bluuebunny/crossref_metadata_2025 huggingface dataset:
Two-dimensional free-surface gravity flow past blunt bodies
Authors: Dagan G. , Tulin M. P.
Published: March 2006

Most of the wave resistance of blunt bow displacement ships is caused by the bow-breaking wave. A theoretical study of the phenomenon for the two-dimensional steady flow past a blunt body of semi-infinite length is presented. The exact equations of free-surface gravity flow are solved approximately by two perturbation expansions. The small Froude number solution, representing the flow beneath an unbroken free surface before the body, is carried out to second order. The breaking of the free surface is assumed to be related to a local Taylor instability, and the application of the stability criterion determines the value of the critical Froude number which characterizes breaking. The high Froude number solution is based on the model of a jet detaching from the bow and not returning to the flow field. The outer expansion of the equations yields the linearized gravity flow equations, which are solved by the Wiener-Hopf technique. The inner expansion gives a nonlinear gravity-free flow in the vicinity of the bow a t zero order. The matching of the inner and outer expansions provides the jet thickness as well as the associated drag.
Turbulent boundary layer on a rotating helical blade
Authors: Lakshminarayana B. , Jabbari A. , Yamaoka H.
Published: March 2006

This paper investigates the boundary-layer characteristics on a helical blade of large chord length, enclosed in an annulus and rotating in a fluid otherwise at rest. The three-dimensional form of momentum integral equations is derived, and used to predict the boundary-layer growth and limiting streamline angles on the blade surface. The measurements are in general agreement with the predictions. The wall shear stress correlation, which includes both Reynolds number and rotation parameters, valid for a rotating blade operating at zero pressure gradient, is derived. Radial and tangential velocity profiles, the tangential component of turbulence intensity and blade static pressures are measured at several locations on the blade surface. The nature of flow near the blade tip is discussed. An expression for the radial velocity profile, valid in the outer region of the boundary layer, is derived theoretically.
The use of the loaded-sphere molecular model for computer simulation of diatomic gases
Authors: Melville W. K.
Published: March 2006

An approximate binary collision procedure is devised for the loaded-sphere molecular model and is used with Bird's direct simulation technique for computer experiments on diatomic gases. The collision procedure is tested by simulating the approach to equilibrium of a constant-speed gas of loaded spheres and good agreement with Jeans's (1904) theoretical prediction is obtained. The procedure is then used to study the structure of normal shock waves in the diatomic gas, giving mean velocity, density and temperature profiles. It is found that the present procedure consumes considerably more computer time than comparable simulations of monatomic gases.
On fluid motions induced by an electromagnetic field in a liquid drop immersed in a conducting fluid
Authors: Sozou C.
Published: March 2006

The deformation of a liquid drop immersed in a conducting fluid by the imposition of a uniform electric field is investigated. The flow field set up is due to the surface charge and the tangential electric field stress over the surface of the drop, and the rotationality of the Lorentz force which is set up by the electric current and the associated magnetic field. It is shown that when the fluids are poor conductors and good dielectrics the effects of the Lorentz force are minimal and the flow field is due to the stresses of the electric field tangential to the surface of the drop, in agreement with other authors. When, however, the fluids are highly conducting and poor dielectrics the effects of the Lorentz force may be predominant, especially for larger drops.
Global stability of spiral flow. Part 2
Authors: Hung W. L. , Joseph D. B. , Munson B. R.
Published: March 2006

The stability of spiral flow between rotating and sliding cylinders is considered. In the limit of narrow gap, a’ modified’ energy theory is constructed. This theory exploits the consequences of assuming the existence of a preferred spiral direction along which disturbances do not vary. The flow is also analyzed from the viewpoint of linearized theory. Both problems depend strongly on the sign of Rayleigh's discriminant, – 2Ωζ. Here Ω is the component of angular velocity, and ζ is the component of total vorticity of the basic flow in the direction perpendicular to the spiral ribbons on which the disturbance is constant. When the discriminant is negative, there is evidently no instability to infinitesimal disturbances, and the spiral disturbance whose energy increases at the smallest R is a roll whose axis is perpendicular to the stream. This restores and generalizes Orr's non-linear results for disturbances having a preferred spiral direction. When the discriminant is positive, the critical disturbances of linear theory and the modified energy theory are spiral vortices. The differences between the energy and linear limits can be made smaller in the restricted class of disturbances with coincidence achieved for axisymmetric disturbances in the rotating cylinder problem in the limit of narrow gap. For the sliding-rotating case, the critical disturbance of the linear theory appears as a periodic wave in a co-ordinate system fixed on the outer cylinder. This wave has a dimensionless frequency equal to - ½ a sin (χ-ψ), where a is the wave-number, χ is the angle between the pipe axis and the direction of motion of the inner cylinder relative to the outer one, and ψ is the disturbance spiral angle.

