bluuebunny/crossref_metadata_2025 huggingface dataset:
Vortex shedding from bluff bodies in a shear flow
Authors: Maull D. J. , Young R. A.
Published: March 2006

Experiments are described in which the vortex shedding from a bluff body and the base pressure coefficient have been measured in a shear flow. It is shown that the shedding breaks down into a number of spanwise cells in each of which the frequency is constant. The division between the cells is thought to be marked by a longitudinal vortex in the stream direction and this is supported by evidence from experiments where a longitudinal vortex was generated in an otherwise uniform flow.
The bursting of two-dimensional drops in slow viscous flow
Authors: Buckmaster J. D. , Flaherty J. E.
Published: March 2006

We consider the deformation of two-dimensional drops when immersed in a slow viscous corner flow. The problem is formulated as one of analytic function theory and simplified by assuming that both the drop and the exterior fluid have the same viscosity. An approximate analysis is carried out, in which the conditions at the interface are satisfied in an average sense, and this reveals the following features of the solution. A drop of given physical properties (volume, surface tension and viscosity), when immersed in a corner flow, has no steady equilibrium shape if the rate of strain of the applied flow is too large. On the other hand, if the rate of strain is small enough for a steady solution to exist, then in general there are two possible solutions. These features are confirmed by formulating the exact problem in terms of a nonlinear integro-differential equation, which is solved numerically.
An experimental investigation of a magnetically driven rotating liquid-metal flow
Authors: Robinson T. , Larsson Kjell
Published: March 2006

Flow and turbulence in a 50 Hz rotating-field MHD system are investigated using the hot-film constant-temperature anemometer. Factors affecting anemometer disturbances and response time are discussed. From measurements of the magnetic field at points within the liquid the distribution of MHD forces is estimated. The mean rotational velocity of the flow is of the expected order of magnitude but much less dependent on the axial co-ordinate than the corresponding MHD force. With the aid of a thermal transit-time anemometer, a weak secondary flow is detected. A note on scale-model studies of MHD systems envisaged in metallurgical applications of magnetohydrodynamics points out some basic difficulties in modelling large high-powered systems on a small scale.
Experiments on swirling turbulent flows. Part 1. Similarity in swirling flows
Authors: Yajnik K. S. , Subbaiah M. V.
Published: March 2006

The effects of swirl on internal turbulent flows are studied by conducting experiments on turbulent pipe flow with variable initial swirl. This first part of the study is primarily concerned with similarity laws. The mean velocity profiles, both away from and close to the wall, are found to admit similarity representations at sufficiently large Reynolds numbers, provided that flow reversal does not take place near the entrance. While the wall law is not sensibly dependent on swirl, the velocity defect law in its extended form is sensitive to swirl. Further, a logarithmic skin-friction law is obtained in which only the additive coefficient depends on swirl. This coefficient is found to vary linearly with the swirl angle in the range of the present experiments.
The breakup of a turbulent liquid jet in a gaseous atmosphere
Authors: Phinney Ralph E.
Published: March 2006

An electrical method of detecting and measuring the breakup of liquid jets is applied to the turbulent case. New data produced by this means, together with previous data, support the conjecture that the theory and understanding that were developed in connexion with the breakup of laminar jets can be used as a guide for turbulent jets as well.
High-speed water jets from vertically accelerated rotating cones
Authors: Savic P. , Allan J. D. , Van Blokland G. P.
Published: March 2006

Water jets are produced by vertically accelerating a rotating cone partially filled with water. It is shown that the acceleration of the parabolic meniscus results in a motion similar to that observed in a shaped explosive charge (Monroe jet). Acceleration of the cone is effected by means of an inductive electromagnetic accelerating device (conical pinch) whose theory is developed in terms of the WKB approximation. A second-order inviscid theory for the motion of the fluid in the cone in terms of the Penney-Price linearization procedure is presented and it is shown that good agreement for the jet head velocity can be achieved for low velocities. At higher velocities, experimental results appear to lag behind the theoretical ones, probably owing to the dispersal of the jet head through viscous drag with the surrounding atmosphere. The shape of the jet at early times is well represented by first-order theory.
Laser-Doppler measurements on a round turbulent jet in dilute polymer solutions
Authors: Barker Steven J.
Published: March 2006

A laser-Doppler velocimeter suitable for the measurement of mean and fluctuating flow velocities in water is described. Results of a study using this system in an axisymmetric turbulent jet of water and dilute polymer solutions are given. The laser-Doppler technique is better suited for such measurements than either Pitot tubes or heat-transfer gauges because the Doppler velocity measurements are independent of the physical properties of the fluid. Previous velocity measurements in polymer jets have suffered from the effects of the additives upon the sensors.

