bluuebunny/crossref_metadata_2025 huggingface dataset:
Some effects of inclination on elastohydrodynamic squeeze film problems
Authors: Whicker D. , Browne A. L. , Rohde S. M.
Published: April 2006

An analysis is presented for the non-inertial descent of an inclined sinkage element (a rectangular prism) through a viscous fluid onto a rigid surface. The effects of sinkage-element deformability, slip velocity and time-dependent loading conditions are considered. Unlike previous analyses no assumptions are made a priori about the form of the pressure distribution during, or the effect of corners on, inclined sinkage. The results for rigid square plates are compared with those of previous analyses and with the limited amount of experimental data available. Results are also presented for a deformable sinkage element, which is used to model the action of an individual tyre tread element on a wet pavement. An inclination function based on available data on the tyre surface shape in the footprint region is used. The loading function for this case is based on measured values of tyre footprint pressure.
Thermally, mechanically or externally driven flows in a gas centrifuge with insulated horizontal end plates
Authors: Matsuda Takuya , Hashimoto Kiyoshi
Published: April 2006

The axisymmetric motion of a compressible fluid in a rapidly rotating cylinder is considered using a linear approach and boundary-layer techniques. The deviation of the fluid motion from rigid-body rotation is caused either by an applied temperature distribution on the side wall, a differential rotation of the top and bottom end plates or sources and sinks of fluid distributed on the end plates. The horizontal end plates are assumed to be thermally insulated, while the side wall is conducting. The critical parameter governing the problem is found to be E−½(γ − 1) PrG0/4γ, where E is the Ekman number, γ the ratio of specific heats, Pr the Prandtl number and G0 the square of a rotational Mach number. If this parameter is larger than unity, the coupled effect of the compressibility of the fluid and the thermal condition on the end plates suppresses the flow in the cylinder. The flow in the inner inviscid core is strongly coupled with the Ekman-layer flow through the boundary conditions on the end plates, something which does not occur if the fluid is Boussinesq nor if the fluid is compressible and the end plates are conducting.
Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations
Authors: Fasel H.
Published: April 2006

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.
The lateral migration of a spherical particle in two-dimensional shear flows
Authors: Vasseur P. , Cox R. G.
Published: April 2006

The lateral migration of a solid spherical particle suspended in a fluid flowing between parallel vertical walls is investigated theoretically using a method developed by Cox & Brenner (1968). Buoyant and neutrally buoyant, freely rotating and non-rotating particles in the fluid flow are considered as is also the case of a sedimenting particle in a quiescent fluid. The results obtained are applied to the special cases of plane Poiseuille flow and of plane shear flow, these situations being investigated in detail.
The design of piezometer rings
Authors: Blake K. A.
Published: April 2006

A mathematical model is developed with which the reading from a piezometer ring may be predicted from the individual wall static measurements and from this the conventional form of ring is shown to be unreliable in asymmetrical flow. An alternative form of ring known as the Triple-T is analysed and shown to provide a true mean pressure in all cases. It is recommended that this form be used in all future test work. Tests demonstrating the validity of the theory are described.
A stationary oblique breaking wave for laboratory testing of surfboards
Authors: Hornung H. G. , Killen P.
Published: April 2006

A surface gravity wave obliquely incident on a sloping beach is broken near the beach and has a smooth surface further out. Viewed in the frame of reference of the transition from the smooth to the broken part, the flow is steady, and the wave is oblique to the free stream. By placing a suitably shaped obstacle in a flume operated at high Froude number, such a wave can be generated. Experiments in which a wave of 18 cm height was generated are described and the wave shape and some of its characteristics presented. In particular, the dividing stream surface separating that part of the flow which curls over into the break from the part that flows smoothly over the obstacle is discussed.

Model surfboards can ride this wave unsupported, provided the correctly scaled weight loads them at the right centre-of-mass position. This makes it possible to determine the forces on the board without a balance. A comparison of the measured forces with estimates, particularly of the drag, indicate that viscous and surface-tension phenomena introduce only small scale effects in the Froude number modelling. While the results are not sufficiently accurate to draw definite conclusions about the effects of surf board shape, they indicate clearly that surf board flows may be modelled with quantitative success in the laboratory.
Motion of a bore over a sloping beach: an approximate analytical approach
Authors: Sachdev P. L. , Seshadri V. S.
Published: April 2006

The motion of a bore over a sloping beach, earlier considered numerically by Keller, Levine & Whitham (1960), is studied by an approximate analytic technique. This technique is an extension of Whitham's (1958) approach for the propagation of shocks into a non-uniform medium. It gives the entire flow behind the bore and is shown to be equivalent to the theory of modulated simple waves of Varley, Ventakaraman & Cumberbatch (1971).
Selective withdrawal from a finite rectangular tank
Authors: Imberger Jorg , Thompson Rory , Fandry Chris
Published: April 2006