Instability limits, frequencies and wave-numbers are computed numerically when the cylinder gap is not narrow. These are in even closer agreement with Ludwieg's experimental results than the approximate results which were given in part 1.
Wake collapse in a stratified fluid: linear treatment
Authors: Hartman R. J. , Lewis H. W.
Published: March 2006

The linear initial-value problem of a partially mixed cylindrical wake in a, uniformly stratified fluid is formulated and exact solutions are given for the density and velocity fields inside and just outside the original cylinder. An asymptotic expression for the far-field internal wave radiation is given and the corresponding solutions for a spherical wake geometry are noted. The treatment emphasizes the inadequancy of the usual linear Boussinesq approximation to describe the detailed nature of similar problems, in particular the fully mixed wake-collapse problem.
Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
Authors: Richardson S.
Published: March 2006

A blob of Newtonian fluid is sandwiched in the narrow gap between two plane parallel surfaces so that, a t some initial instant, its plan-view occupies a simply connected domainD0. Further fluid, with the same material properties, is injected into the gap at some fixed point withinD0, so that the blob begins to grow in size. The domainDoccupied by the fluid at some subsequent time is to be determined.

It is shown that the growth is controlled by the existence of an infinite number of invariants of the motion, which are of a purely geometric character. For sufficiently simple initial domainsD0these allow the problem to be reduced to the solution of a finite system of algebraic equations. For more complex initial domains an approximation scheme leads to a similar system of equations to be solved.
The relaxation of stress in a ≠-fluid with reference to the decay of homogeneous turbulence
Authors: Dowden J. M.
Published: March 2006

It was suggested by Proudman (1970) that many of the phenomena of turbulence at high Reynolds number could be modelled by a suitably chosen member of a class of non-Newtonian fluids, ν-fluids, all of whose properties depend only on a single dimensional constant with the dimensions of viscosity. This paper investigates the relaxation of homogeneous stress in a doubly degenerate third-order ν-fluid (which is the simplest member of the class that can possibly be used to model turbulence) in the limit ν → 0.

The equation which governs the stress tensor S is of the form
\[
AS\ddot{S} + B\dot{S}^2 = 0,
\]
where A and B are isotropic tensor constants of the fluid; its differential structure can be of four distinct types. A list of properties required of the solutions of the equation is set out, and it is shown that only one of the four types has all the properties demanded of it. The behaviour of solutions of this equation is found to be consistent with the theoretical and experimental results on the decay of homogeneous turbulence.
Heat transfer from hypersonic turbulent flow at a wedge compression corner
Authors: Coleman G. T. , Stollery J. L.
Published: March 2006

A hypersonic gun tunnel has been used to measure the heat-transfer-rate distribution over a compression corner under turbulent boundary-layer conditions. Attached, incipient and separated flows are considered. The results are compared with other experimental data and with the predictions of a simple theory.
Compressible corner flow
Authors: Weinberg Bernard C. , Rubin Stanley G.
Published: March 2006

The viscous compressible flow in the vicinity of a right-angle corner, formed by the intersection of two perpendicular flat plates and aligned with the free stream, is investigated. In the absence of viscous-inviscid interactions and imbedded shock waves, a theory is developed that is valid throughout the subsonic and supersonic Mach number range. Within this limitation and the additional assumptions of unit Prandtl number and a linear viscosity-temperature law, a consistent set of governing equations and boundary conditions is derived. The method of matched asymptotic expansions is applied in order to distinguish the relevant regions in the flow field.

In the corner region the Crocco integral is shown to apply, even for a three-dimensional flow field. The equations governing the flow in the corner layer consist of four coupled nonlinear elliptic partial differential equations of the Poisson variety. Since they do not lend themselves to analytic solution, numerical methods are employed. Two such methods used here are the Gauss-Seidel explicit technique and the alternating direction implicit method. The merits of both techniques are discussed with regard to convergence rate, accuracy and stability. The calculations show that in cases where the Gauss-Seidel method fails to give converged solutions, owing to instability, the alternating direction implicit method does provide converged solutions. However, in cases where both methods are convergent, there is no appreciable difference in convergence rates. The numerical calculations were done on a CDC 6600 computer.

Results of calculations are presented for representative compressible-flow conditions. The extent of the corner disturbance is controlled by the Mach number and wall temperature ratio in a manner analogous to the two-dimensional boundary layer. A swirling motion is noted in the corner layer which is influenced to a great extent by the asymptotic cross-flow profiles. The skin-friction coefficient is shown to increase monotonically from zero at the corner point to its asymptotic two-dimensional value. For cold wall cases, this value is approached more rapidly. The asymptotic analysis indicates that for even colder wall cases, not considered here, an overshoot is possible.
Wave mechanics of breakdown
Authors: Landahl M. T.
Published: March 2006

Kinematic wave theory is used to determine under what conditions breakdown of a steady or unsteady laminar flow into high frequency oscillations should occur. The analysis of a small-scale secondary wave riding on a large-scale inhomogeneity, such as that produced by a finite amplitude primary instability wave, reveals that the breakdown mechanism has three basic ingredients: (i) a self-excited secondary wave with a group velocity near the propagation velocity (phase velocity) of the primary wave, (ii) space-time focusing of the secondary wave train on the primary wave crest and (iii) a nonlinear filtering mechanism leading to rectification of the secondary wave.