Turbulent round jets with Reynolds numbers between 5000 and 50000 were studied. For a jet issuing from a convergent nozzle the additives were found to have no effect upon the mean axial velocity or turbulence intensity at any point in the jet. However, for a jet issuing from a long length of circular pipe, the additives reduced the centre-line velocity and increased the turbulence level in the early part of the jet. Thus the principal effect of a polymer additive upon the jet appears to result from its effect upon the initial conditions.
Nonlinear resonant oscillations in open tubes
Authors: Seymour Brian R. , Mortell Michael P.
Published: March 2006

A gas in a tube, one end of which is open, is driven by a periodic applied velocity or pressure at or near a resonant frequency. Damping is introduced into the system by radiation of energy through the open end. It is shown that shocks are possible at an open end and that there is a critical level of damping which ensures a continuous gas response for all frequencies. At the critical level the amplitude of the response is O(ε1/3), where ε is the amplitude of the input, and it is bounded by the amplitude predicted by linear theory. There is agreement with the qualitative experimental results available.
Amplitude-dependent behaviour of a liquid-filled gyroscope
Authors: Scott W. E. , D'Amico W. P.
Published: March 2006

An analysis of the experimentally determined resonant amplitude and frequencies of oscillation of a gyroscope whose rotor contains liquid-filled cylindrical cavities reveals a surprising small amplitude instability region that is not predicted by the Stewartson instability criterion for a liquid-filled spinning top. Along with the experimental results and speculation concerning the cause of the observed phenomenon, there are presented some practical implications of the observations of use to designers of spinning vehicles containing liquid.
The phase configuration of internal waves around a body moving in a density stratified fluid
Authors: Stevenson T. N.
Published: March 2006

A body is started impulsively from rest and moves in a curved path in a stably stratified fluid. The phase configuration of the internal waves which are generated is studied using small amplitude wave theory. The theory is compared with experiment for a few special cases which include a horizontal cylinder moving in a circular path in a vertical plane, oscillating through a large amplitude in a horizontal plane, and moving with constant velocity past stationary plates. Theory and experiment show reasonable agreement except where the waves produced by the wake dominate the flow.
A note on tsunamis: their generation and propagation in an ocean of uniform depth
Authors: Hammack Joseph L.
Published: March 2006

The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion.

Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion duringpropagationand the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and morerecently advocated by Ben jamin, Bona & Mahony (1972) as a preferable model to the more commonly used equation of Korteweg & de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case.
Deformation and burst of a liquid droplet freely suspended in a linear shear field
Authors: Barthès-Biesel D. , Acrivos A.
Published: March 2006

A theoretical method is presented for predicting the deformation and the conditions for breakup of a liquid droplet freely suspended in a general linear shear field. This is achieved by expanding the solution to the creeping-flow equations in powers of the deformation parameter ε and using linear stability theory to determine the onset of bursting. When compared with numerical solutions and with the available experimental data, the theoretical results are generally found to be of acceptable accuracy although, in some cases, the agreement is only qualitative.
Analysis of turbulent pipe and channel flows at moderately large Reynolds number
Authors: Afzal Noor , Yajnik Kirit
Published: March 2006

Effects of moderately large Reynolds numbers R are studied by considering higher order terms in the expansions for turbulent pipe and channel flows for R → ∞. Matched asymptotic expansions using two length scales are employed to emphasize the two-layer structure of turbulent shear flows near solid walls. The effects appear as additional terms in extended forms of the law of the wall, the logarithmic velocity law, the velocity defect law and the logarithmic skinfriction law. These generalizations are critically compared with experimental results for pipe flows of Patel & Head and extremely good agreement is obtained. Also, possible applications are discussed for extending the range of skin-friction and heat-transfer devices which are based on wall similarity.
Measurements in a self-preserving plane wall jet in a positive pressure gradient
Authors: Irwin H. P. A. H.
Published: March 2006

Measurements of a wall jet in a self-preserving pressure gradient are described. The quantities measured with a linearized hot-wire anemometer were the mean velocity, the turbulence stresses, triple and quadruple velocity correlations, intermittency and spectra of the longitudinal turbulence intensity. The turbulence, as well as the mean flow, reached a self-preserving state in which the ratio of the maximum velocity to the free-stream velocity was 2·65. Skin friction was also measured using the razor-blade technique in the viscous sublayer and buffer region. The values of the constants in the logarithmic law of the wall are found to be similar to those in boundary-layer and pipe flows. The skin-friction coefficient is slightly lower than that found for the wall jet in still air (Guitton 1970), but close to the formula of Bradshaw & Gee (1962) for the wall jet in an external stream with zero pressure gradient.