The time development of two-dimensional fluid motion induced by a line sink in a rectangular, density stratified reservoir with a free surface is given. It is shown that the initiation of such a sink gives birth to a spectrum of internal expanding shear fronts with a progressively decreasing vertical wavelength. These fronts move out from the sink and travel towards the far wall, where they are reflected. This process ceases once the front with a vertical wavelength equal to the steady withdrawal-layer thickness has reached the end wall. The fronts so introduced continue to move back and forth, expanding to standing waves if the viscosity of the fluid is small enough. The evolution and nature of the withdrawal layer are shown to depend critically on the relative magnitude of the convective inertia and viscous forces, the number of reflexions from the rear wall and the Prandtl number.
Stokes flow past a slender body of revolution
Authors: Geer James
Published: April 2006

The complete uniform asymptotic expansion of the velocity and pressure fields for Stokes flow past a slender body of revolution is obtained with respect to the slenderness ratio ε of the body. A completely general incident Stokes flow is assumed and hence these results extend the special cases treated by Tillett (1970) and Cox (1970). The part of the flow due to the presence of the body is represented as a superposition of the flows produced by three types of singularity distributed with unknown densities along a portion of the axis of the body and lying entirely inside the body. The no-slip boundary condition on the body then leads to a system of three coupled, linear, integral equations for the densities of the singularities. The complete expansion for these densities is then found as a series in powers of ε and ε log ε. It is found that the extent of these distributions of singularities inside the body is the same for all the singular flows and depends only upon the geometry of the body. The total force, drag and torque experienced by the body are computed.
On the dynamics of finite-amplitude baroclinic waves as a function of supercriticality
Authors: Pedlosky Joseph
Published: April 2006

A finite-amplitude model of baroclinic instability is studied in the case where the cross-stream scale is large compared with the Rossby deformation radius and the dissipative and advective time scales are of the same order. A theory is developed that describes the nature of the wave field as the shear supercriticality increases beyond the stability threshold of the most unstable cross-stream mode and penetrates regions of higher supercriticality. The set of possible steady nonlinear modes is found analytically. It is shown that the steady cross-stream structure of each finite-amplitude mode is a function of the supercriticality.

Integrations of initial-value problems show, in each case, that the final state realized is the state characterized by the finite-amplitude mode with the largest equilibrium amplitude. The approach to this steady state is oscillatory (nonmonotonic). Further, each steady-state mode is a well-defined mixture of linear cross-stream modes.
Wind-induced turbulent heat and mass transfer over large bodies of water
Authors: Shaw C. Y. , Lee Y.
Published: April 2006

A semi-theoretical study has been made of the problem of stable turbulent heat and mass transfer between a water surface and surrounding atmosphere under the influence of wind. The equations derived are based on the principle of similarity and are therefore expected to be valid under both laboratory and field conditions. The predicted heat- and mass-transfer Stanton numbers appear to be in satisfactory agreement with the available field data.
The moving contact line: the slip boundary condition
Authors: Dussan V. E. B.
Published: April 2006

The singularity at the contact line which is present when the usual fluidmechanical modelling assumptions are made is removed by permitting the fluid to slip along the wall. The aim of this study is to assess the sensitivity of the overall flow field to the form of the slip boundary condition. Explicit solutions are obtained for three different slip boundary conditions. Two length scales emerge: the slip length scale and the meniscus length scale. It is found that on the slip length scale the flow fields are quite different; however, when viewed on the meniscus length scale, i.e. the length scale on which almost all fluidmechanical measurements are made, all of the flow fields appear the same. It is found that the characteristic of the slip boundary condition which affects the overall flow field is the magnitude of the slip length.
Baroclinic instability in an eccentric annulus
Authors: Gent P. R. , Leach H.
Published: April 2006

A study has been made of baroclinic instability in a differentially heated, rotating fluid annulus whose channel width varies azimuthally. Both laboratory experiments and an a.nalytica1 model employing a linear normal-mode analysis have been used. The experiments show three types of flow. For slow rotation the flow is 'symmetric’, whereas at high rotation speeds baroclinic waves occur at all azimuths. At intermediate rotation speeds it is possible to have a mixed flow which is ‘symmetric’ in the narrow part but has baroclinic waves in the wide part of the annulus. This result suggested the analytical investigation of the stability of a barocIinic flow whose meridional scale varies downstream. It was found that this model also permits three possible types of flow: everywhere stable, everywhere unstable, and also a mixed flow which is locally unstable where the meridional scale is largest but locally stable where the scale is smallest.
On the diffusion of momentum and mass by internal gravity waves
Authors: Mtfller Peter
Published: April 2006

