, depending upon the magnitude of $RLe^{\frac{1}{3}}$.
Unsteady separation in a boundary layer produced by an impinging jet
Authors: Didden Norbert , Ho Chih-Ming
Published: April 2006

A vortex-induced unsteady separation was investigated experimentally in the laminar boundary layer produced by an axisymmetric jet impinging normally onto a flat plate. By forcing the air jet, primary ring vortices were periodically generated in the jet shear layer. Phase-locked flow visualization showed that the wall-jet boundary layer separated periodically and evolved into a secondary vortex counter rotating with respect to the primary vortex. The unsteady separation is induced by the primary vortex and moves downstream in the radial mean-flow direction. Phase-averaged hot-wire measurements using a parallel-wire sensor in the vicinity of the unsteady separation provided data for locating the onset of separation in space and time. The data revealed that the unsteady separation originated from a local shear layer which was initiated by the unsteady adverse pressure gradient produced by the primary vortex.
The flow of a viscous incompressible fluid past a normal flat plate at low and intermediate Reynolds numbers: the wake
Authors: Hudson J. D. , Dennis S. C. R.
Published: April 2006

The Navier-Stokes equations are solved numerically for the steady separated flow past a normal flat plate for Reynolds numbers in the range 0.1 ≤ R ≤ 20. Eddy dimensions together with the position of the vortex centre are presented and compared with the few other estimates and predictions available. Streamlines and equivorticity lines are also given. The main result of interest is the extremely good comparison with experimental results over this range of Reynolds numbers. The method of solution is based on an artificial time-dependent procedure using a distorted time. Results are given only for the steady-state flow.