A balance of the terms in the turbulence energy equation is presented and discussed. The shearing stress is not zero at the point of maximum velocity but is of opposite sign to that at the wall and hence the contribution of this stress to turbulence production is negative in the outer part of the boundary-layer region. However, the total turbulence production remains positive because the contribution of the normal stresses is positive and slightly larger. The pressure—velocity gradient correlations are evaluated by difference from the Reynolds stress equations and are compared with the theoretical model of Hanjalić & Launder (1972b). Agreement is quite good in the outer region of the wall jet. The above model is also compared with the triple velocity correlations and again found to be in fair agreement.
Plane jet flows from slowly varying nozzles
Authors: Lesser M. B.
Published: March 2006

The solution to the steady problem of an inviscid jet emerging from a symmetric nozzle of slowly varying profile is sought as an asymptotic series in the wall slope. The expansion of the solution in the region near the nozzle lip is singular at infinity, so that a matched expansion technique is evolved to solve the problem. To the order to which the solution is obtained in the present paper, the jet contraction ratio is shown to be the same as that from a nozzle formed by two inclined planes with inclination angle the same as the exit slope of the nozzle. Composite expansions are formed and used to check the consistency of expansion and matching procedures.
Resonant oscillations in radiative magnetogasdynamics
Authors: Helliwell J. B.
Published: March 2006

Investigations are made of the wave motion which arises near resonance in a tube with an applied transverse magnetic field filled with a highly electrically conducting gas and closed by two rigid walls. The wave motion is driven by the sinusoidal radiative flux emitted by one of the walls as a consequence of its oscillatory temperature; the other wall is taken to be a perfect reflector of thermal radiation. The effects of radiative transfer are treated by the use of the differential approximation. The analysis leads to the same formal governing integral equation for the solution as arises in the ordinary gasdynamic case in the absence of electromagnetic effects. Within a narrow frequency band around resonance the theory predicts the occurrence of magnetogasdynamic shock waves which become dispersed as the thermal radiation is strengthened and may be totally dispersed to leave a continuous, periodic, but not necessarily sinusoidal, wave motion. The effect of the magnetic field is to delay the onset of dispersion.
An examination of the influence of waves on the ventilation of surface-piercing struts
Authors: Mcgregor R. C. , Wright A. J. , Swales P. D. , Crapper G. D.
Published: March 2006

The paper examines the results of an experiment which was designed to elucidate the manner in which wave characteristics, strut geometry and aspect ratio influence the angles at which struts ventilate. The experiment was conducted using small-scale models in a towing tank which allowed the wave parameters to be varied independently. The results indicate which parameters of a seaway are most hazardous to the operation of a hydrofoil ship in high seas and suggest design features which may extend the capability range of such craft.
The least-damped disturbance to Poiseuille flow in a circular pipe
Authors: Gill A. E.
Published: March 2006

The properties of infinitesimal disturbances to Poiseuille flow in a circular pipe have been found for a wide range of wavenumbers through recent numerical work (Salwen & Grosch 1972; Garg & Rouleau 1972). These studies did not, however, find the least-damped disturbances. In this paper, the properties of disturbances are found in a limiting case. These disturbances are thought to have decay rates which are equal to or very close to the smallest value possible for any given large value of the Reynolds number R. For disturbances which decay in time, the limiting disturbances can be found analytically. They have the property that the axial wavenumber α tends to zero as R → ∞. The smallest decay rate -βi is given by
\[
-\beta_iR = j^2_{1,1}\approx 14.7,
\]
where j1,1 is the first zero of the Bessel function J1. Two modes have this decay rate. One is axisymmetric with motion only in the azimuthal direction, and the other has azimuthal wavenumber n = 1. For disturbances which decay in space, the limiting solutions can be found by numerically evaluating power series. They have the property that the frequency β tends to zero as R tends to infinity. The smallest decay rate αi for these disturbances is given by αiR ≈ 21·4, corresponding to an axisymmetric mode with motion only in the azimuthal direction. A mode with azimuthal wavenumber n = 1 has a slightly larger decay rate given by αiR ≈ 28·7.
Reflexion and transmission at a plane screen with periodically arranged circular or elliptical apertures
Authors: Leppington F. G. , Levine H.
Published: March 2006