The theory is applied to a laminar shear flow. Good quantitative agreement with the experiments on boundary-layer transition by Klebanoff, Tidstrom & Sargent (1962) is found for the critical condition leading to breakdown. Also, the theory is able to explain all the main qualitative breakdown features observed by Klebanoff et al. and others, such as the rapid localized onset, and the formation of a hairpin vortex lifting up from the surface downstream of the primary wave crest.
Note on the rheology of a dilute suspension of dipolar spheres with weak Brownian couples
Authors: Hinch E. J. , Leal L. G.
Published: March 2006

A problem of theoretical interest in suspension rheology is the calculation of bulk rheological properties for a dilute suspension of spherical dipolar particles in the presence of weak Brownian rotation, when the applied field is perpendicular to the local vorticity of the bulk flow. In the present note, we determine the asymptotic form for the orientation distribution of the dipole axis in the limit of weak Brownian motion and use this distribution to determine the corresponding rheological properties of the suspension. The bulk stress is then discussed in terms of an effective viscosity for shear flow.
A Reynolds stress model of turbulence and its application to thin shear flows
Authors: Hanjalić K. , Launder B. E.
Published: March 2006

The paper provides a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor$\overline{u_iu_j}$and for the turbulence energy-dissipation rate ε. In its most general form the model thus entails the solution of seven transport equations for turbulence quantities but contains only six constants to be determined by experiment. It is demonstrated that the proposed approximation to the pressure-rate-of-strain correlations leads to satisfactory predictions of the component stress levels in plane homogeneous turbulence, including the non-equality of the lateral and transverse normal-stress components.

For boundary-layer flows a simpler version of the model is derived wherein transport equations are solved only for the shear stress$-\overline{u_1u_2}$the turbulence energy κ and ε. This model has been incorporated in the numerical solution procedure of Patankar & Spalding (1970) and applied to the prediction of a number of boundary-layer flows including examples of flow remote from walls, those developing along one wall and those confined within ducts. Three of the flows are strongly asymmetric with respect to the surface of zero shear stress and here the turbulent shear stress does not vanish where the mean rate of strain goes to zero. In most cases the predicted profiles and other quantities accord with the data within the probable accuracy of the measurements.
The tearing of an adhesive layer between flexible tapes pulled apart
Authors: Williamson A. S.
Published: March 2006

The tearing of a pressure-sensitive (‘tacky’) adhesive is examined. Two flexible strips bonded by a layer of adhesive are passed between adjacent cylindrical guides and peeled apart, causing the adhesive layer to separate into two about a surface tension membrane. Treating the adhesive as a Newtonian viscous fluid, the slow-flow problem is solved by an iterative numerical scheme in which the surface tension membrane boundary in the vicinity of the region of separation is approximated by a shear-free boundary given by a sixth-degree polynomial expression. The energy dissipation rate, a measure of the ‘strength’ of the adhesive, is obtained from the flow.

The solution method is also used to determine the similar flow induced by two counter-rotating rollers partially immersed in a large bath of fluid. The results are in fairly good agreement with available experimental data. The symmetrical eddies observed under the lowest point of the surface tension membrane in the stable flow between the rollers are reproduced in the solution, proving that fluid inertia effects are not essential for their existence.
A parametric study of self-similar blast waves
Authors: Oppenheim A. K. , Kuhl A. L. , Lundstrom E. A. , Kamel M. M.
Published: March 2006

The paper presents a comprehensive examination of self-similar blast waves with respect to two parameters, one describing the front velocity and the other the variation of the ambient density immediately ahead of the front. All possible front trajectories are taken into account, including limiting cases of the exponential and logarithmic form. The structure of the waves is analysed by means of a phase plane defined in terms of two reduced co-ordinatesF≡ (t/rμ)uandZ≡ [(t/rμ)a]2, wheretandrare the independent (time and space) variables, μ ≡dlnrn/dIntnthe subscriptndenoting the co-ordinates of the front, anduandaare, respectively, the particle velocity and the speed of sound. Loci of extrema of the integral curves in the phase plane are traced and loci of singularities are determined on the basis of their intersections. Boundary conditions are introduced for the case when the medium into which the waves propagate is at rest. Representative solutions, pertaining to all the possible cases of blast waves bounded by shock fronts propagating into an atmosphere of uniform density, are obtained by evaluating the integral curves and determining the corresponding profiles of the gasdynamic parameters. Particular examples of integral curves for waves bounded by detonations are given and all the degenerate solutions, corresponding to cases where the integral curve is reduced to a point, are delineated.
Nonlinear gravity waves on steady non-uniform currents
Authors: Crapper G. D.
Published: March 2006