The interaction between short internal gravity waves and a larger-scale mean flow in the ocean is analysed in the Wkbj approximation. The wave field determines the radiation-stress term in the momentum equation of the mean flow and a similar term in the buoyancy equation. The mean flow affects the propagation characteristics of the wave field. This cross-coupling is treated as a small perturbation. When relaxation effects within the wave field are considered, the mean flow induces a modulation of the wave field which is a linear functional of the spatial gradients of the mean current velocity. The effect that this modulation itself has on the mean flow can be reduced to the addition of diffusion terms to the equations for the mass and momentum balance of the mean flow. However, there is no vertical diffusion of mass and other passive properties. The diffusion coefficients depend on the frequency spectrum and the relaxation time of the internal-wave field and can be evaluated analytically. The vertical viscosity coefficient is found to be vv [ape ] 4 x 103cm2/s and exceeds values typically used in models of the general circulation by at least two orders of magnitude.
Axisymmetric laminar wake behind a slender body of revolution
Authors: Hama Francis R. , Peterson Leigh F.
Published: April 2006

At the body-diameter Reynolds number 2000, the axisymmetric wake behind a slender streamlined body of revolution remained laminar without any indication of breakup far beyond the five-body-lengths test section. The mean-velocity profiles were measured with close spacings in order to obtain experimental information on the transient process from boundary layer to fully developed wake. A semi-empirical theory was developed to describe the flow-field characteristics.
On the virtual-mass and damping coefficients for long waves in water of finite depth
Authors: Ursell F.
Published: April 2006

A half-immersed circular cylinder is making vertical oscillations on water of finite constant depth. The virtual-mass and damping coefficients are studied in the limit as the wavelength tends to infinity. It is found that the virtual-mass coefficient tends to a finite limit and that the amplitude ratio ultimately varies as the frequency. This behaviour differs from the behaviour for infinite depth, where the virtual-mass coefficient tends to infinity and the amplitude ratio ultimately varies as (frequency).
Axially symmetric turbulent boundary layers on cylinders: mean velocity profiles and wall pressure fluctuations
Authors: Willmarth W. W. , Winkel R. E. , Sharma L. K. , Bogar T. J.
Published: April 2006

Experimental measurements of the mean velocity profiles produced by axially symmetric turbulent boundary layers on cylinders of various diameters are described. The profile measurements were made with very small hot wires developed for this investigation. Measurements of the wall shear stress on cylinders ranging from 0.02 to 2.0 in. in diameter are also reported. In the boundary layer on cylinders, well-defined regions exist in which the two-dimensional law of the wall and a three-dimensional wake law are valid. There was no evidence that the boundary layer was not fully turbulent even on the cylinders of smallest diameter. Measurements of wall pressure fluctuations beneath the boundary layer on a 1 in. diameter cylinder are also described. The results were much the same as those previously reported by Willmarth & Yang (1970) for a 3 in. diameter cylinder. The only difference was the discovery that the wall pressure was correlated in the transverse direction approximately half-way around the cylinder. This was not true on the 3 in. diameter cylinder.
Nonlinear aspects of an internal gravity wave co-existing with an unstable mode associated with a Helmholtz velocity profile
Authors: Grimshaw R. H. J.
Published: April 2006

Recently Lindzen (1974) has proposed a model of a shear-layer instability which allows unstable modes to co-exist with radiating internal gravity waves. The model is an infinite, continuously stratified, Boussinesq fluid, with a simple jump discontinuity in the velocity profile. Linear stability theory shows that the model is stable for wavenumbers k such that k2 < N2/2U2, where N is the Brunt—Väisälä frequency and 2U is the change in velocity across the discontinuity. For N2/2U2 < k2 < N2/U2 an unstable mode may co-exist with an internal gravity wave. This paper examines the weakly nonlinear aspects of this model for wavenumbers k close to the critical wavenumber N/2½U. An equation governing the evolution of the amplitude of the interfacial displacement is derived. It is shown that the interface may support a stable finite amplitude internal gravity wave.
A relation between the radiation and scattering of surface waves by axisymmetric bodies
Authors: Davis A. M. J.
Published: April 2006

Results corresponding to those of Newman (1975) for wholly or partially immersed cylinders are obtained, namely relations between the phase angles of the cylindrical outgoing surface waves generated either by the forced oscillations of an immersed axisymmetric body or by the scattering effect of the body on a plane wave.
On the wall structure of the turbulent boundary layer
Authors: Blackwelder R. F. , Kaplan R. E.
Published: April 2006