A plane harmonic sound wave is considered to be incident upon a rigid plane screen that contains a periodic rectangular array of circular or elliptical apertures, and a characterization is sought for the reflexion and transmission coefficients of the scattered waves when the relationships aperture dimension [Lt ] spacing [Lt ] wavelength apply. The problem is analysed with the help of an integral equation over a single aperture and, as a consequence of the determination of the leading terms in its asymptotic solution, some prior results for more general (that is, irregular) aperture spacing are confirmed and specific features of the interaction in the periodic arrangement are established. Similar formulations are devised and given attention for the related problems in which (i) the screen is backed by a rigid infinite plane and (ii) the apertures contain rigid pistons capable of executing normal displacements compatible with an assigned and common impedance. A section is devoted to the solution, based on expansion of its kernel, for an integral equation of the first kind with a plane circular or elliptical domain.
Spectral measurements of turbulent momentum transfer in fully developed pipe flow
Authors: Bremhorst K. , Walker T. B.
Published: March 2006

Measurements of the spectral components of turbulent momentum transfer for fully developed pipe flow are presented. The results indicate that near the wall (y+ < 15) two types of momentum transfer processes occur. A net positive transfer takes place in the higher frequency range of the energy-containing part of the turbulence spectrum whereas a net negative transfer returns low momentum to the wall region at the lower end of the spectrum. Examination of the turbulence at various y+ shows that the significant features of the turbulence spectra scale on frequency at any given Reynolds number, thus leading to an interpretation of the flow structure which is consistent with the hydrogen-bubble visualization data of Runstadler, Kline & Reynolds (1963). The results are consistent with a flow model in which disturbances extend from the sublayer to the core of the flow. Recent turbulent heat transfer measurements are also interpreted successfully by this model.
On the existence of multiple Kármán vortex-street modes
Authors: Weihs D.
Published: March 2006

An inviscid Kármán-type vortex-shedding model is employed to show that multiple modes of vortex streets are possible, for flow around a given obstacle. This is in confirmation of various experimental observations in recent years, which were challenged by opposing claims that these were due to experimental inaccuracies.
Fluid flow generated by switching a magnetic field on or off
Authors: Sneyd Alfred
Published: March 2006

A uniform magnetic field is switched on at time t = 0 outside a body of conducting fluid. It is assumed that the field strength increases in time in proportion to 1 -e−αt, where α is a constant of the circuit generating the field. Under the assumption of small magnetic Reynolds number and small magnetic Prandtl number the equations governing the diffusion of the field into the fluid are derived and a simple expression is given for the initial vorticity distribution produced in the fluid. The situation in which an initially uniform field is switched off is also considered. It is shown that, for sufficiently symmetrically shaped bodies of fluid, the vorticity generated by the switching-on of the field is the same as that generated by the switching-off. The particular case of an infinitely long circular cylinder of conducting fluid is considered in detail and an explicit expression is derived for the vorticity distribution.
Instability, coalescence and fission of finite-area vortex structures
Authors: Christiansen J. P. , Zabusky N. J.
Published: March 2006

We have made computational experiments to study the stability and long-time evolution of two-dimensional wakes. We have used the VORTEX code, a finite-difference realization of two-dimensional motions in incompressible inviscid fluids. In the first experiment an initial shear-unstable triangular velocity profile evolves into a non-homogeneous, finite-area, asymmetric vortex array and like-signed regions attract andfuse(or coalesce). Enhanced transport across the profile is due to ‘capture’ and convection of small-scale vortex regions by larger opposite-signed vortex regions. In the following experiments we study the stability of an asymmetric four-vortexfinite-areasystem corresponding to a von Kármán street of point vortices. Here the critical parameter isb/a, the initial transverse-to-longitudinal separation ratio of vortex centres. At\[ b/a = 0.281 \]the four-vortex system is stable and we observe that large-area vortex regions develop elliptical (m= 2), triangular (m= 3), etc. surface modes owing to mutual interactions. Atb/a= 0 the measured growth rate is smaller than that for the corresponding von Kármán system and atb/a= 0·6 the measured growth rate is larger. Atb/a= 0 one vortex undergoes fission in the high-shear field produced by two nearest-neighbour opposite-signed vortex regions. Heuristic comparisons are made with the two-dimensional tunnel experiments of Taneda and others.
Turbulent dispersion from sources near two-dimensional obstacles
Authors: Hunt J. C. R. , Mulhearn P. J.
Published: March 2006