The wall structure of the turbulent boundary layer was examined using hot-wire rakes and conditional sampling techniques. Instantaneous velocity measurements indicate a high degree of coherence over a considerable area in the direction normal to the wall. Aty+= 15, there is some evidence of large-scale correlation in the spanwise direction, but almost no indication of the streamwise streaks that exist in the lower regions of the boundary layer. Conditional sampling showed that the normal velocity is directed outwards in regions of strong stream-wise-momentum deficit, and inwards when the streamwise velocity exceeds its mean value. The conditionally averaged Reynolds shear stress was approximately an order of magnitude greater than its conventionally averaged value and decayed slowly downstream.
Large scales in the developing mixing layer
Authors: Browand F. K. , Weidman P. D.
Published: April 2006

A new experimental technique is described for the study of the interactions between the large-scale vortical features in the two-dimensional mixing layer. Detector probes above and below the mixing layer are used to monitor the large-scale structure. Conditional sampling is performed in a moderate Reynolds number developing flow, by using phase and amplitude information from these detector probes. It is shown that significant Reynolds-stress production is associated with the pairing interaction in which two vortical structures combine to form a single, larger vortical structure.
Numerical solutions of single-mode convection equations
Authors: Toomre Juri , Gough D. O. , Spiegel E. A.
Published: April 2006

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Harbour resonance due to set-down beneath wave groups
Authors: Bowers E. C.
Published: April 2006

Natural modes of water oscillation inside harbours are known to occur with periods of the order of minutes. It seems likely that these oscillations are excited by water fluctuations of similar period outside the harbour and an often quoted cause of such fluctuations is the phenomenon of surf beats. These are thought to be long waves which are reflected back out to sea when a primary wave system breaks upon a beach. In this paper it is shown theoretically that the natural oscillations of a harbour can be excited directly, without breaking of the primary wave system, by set-down beneath wave groups, which is a long-period disturbance travelling towards the shore line at the group velocity. This theory is in agreement with model experimental results which show that, when the group period is close to a natural period of the harbour, resonance will occur with the set-down behaving as if it were a real long wave.
Resonantly interacting solitary waves
Authors: Miles John W.
Published: April 2006

Resonant (phase-locked) interactions among three obliquely oriented solitary waves are studied. It is shown that such interactions are associated with the parametric end points of the singular regime for interactions between two solitary waves. The latter include regular reflexion at a rigid wall, which is impossible for ϕi < (3α)½ (ϕ = angle of incidence, α = amplitude/depth [Lt ] 1), and it is shown that the observed phenomenon of ‘Mach reflexion’ can be described as a resonant interaction in this regime. The run-up at the wall is calculated as a function of ϕi/(3α)½ and is found to have a maximum value of 4αd for ϕi = (3α)½. This same resonant interaction also describes diffraction of a solitary wave at a corner of internal angle π − ψi, −(3α)½, and suggests that a solitary wave cannot turn through an angle in excess of (3α)½ at a convex corner without separating or otherwise losing its identity.
Self-diffusion of particles in shear flow of a suspension
Authors: Eckstein Eugene C. , Bailey Douglas G. , Shapiro Ascher H.
Published: April 2006

Self-diffusion coefficients were determined experimentally for lateral dispersion of spherical and disk-like particles in linear shear flow of a slurry at very low Reynolds number. Using a concentric-cylinder Couette apparatus, recurrent observations were made of the lateral position of a particular radioactively labelled particle. The self-diffusion coefficientDwas calculated by means of random-walk theory, using the ergodic hypothesis. Owing to great experimental difficulties, the calculated values ofDare not of high accuracy, but are correct to within a factor of two. In the range 0 < ϕ < 0·2,D/a2ω increases from zero linearly with ϕ up toD/a2ω ≅ 0·02 (where ϕ = volumetric concentration of particles,a= particle radius, ω = mean shear rate of suspending fluid). In the range 0·2 < 0·5, the trend ofD/a2ω is not clear because of experimental scatter, but in this rangeD/a2ω ≅ 0·025 to within a factor of two. Within the experimental accuracy, spheres and disks have the same value ofD/a2ω.
Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 2. Unsteady flow
Authors: Coutanceau Madeleine , Bouard Roger
Published: April 2006

The plane flow induced by the impulsive start of a circular cylinder previously at rest in a still fluid is investigated experimentally by a visualization technique. The details of the flow field at the different stages of its establishment are pointed out, and the effect of the wall upon the evolution of the flow in time is examined. Photographs of the flow patterns are presented. This study corresponds to that range of Reynolds numbers for which a closed wake exists and adheres stably to the cylinder.
The flow around a surface-mounted cube in uniform and turbulent streams
Authors: Castro I. P. , Robins A. G.
Published: April 2006

An experimental investigation of the flow around surface-mounted cubes in both uniform, irrotational and sheared, turbulent flows is described. The shear flow was a simulated atmospheric boundary layer with a height ten times the body dimension. Measurements of body surface pressures and mean and fluctuating velocities within the wake are presented. In the latter case a pulsed-wire anemometer was used extensively since the turbulent intensities were much too high for effective use of more standard instrumentation. The clear effects of upstream turbulence and shear on the wake flow are described, comparisons with the somewhat sparse measurements of previous workers are made and the relevance of recent theoretical attempts to describe the flow, as opposed to numerical calculation techniques to predict it, is briefly discussed.
Waves on water of varying depth: a report on an IUTAM symposium
Authors: Mysak L. A. , Peregrine D. H. , Provis D. G. , Smith Ronald
Published: April 2006

This is a review of an IUTAM symposium held in Canberra on 20–23 July 1976. The subject matter ranged widely: from surf on beaches to waves of oceanic scale, and from elegant analysis to observations from tide gauges.
The wave system attached to a slender body in a supersonic relaxing gas stream. Basic results: the cone
Authors: Clarke J. F. , Sinai Y. L.
Published: April 2006

The results of the linear theory for the flow of a supersonic relaxing gas past a slender body of revolution are analysed in regions where its predictions of wavelet position begin to break down. In this way new variable systems can be found which make it possible to discuss the correct nonlinear wave behaviour far from the body. The situation depends upon three especially important parameters, namely the thickness ratio ε of the body, the ratio δ of relaxing-mode energy to thermal energy and the ratio λ of a relaxation length to a typical body length. After establishing general results from the linear theory, the conical body is treated in some detail. This makes it possible to demote λ as an important parameter, although its restoration does prove useful at one point in the analysis, and results are derived for shock-wave behaviour when ord 1 [ges ] δ > ord ε4, δ = ord ε4and δ < ord ε4. In the first range of δ fully dispersed waves are essential, although they are fully established only at great distances from the cone; in the second range of δ partly dispersed waves seem to be the most likely to appear, and in the third range relaxation effects are second-order modifications of a basically frozen-flow field. Practical situations may well fall into the first of these categories.
Features of a separating turbulent boundary layer in the vicinity of separation
Authors: Simpson Roger L. , Strickland J. H. , Barr P. W.
Published: April 2006

Measurements of a separating two-dimensional incompressible boundary layer with an airfoil-type pressure distribution are reported. Unique mean and fluctuation velocity measurements and the distribution of the fraction of the time γp during which the flow moves downstream were obtained in the separated region using a directionally sensitive laser anemometer. Linearized hot-film anemometer measurements of mean velocities, turbulent shearing stress and intensities, eddy speeds, spectra and dissipation were made for γp > 0·8. The wall shearing stress, bursting frequencies, wall speed and spanwise structure were obtained using flush-surface hot-film sensors. The turbulent/non-turbulent interfacial intermittency γ and the frequency of passage of turbulent bulges were determined using smoke as a turbulence marker and the laser anemometer system for illumination and signal detection.

Upstream of separation the velocity profile correlations of Perry & Schofield (1973) are supported within the uncertainty of the data. Normal-stress effects are very important, influencing $-\overline{uv}/\overline{q^2} $ and the dissipation length correlations, and directly providing sizable terms in the momentum and turbulence energy equations. The criteria of Sandborn for turbulent separation and fully developed separation are found to hold. Downstream of separation there is apparent similarity of $\overline{u^2}$, U and γp throughout the shear flow. The passive low velocity backflow near the wall apparently just serves to satisfy continuity requirements after the energetic outer-region flow has deflected away from the wall upon separation.

The wall bursting frequency nA scales on outer velocity and length scales, with U∞/δnA ≈ 10, or about twice the value observed for zero-pressure-gradient flows. The non-dimensional spanwise spacing of wall eddies is given approximately by the relation λzUM/v ≈ 100 upstream of separation, where $U_M = (- \overline{uv}_{\max})^{\frac{1}{2}}$. The speed of wall eddies is found to be about 14Uτ.
Computing internal viscous flow problems for the circle by integral methods
Authors: Mills R. D.
Published: April 2006

Steady two-dimensional viscous motion within a circular cylinder generated by (a) the rotation of part of the cylinder wall and (b) fluid entering and leaving through slots in the wall is considered. Studied in particular are moving-surface problems with continuous and discontinuous surface speeds, simple inflow–outflow problems and the impinging-jet problem within a circle. The analytical solutions at zero Reynolds number are given for the last two types of problem. Numerical results are obtained at various Reynolds numbers from the integral representation of the solution. At zero Reynolds number this approach involves a quadrature around the circumference of the cylinder. At other Reynolds numbers it involves an iterative–integral technique based on the use of the ‘clamped-plate’ biharmonic Green's function.
Asymmetric two-dimensional jet efflux from a channel
Authors: Martin C. Samuel
Published: April 2006