The first part of the paper is an extension of the statistical theory of turbulent diffusion to the problem of turbulent diffusion from a point or line source in an inhomogeneous straining flow such as flow round a two-dimensional body. The new effects which have to be considered are the convergence and divergence of mean streamlines, the inhomogeneity of the mean and turbulent velocities, and the presence of a boundary. We assume that the upstream turbulence intensity$u^{\prime}_{\infty}/\overline{u}_{\infty} $is weak, i.e.$u^{\prime}_{\infty}/\overline{u}_{\infty} $[Lt ] 1, and that molecular diffusion is negligible, i.e.$(\overline{u}_{\infty}/u^{\prime}_{\infty})^2[D/(a\overline{u}_{\infty})] $[Lt ] 1,Dandabeing the molecular diffusivity and the scale of the obstacle respectively. The theory predicts the mean-square dispersion of the plume about the mean streamline through the source in terms of the Lagrangian statistics of the turbulence. Making the further assumption that the scaleLEof the turbulence is large enough to satisfy the condition that ($(u^{\prime}_{\infty}/\overline{u}_{\infty}) $) (a/LE) [Lt ] 1, it is shown that the turbulent dispersion can be calculated in terms of the Eulerian statistics, which can either be measured or in some cases calculated. In the second part we analyse diffusion from various sources in potential flows over two-dimensional obstacles assuming constant (or variable) eddy diffusivity, and compare the results with those of the more rigorous statistical analysis for sources one or two diameters upwind of the obstacle. However, unlike the statistical analysis, this eddy-diffusivity analysis can also be extended to calculate diffusion from sources placed some distance upwind of an obstacle, and an example is given of how this analysis may be applied to calculating concentrations on hills due to distant sources.
A perturbation analysis of the laminar far wake behind a symmetrical two-dimensional body in a uniform shear flow
Authors: Kiya Masaru , Arie Mikio
Published: March 2006

An aspect of the laminar far wake behind a symmetrical two-dimensional body placed in a uniform shear flow is described theoretically by means of the Oseen type of successive approximation, in which the shear is regarded as a small perturbation on a uniform stream. The expression for the stream function is determined up to the third approximation both in and outside the wake region, and the region in which the results of the perturbation analysis are valid is also determined. The stream function is found to contain four constants which cannot be determined from the boundary conditions for the far wake. The analysis also shows that the spreading of the wake is greater towards the side of smaller velocity than the side of larger velocity, the asymmetrical feature of the velocity defect becoming more evident as the distance from the obstacle is increased: the point which shows the maximum velocity defect shifts to the low-velocity side.
An experimental study of nonlinear disturbance behaviour in natural convection
Authors: Jaluria Yogesh , Gebhart Benjamin
Published: March 2006

An experimental investigation has been carried out to determine the behaviour of three-dimensional disturbances in laminar natural convection flow adjacent to a flat vertical surface with uniform heat flux input. A controlled two-dimensional disturbance, with a superimposed transverse variation, was introduced into the boundary region by a vibrating ribbon. The downstream propagation and amplification of these disturbances were studied in detail. Of principal interest was their nonlinear interaction with the base flow and any secondary mean flows that might arise therefrom. Measurements of the transverse mean velocity component indicate a double longitudinal vortex system. These results also show a distortion of the longitudinal base velocity profile which rapidly increases downstream. An alternate spanwise steepening and flattening of the profile is found to result. These mean flow modifications are found to be in good general agreement with existing theoretical and experimental studies of such flows. Our results are also compared with those obtained for forced flow. Several very important differences and similarities are indicated.
Hysteresis and nonlinear detuning in a spatial-resonance phenomenon
Authors: Huntley Ian , Smith Ronald
Published: March 2006

The experimental work of Franklin, Price & Williams (1973) shows that for moderately large driving amplitudes there are features of spatial resonance that are not predicted by the model representation of Mahony & Smith (1972). We here derive an alternative model, which remains valid for moderately large driving amplitudes, and we are able to obtain a theoretical description of both hysteresis and nonlinear detuning of the low frequency wave response. An experiment in which surface waves were generated by a sinusoidal pressure field at the free surface (and which corresponds almost exactly to the theoretical problem) was conducted in order to test these predictions.
Relaminarization in highly accelerated turbulent boundary layers
Authors: Narasimha R. , Sreenivasan K. R.
Published: March 2006

The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.