Irrotational flow of two-dimensional jets from a channel is treated without direct use of a logarithmic hodograph plane. An analytical approach is introduced for solving the general problem of two jets issuing from a channel with three end plates. Numerical values of the contraction coefficient and the angle of jet deflexion are obtained for the special case where the two jets are located symmetrically and all the end plates are in line. Limiting cases of the resulting single-jet problem are the symmetric and asymmetric configurations solved by von Mises. Results for the asymmetric case improve upon the theoretical values reported by von Mises, and compare favourably with existing experimental data.
A study of transonic flow around spheres
Authors: Jaikrishnan K. R. , Szeri A. Z. , Rohrer W. M.
Published: April 2006

The paper presents a new analytical and experimental study of transonic flow around spheres. The results of the analytical study, which employs the method of orthogonal collocation for simultaneous solution of the momentum equations, the equation of continuity and the energy equation, are compared with hitherto unpublished measurements obtained on spheres of various sizes (1·02, 2·54 and 3·81 cm in diameter) in air, in dry steam and in wet steam with free-stream Mach numbers in the transonic range (0·58 <M∞< 0·97). The relationship θh= 91·78 + 8·59M∞between the attached-shock angle and the free-stream Mach number was obtained by fitting the theoretical pressure distributions to the experimental ones.
The initial development of longitudinal dispersion in straight tubes
Authors: Chatwin P. C.
Published: April 2006

When a contaminant molecule is released in a laminar flow in a straight tube its motion differs from that of the fluid particle with which it initially coincided because of its random motion, whose intensity is measured by the molecular diffusivity κ. For T = kt/a2 ≤ 0·25, where t is the time after release and a is a length characteristic of the cross-section, the statistics of its motion can be determined in the way described by Taylor (1953), Aris (1956) and Chatwin (1970). However, in many applications, including blood flow, the values of T which are attained are much smaller, and the purpose of this paper is to present first approximations for T [Gt ] 1 to some of the statistics measuring the deviations between the motion of the molecule and that of the fluid particle with which it initially coincided. To obtain these a technique due to Saffman (1960) is used for molecules released well away from the tube wall, and an extension of the same technique is used for molecules released near the tube wall. It is shown how the results can be used to describe the initial stages of dispersion of a cloud of contaminant molecules distributed arbitrarily over the cross-section in any laminar flow, steady or unsteady. Comparisons with some exact results for steady Poiseuille flow in a circular tube confirm that the approximations are formally correct, but show that in certain cases their practical use is limited to very small values of T, because of the high coefficients of the first two terms neglected in deriving the approximation.
Spatial resonance of a liquid-filled vibrating beaker
Authors: Huntley Ian
Published: April 2006

Mahony & Smith (1972) put forward a model to explain the phenomenon of energy transfer between nearly resonant oscillations at greatly differing frequencies. However, their model of ‘spatial resonance’ is restricted to situations where the geometry of the system is very simple. The present paper shows how to derive Mahony & Smith's equations in a general manner, and compares the theoretical predictions for a situation with circular symmetry with existing experimental results (Huntley 1972). In addition, it suggests a simple method for evaluating the resonance frequencies when a liquid-filled beaker is vibrated in one of its bell modes.
Laser light-scattering measurements of particle concentration in a turbulent jet
Authors: Shaughnessy E. J. , Morton J. B.
Published: April 2006

A laser light-scattering technique has been used to study the relative particle concentration field in a round turbulent air jet. Measurements were made in the far field of a smoke-marked turbulent jet exhausting into a secondary air stream. Radial distributions of mean particle concentration, concentration fluctuation intensity and intermittency were measured at several streamwise locations. Concentration fluctuation power spectra and the micro- and integral scales of the concentration fluctuations were measured on the jet axis. The effects of ambiguity noise and noise due to optical path attenuation on the performance of the laser light-scattering system are discussed.
Note on a solitary wave in a slowly varying channel
Authors: Miles John W.
Published: April 2006

Johnson's (1973) description of a solitary wave in water of slowly varying depth is extended to a channel of slowly varying breadth and depth b and d on the assumption that the scale for the variation of b and d is large compared with d5/2a3/2. It is inferred from conservation of energy that the amplitude of the wave is proportional to $b^{-\frac{2}{3}}d^{-1}$ (cf. Green's law $a\propto b^{-\frac{1}{2}}d^{-\frac{1}{4}}$ for long waves of small amplitude). Comparison with experiment (Perroud 1957) yields fairly satisfactory agreement for a linearly converging channel of constant depth. The agreement for a linearly diverging channel is not satisfactory, but the experimental data are inadequate to support any firm conclusion.
Response of a turbulent boundary layer to a step change in surface heat flux
Authors: Antonia R. A. , Danh H. Q. , Prabhu A.
Published: April 2006