It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.
The buckling of thin viscous jets
Authors: Buckmaster J.
Published: March 2006

Thin viscous jets are considered as they slowly fall, in a state of near-neutral buoyancy, through a liquid. An equation is derived which describes the path of the jet. A small perturbation analysis of nearly vertical jets is carried out, and shows that they are necessarily unstable and will eventually deviate significantly from the vertical. Numerical integration of the nonlinear equation describes the nature of this deviation. These results model some experimental observations made by Taylor (1969).
The interaction between a pair of circular cylinders normal to a stream
Authors: Bearman P. W. , Wadcock A. J.
Published: March 2006

This paper describes how the flows around two circular cylinders, displaced in a plane normal to the free stream, interact as the two bodies are brought close together. Surface pressure measurements at a Reynolds number of 2·5 × 104, based on the diameter of a single cylinder, show the presence of a mean repulsive force between the cylinders. An instability of the flow was found when the gap between the cylinders was in the range between one diameter and about 0·1 of a diameter. Correlation measurements of hot-wire outputs indicate how mutual interference influences the formation of vortex streets from the two cylinders. Spanwise correlation measurements show that the correlation length doubles as the cylinders are brought into contact.
A visual study of turbulent shear flow
Authors: Nychas Stavros G. , Hershey Harry C. , Brodkey Robert S.
Published: March 2006

The outer region of a turbulent boundary layer along a flat plate was photographed and analysed; in addition, limited observations of the wall area were also made. The technique involved suspending very small solid particles in water and photographing their motion with a high-speed camera moving with the flow.

The single most important event observed in the outer region was fluid motion which in the convected view of the travelling camera appeared as a transverse vortex. This was a large-scale motion transported downstream almost parallel to the wall with an average velocity slightly smaller than the local mean. It appeared to be the result of an instability interaction between accelerated and decelerated fluid, and it is believed to be closely associated with the wall-region ejections. The transverse vortex was part of a deterministic sequence of events; although these events occurred randomly in space and time. The first of these events was a decelerated flow exhibiting velocities considerably smaller than the local mean. It was immediately followed by an accelerated flow. Both these events extended from near the wall to the far outer region. Their interaction resulted in the formation of one or more transverse vortices. While the transverse vortex was transported downstream, small-scale fluid elements, originating in the wall area of the decelerated flow, were ejected outwards (ejection event). After travelling some distance outwards the ejected elements interacted with the oncoming accelerated fluid in the wall region and were subsequently swept downstream (sweep event). The sequence of events closed with two large-scale motions.

Estimated positive and negative contributions to the instantaneous Reynolds stress during the events were many times higher than the local mean values.
Hydromagnetic wavelike instabilities in a rapidly rotating stratified fluid
Authors: Acheson D. J.
Published: March 2006

We examine the hydromagnetic stability of a radially stratified fluid rotating between two coaxial cylinders, with particular emphasis on the case when the angular velocity greatly exceeds both buoyant and Alfvén frequencies. If the magnetic field is predominantly azimuthal instabilities then have an essentially non-axisymmetric and wavelike character. Various bounds on their phase speeds and growth rates are derived, including a ‘quadrant’ theorem analogous to Howard's semicircle theorem for Kelvin–Helmholtz instability. Their strong tendency to propagate against the basic rotation (i.e. ‘westward’), previously noted by the author in the study of a more simplified (homogeneous) model, seems relatively insensitive to the generation mechanism (e.g. unstable gradient of magnetic field, angular velocity or density), but a number of counterexamples show that this constraint need not apply if the magnetic field displays significant spatial variations of direction as well as magnitude and that eastward-propagating amplifying modes are then possible.
A theory of turbulent flow round two-dimensional bluff bodies
Authors: Hunt J. C. R.
Published: March 2006

By generalizing the theory of ‘rapid distortion’ of turbulence developed by Batchelor & Proudman (1954) it is shown in this paper that the turbulent velocity around a bluff body placed in a turbulent flow can be calculated outside and upstream of the regions of separated flow, if the incident turbulent flow satisfies the following conditions: (i) if a/Lx [Lt ] 1 or = O(1), Re−1$u^{\prime}_{\infty}/\overline{u}_{\infty} $ [Lt ] 1 [Lt ] Re½; (ii) if a/Lx [Gt ] 1, Re−1 [Lt ] $u^{\prime}_{\infty}$ [Lt ] 1/(a/Lx) and Re [Gt ] (a/Lx)2, where $Re = \overline{u}_{\infty} a/ν$, is the mean uniform incident velocity, $u^{\prime}_{\infty}$ is the r.m.s. velocity of the homogeneous incident turbulence, a is a transverse dimension of the body (the radius in the case of a circular cylinder), Lx is the integral scale of the incident turbulence and v is the kinematic viscosity.

Detailed calculations are given for the flow around a circular cylinder with particular emphasis on the turbulence very close to the surface. (The results can be generalized to other cylindrical bodies.) Mean-square values and spectra of velocity have been found only in the limiting situations where the turbulence scale is very much larger or smaller than the size of the body, i.e. Lx [Gt ] a or Lx [Lt ] a. But, whatever the value of a/Lx, if the frequency is sufficiently large the results for spectra tend to those of the limiting situation where Lx [Lt ] a. The reason why the turbulence velocities have not been calculated for intermediate values of a/Lx is that closed-form solutions cannot be found and that the computing time then required is quite excessive. However, some computed results are used in the paper to suggest the qualitative behaviour of the turbulence when Lx is of order a. An important result of the theory is that it illuminates and distinguishes between the governing physical processes of distortion of the turbulence by the mean flow, the direct ‘blocking’ of the turbulence by the body, and concentration of vortex lines at the body's surface.

The results of the theory have many applications, for example in calculating turbulent dispersion and fluctuating pressures on the body, as shown elsewhere by Hunt & Mulhearn (1973) and Hunt (1973).

In conclusion the theoretical results are briefly compared with experimental measurements of turbulent flows round non-circular cylinders. A detailed comparison with measurements round circular cylinders will be published later by Petty (1974).
Experiments on instability and turbulence in a stratified shear flow
Authors: Thorpe S. A.
Published: March 2006

This is a study of turbulence which results from Kelvin—Helmholtz instability at the interface between two miscible fluids in a two-dimensional shear flow in the laboratory. The growth of two-dimensional ‘billows’, their disruption by turbulence, and the eventual decay of this turbulence and the re-establishment of a gravitationally and kinematically stable interface are described. Continuous measurements of density and horizontal velocity from both fixed and vertically moving probes have been made, and the records obtained are presented, together with photographs showing the simultaneous appearance of the flow, which serve to identify the physical nature of events seen in the records. The measurements show how the fine-structure of the density field described in earlier experiments is related to velocity fluctuations. The vertical length scales of the final mean velocity and density structure are found to be different, and to depend on the Richardson number at which instability first occurred. The eventual Richardson number at the centre of layer is, however, not dependent on the initial Richardson number and has a value of about one third. The implications of these results to the eddy diffusion coefficients, to the energy exchange, and to turbulence in the ocean and the atmosphere are discussed.
Oscillating flow over a cylinder at large Reynolds number
Authors: Dwyer H. A. , Mccroskey W. J.
Published: March 2006

The boundary-layer flow over a circular cylinder at a Reynolds number of 1·06 × 105 has been studied both experimentally and theoretically. The investigation was designed to concentrate on the self-induced oscillations occurring in the flow; at this Reynolds number, these oscillations have generally been ignored heretofore. In the experimental part of the investigation both the inviscid flow and boundary-layer flow reversals were measured as functions of time. The theoretical part of the study started with the measured inviscid flow and calculated all the boundary-layer characteristics. The boundary-layer calculations themselves revealed some very interesting fine-scale structure of the flow, which strongly indicated that the vanishing of wall shear does not signal the onset of separation for unsteady flow. In general, the agreement between the theoretical calculations and the experimental results was excellent and the unsteady component of this supposedly steady flow was found to be very significant.
Upstream MGD phenomenon in a jet-threaded cylindrical field
Authors: Chee-Seng Lim
Published: March 2006

An exact analytic solution is derived for the perturbation of a magnetic field while exposed to an immersed, axisymmetric, azimuthal, steady current source of arbitrary distribution in the presence of a slender, electrically conducting, independently permeated, compressible jet threading the axis of symmetry, subject to an equilibrium pressure balance. A further influence is the enclosure of the magnetic field by a coaxial cylindrical wall. The steady-state result invariably exhibits an infinite discrete superposition of axially decaying terms. In addition, there arise two admissible alternatives involving a fluid parameter λ (dependent on the flow speed, sound speed and both Alfvén speeds pertaining to the jet) together with a scale parameter χ(0) (equal to twice the ratio of the cross-sectional area of the jet to that of its externally enveloping field). Provided that λ exceeds χ(0), each element constituting the current distribution induces a stationary-wave contribution confined, as a consequence of an applied radiation condition, to the upstream domain, corresponding to an upstream-directed group velocity. However, if λ is exceeded by χ(0), this upstream wave is replaced by another decaying term, acting on both sides of every current constituent, like all other decaying terms.
An experimental investigation of an axisymmetric jet in a co-flowing air stream
Authors: Antonia R. A. , Bilger R. W.
Published: March 2006