Measurements of both the velocity and the temperature field have been made in the thermal layer that grows inside a turbulent boundary layer which is subjected to a small step change in surface heat flux. Upstream of the step, the wall heat flux is zero and the velocity boundary layer is nearly self-preserving. The thermal-layer measurements are discussed in the context of a self-preserving analysis for the temperature disturbance which grows underneath a thick external turbulent boundary layer. A logarithmic mean temperature profile is established downstream of the step but the budget for the mean-square temperature fluctuations shows that, in the inner region of the thermal layer, the production and dissipation of temperature fluctuations are not quite equal at the furthest downstream measurement station. The measurements for both the mean and the fluctuating temperature field indicate that the relaxation distance for the thermal layer is quite large, of the order of 1000θ0, where θ0is the momentum thickness of the boundary layer at the step. Statistics of the thermal-layer interface and conditionally sampled measurements with respect to this interface are presented. Measurements of the temperature intermittency factor indicate that the interface is normally distributed with respect to its mean position. Near the step, the passive heat contaminant acts as an effective marker of the organized turbulence structure that has been observed in the wall region of a boundary layer. Accordingly, conditional averages of Reynolds stresses and heat fluxes measured in the heated part of the flow are considerably larger than the conventional averages when the temperature intermittency factor is small.
Magnetohydrodynamic entry flow for a plane channel in an axial magnetic field
Authors: D'Arcy Gerald P. , Schmidt Philip S.
Published: April 2006

An integral solution is described for flow of an electrically conducting fluid in a plane channel in a magnetic field which is aligned with the direction of the mean flow. It is shown that the presence of the magnetic field retards the development of the velocity profile by producing Lorentz forces which oppose the movement of fluid from the viscous wall region to the core. Solutions are presented for the entry length as a function of the magnetic interaction parameter. Solutions are also given for the dependence of the frictional component of the pressure drop on the magnetic field strength. The transverse pressure gradient produced by Lorentz forces is discussed for a typical case.
Propagation and reflexion of Alfvén-acoustic-gravity waves in an isothermal compressible fluid
Authors: Rudraiah N. , Venkatachalappa M. , Kandaswamy P.
Published: April 2006

The propagation of internal Alfvén-ácoustic-gravity waves in a compressible, stratified, inviscid, perfectly conducting, isothermal atmosphere in the presence of a horizontal magnetic field is investigated by considering both the horizontal and the vertical component of the group velocity. The vertical component of the group velocity is important because it determines the speed at which energy travels upwards and becomes available for heating the upper regions. The regions of propagation and no propagation of waves are delineated for different magnetic Mach numbers, in a refractive-index domain. The horizontal and vertical group velocities are compared with the corresponding phase velocity of the wave motion. It is found that the horizontal group velocity of the internal waves is always less than the horizontal phase velocity for small magnetic fields and vice versa for large magnetic fields, whereas the vertical group velocity is always opposite in direction to the vertical phase velocity for small magnetic fields and vice versa for large magnetic fields. We have also drawn the reflexion condition in a wave-number-frequency domain for different Mach numbers.
Experiments on the fine structure of turbulence
Authors: Narayanan M. A. Badri , Rajagopalan S. , Narasimha R.
Published: April 2006

Investigations have been carried out of some aspects of the fine-scale structure of turbulence in grid flows, in boundary layers in a zero pressure gradient and in a boundary layer in a strong favourable pressure gradient leading to relaminarization. Using a narrow-band filter with suitable mid-band frequencies, the properties of the fine-scale structure (appearing as high frequency pulses in the filtered signal) were analysed using the variable discriminator level technique employed earlier by Rao, Narasimha & Badri Narayanan (1971). It was found that, irrespective of the type of flow, the characteristic pulse frequency (say Np) defined by Rao et al. was about 0·6 times the frequency of the zero crossings.

It was also found that, over the small range of Reynolds numbers tested, the ratio of the width of the fine-scale regions to the Kolmogorov scale increased linearly with Reynolds number in grid turbulence as well as in flat-plate boundarylayer flow. Nearly lognormal distributions were exhibited by this ratio as well as by the interval between successive zero crossings.

The values of Np and of the zero-crossing rate were found to be nearly constant across the boundary layer, except towards its outer edge and very near the wall. In the zero-pressure-gradient boundary-layer flow, very near the wall the high frequency pulses were found to occur mostly when the longitudinal velocity fluctuation u was positive (i.e. above the mean), whereas in the outer part of the boundary layer the pulses more often occurred when u was negative. During acceleration this correlation between the fine-scale motion and the sign of u was less marked.
A porous prolate-spheroidal model for ciliated micro-organisms
Authors: Keller Stuart R. , Wu Theodore Y.
Published: April 2006

A fluid-mechanical model is developed for representing the mechanism of propulsion of a finite ciliated micro-organism having a prolate-spheroidal shape. The basic concept is the representation of the micro-organism by a prolate-spheroidal control surface upon which certain boundary conditions on the tangential and normal fluid velocities are prescribed. Expressions are obtained for the velocity of propulsion, the rate of energy dissipation in the fluid exterior to the cilia layer, and the stream function of the motion. The effect of the shape of the organism upon its locomotion is explored. Experimental streak photographs of the flow around both freely swimming and inert sedimenting Paramecia are presented and good agreement with the theoretical prediction of the streamlines is found.
The role of shear-layer instability waves in jet exhaust noise
Authors: Moore C. J.
Published: April 2006

Large-scale structures in the form of instability waves are an inherent part of a shearlayer mixing process. Such structures are shown to be present in an acoustically and aerodynamically well behaved jet even at high Mach numbers. They do not directly radiate significant acoustic power in a subsonic jet, but do govern the production of the turbulent fluctuations which radiate broad-band jet noise. Over the whole subsonic Mach number range, a significant increase in jet noise can be produced by exciting the shear layer with a fluctuating pressure at the nozzle of only 0·08 % of the jet dynamic head but with the correct Strouhal number. Such excitation by internal acoustic, aerodynamic or thermal fluctuations could explain the variability of jet noise measurements between different rigs and could also be responsible for some components of ‘excess’ noise.
Second-order spectral local isotropy in turbulent scalar fields
Authors: Atta C. W. Van
Published: April 2006

This work was motivated by recent experimental results on the spectra of fluctuating temperature gradients in a heated turbulent boundary layer obtained by Sreenivasan, Danh & Antonia. Standard techniques of turbulence theory are used herein to derive expressions relating the individual one-dimensional spectra of each of the three components of the spatial gradient ∂θ/∂xiin a locally isotropic turbulent scalar field. The results of the isotropic theory explain all of the new observed features of the temperature-gradient spectra. The spectra of ∂θ/∂yand ∂θ/∂zdecrease monotonically with increasing wavenumber, in contrast to the well-known behaviour of the spectrum of ∂θ/∂x, which reaches a maximum value at roughly one-tenth the Kolmogorov wavenumber. The spectra of ∂θ/∂yand ∂θ/∂zare relatively rich in low frequency energy and relatively poor in high frequency energy compared with the spectrum of ∂θ/∂x. The absolute magnitudes of the spectra of ∂θ/∂yand ∂θ/∂zcalculated from the spectrum of ∂θ/∂xusing the isotropic relations are in generally good agreement with the corresponding measured spectra for a large range of wavenumbers, indicating second-order spectral local isotropy of the fine-scale scalar structure for sufficiently large wavenumbers. The form of the spectra of ∂θ/∂yand ∂θ/∂zin the inertial subrange is derived analytically.
The round laminar jet: the development of the flow field
Authors: Sozou C. , Pickering W. M.
Published: April 2006

The development of the flow field of a jet emanating from a point source of momentum in an infinite incompressible fluid of density σ is considered. The flow field is assumed to be due to the application of a constant force F0 at the origin. The problem is formulated in terms of the dimensionless variable λ = (vt)½/r, where v is the kinematic viscosity of the fluid, t the time from the application of the force and r the distance from the origin. At a station r the flow field is dipolar, with the dipole axis in the direction of F0, for all t satisfying the inequalities vt Lt; r2 and F0t2 [Lt ] 4πρr4. Also, at a given time t the streamlines of the developing flow field in a section through the axis of symmetry of the problem form closed loops about a stagnation point. If this occurs at λ = λm, the stagnation point propagates to infinity, along a straight line emanating from the origin, with speed v½/2λmt½, where λm = λm(F0) decreases as F0 increases. The larger F0 is the faster the steady state is established.
Continuation or breakdown in tornado-like vortices
Authors: Burggraf Odus R. , Foster M. R.
Published: April 2006

Laboratory experiments on swirling flows through tubes often exhibit a phenomenon called vortex breakdown, in which a bubble of reversed flow forms on the axis of swirl. Mager has identified breakdown with a discontinuity in solutions of the quasicylindrical flow equations. In this study we define a tornado-like vortex as one for which the axial velocity falls to zero for sufficiently large radius, and seek to clarify the conditions under which the solution of the quasi-cylindrical flow equations can be continued indefinitely or breaks down at a finite height. Vortex breakdown occurs as a dynamical process. Hence latent-heat effects, though doubtless important to the overall structure and maintenance of the tornado, are neglected here on the scale of the breakdown process. The results show that breakdown occurs when the effective axial momentum flux (flow force) is less than a critical value; for higher values of the flow force, the solution continues indefinitely, with Long's (1962) similarity solution as the terminal state. When applied to the conditions of the 1957 Dallas tornado, the computed breakdown location is in agreement with Hoecker's analysis of the observations.