An experimental investigation of the flow development of an axisymmetric jet exhausting into a moving air stream is made for two values of the ratio of jet velocity to external air velocity. The u-component turbulence intensity and Reynolds shear stress measurements together with the dissipation length scales inferred from measured u-component spectra suggest that the turbulence similarity assumptions are incorrect for the present flow situation. A discussion of the turbulence structure of the flow indicates that self-preservation does not apply for this situation and that the flow far downstream depends strongly on the complete past history.
A higher order theory for compressible turbulent boundary layers at moderately large Reynolds number
Authors: Afzal Noor
Published: March 2006

A higher order theory for two-dimensional turbulent boundary-layer flow of a compressible fluid past a plane wall is formulated, for moderately large values of the Reynolds number, by the method of matched asymptotic expansions. The parameters (γ − 1) M2∞and the molecular Prandtl number are assumed to be of order unity. The analysis deals with the set of Reynolds equations of mean motion (which are underdetermined without an additional set of closure hypotheses) and assumes that the non-dimensional fluctuations in velocity, temperature and density are of orderU*, (friction velocity divided by free-stream velocity a t some designation point), while fluctuations in pressure are of orderU2*.The first-order results of the present study lead to asymptotic laws for velocity and temperature distributions which correspond to the law of the wall, logarithmic law and defect law, and also to skin friction and heat-transfer laws. It turns out that the first-order defect law depends upon the gradient of entropy and stagnation enthalpy and the law of the wall is independent of viscous dissipation. The second-order terms of the present work (accounting for mean convection due to turbulent mass flux, viscous dissipation in the inner flow and displacement effects in the outer flow) describe the necessary corrections to first-order terms due to low Reynolds number effects. In the overlap region the second-order results, for the law of the wall and the defect law, show bilogarithmic terms along with logarithmic terms.
Transport and profile measurements of the diffusive interface in double diffusive convection with similar diffusivities
Authors: Shirtcliffe T. G. L.
Published: March 2006

The transport properties of a diffusive interface with diffusivity ratio $\kappa_S/\kappa_T = {\textstyle\frac{1}{3}}$ have been measured, using salt and sugar as the diffusing components. The flux ratio is constant and equal to (κS/κT)½. The normalized salt flux is related to the density anomaly ratio Rρ = βΔS/αΔT by the power law F*T = 2·59Rρ−12.6 over four decades. Optical measurements show that the vertical gradients of concentration of salt and sugar within the interface are those required if molecular diffusion is to account for the whole flux of each component.
Transpiration and natural convection: the vertical-flat-plate problem
Authors: Clarke J. F.
Published: March 2006

A study is made of the natural convective flow which is induced in an infinite expanse of gas by the presence of a vertical hot flat plate from which hot gas of the same chemical type is being blown. The transpiration rate is assumed to be such that a self-similar boundary-layer type of solution is available. It differs from previous analyses in the following respects. Most important, the density is not assumed to be constant a t any stage in the description of the flow field. Also the form of the induced flow in the outer domain is calculated and proves to be substantially independent of the blowing rate in this case; the induced outer flow is found to be of large lateral extent. Finally, the variable-gas-property problem is carried to second order and solutions are obtained by using an ‘exact’ form of Howarth-Dorodnitsyn variable. The opportunity is taken t o make some comments about the comparison between theory and experiment for finite flat plates without transpiration.
Natural convection in a sloping porous layer
Authors: Bories S. A. , Combarnous M. A.
Published: March 2006

This paper describes an experimental and theoretical study of thermal convection in a sloping porous layer. The saturated layer is bounded by two parallel impermeable planes maintained at different temperatures. Several types of flows were observed: a unicellular movement and a juxtaposition of longitudinal coils or of polyhedral cells.

A theoretical analysis has been made using the standard bases of the linear theory of stability and by taking into account some assumptions suggested by experimental observations. The critical conditions for the transition between unicellular and polycellular flows has been determined. For flow in longitudinal coils or with polyhedral cells the average heat transfer depends mainly on the filtration Rayleigh number and on the slope of the layer.

The experimental study was made in a Rayleigh number range 0–800 and for various slopes (0–90°). For both the transition criterion and the heat transfer, a good fit was observed between the experimental and theoretical results. For maximum slope, i.e. 90°, a correlation which connects the Nusselt number with both the Rayleigh number and the vertical extent of the model is proposed.