The interaction of nonlinear gravity waves and steady non-uniform currents is studied using the averaged Lagrangian method due to Whitham (1965a,b). The results are compared with the essentially linear theory of Longuet-Higgins & Stewart (1961, 1964) for three specific problems: waves on a stream (U(x), 0) with variations in the stream balanced by upwelling from below or inflow from the sides, and waves on a shear flow (0, V(x)). It appears that rates of growth of large waves are less than those predicted by linear theory and that the energy density can sometimes decrease when the wave height and steepness are still increasing. The final section discusses the form of the energy equation in terms of the Lagrangian.
The force distribution on a slender twisted particle in a Stokes flow
Authors: Clarke N. S.
Published: March 2006

The theory of Stokes flows about slender particles is considered for the case in which the particle cross-section is arbitrary and non-uniform along the axis of the particle, subject to certain smoothness assumptions. As distinct from previous works on slender particles in which the particle is represented approximately by a line distribution of Stokeslets, the representation adopted here is the exact one of a surface distribution of Stokeslets. This representation may then be used to recover the familiar one-dimensional integral equation for the equivalent line density of Stokeslets, together with estimates for the range of particle shapes for which the equation is valid. Within this range it is found that there is a class of particles for which the established perturbation scheme, which is used to obtain a solution to the integral equation, is singular. This class of particle shapes is illustrated by the example of a uniformly twisted particle whose pitch of twist is large enough compared with the cross-sectional dimension to ensure the validity of the equation, but small enough to make the usual method of solution singular. It is shown how the equation may be transformed so that an approximate solution can be found by means of a regular perturbation scheme. The results indicate that, for each of the axial and transverse components of motion, there is an equivalent particle of circular cross-section for which the total force and couple are the same as for the original particle. However, the radii of the equivalent cylinders are different for each component, the transverse component being affected by the twist while the axial component is not.
A free-streamline theory for bluff bodies attached to a plane wall
Authors: Kiya Masaru , Arie Mikio
Published: March 2006

A free-streamline theory is presented for the separated flow past two-dimensional bluff bodies attached to a long plane wall on which a turbulent boundary layer has developed. The non-uniform velocity profile in the turbulent boundary layer which would be measured if the bluff bodies were absent has been replaced by a hypothetical inviscid parallel shear flow which has a constant vorticity. This model admits analytical solutions and automatically yields closed streamlines in front of the bluff bodies such as the normal plate and the semicircular projection, which are geometrically very similar to observed front separation bubbles. The present theory involves three or four parameters which must be determined on the basis of experimental information, the number of parameters depending upon the shape of bluff bodies. Two typical examples of bluff bodies, i.e. the normal plate and the semicircular projection, are worked out. Pressure distributions around these bodies predicted by the present theory are found to give a good agreement with experimental measurements.
The motion of a plate in a rotating fluid at an arbitrary angle of attack
Authors: Wilcox David C.
Published: March 2006

Slow motion of a thin plate at a finite angle of attack in a rotating container filled with a viscous incompressible fluid is analysed. The Rossby and Ekman numbers are assumed to be small. The solution method is developed by studying horizontal translation of an elliptical plate. The plate is shown to carry a stagnant Taylor column with it as it moves. Detailed analysis of the structure of the vertical shear column bounding the Taylor column is circumvented by integrating the equations of motion across the shear column. A jump condition based upon mass conservation in the shear column which relates the geostrophic regions inside and outside the Taylor column results. This jump condition and its method of derivation can be used to analyse arbitrary (slow) motion of any thin plate at any angle of attack.

The fluid motion resulting when a disk moves using all six degrees of freedom at an infinitesimal angle of attack is discussed. The forces and moments on the disk are calculated and the streamlines of the geostrophic flow are displayed.
The interaction of large amplitude shallow-water waves with an ambient shear flow: non-critical flows
Authors: Blythe P. A. , Kazakia Y. , Varley E.
Published: March 2006

This paper describes the behaviour of large amplitude, long gravity waves as they move over a horizontal bed into a region where the flow is steady but sheared in a vertical direction. A new class of exact solutions to the nonlinear hydraulic flow equations is derived. These solutions describe progressing waves and are sufficiently general to allow both the shape of the free surface at any instant and the shear profile of the undisturbed flow to be specified. The waves are examples of neutrally stable disturbances in the sense that they neither grow nor decay in amplitude, although, like simple waves on an unsheared flow, they can break.
Numerical calculation of internal wave motions
Authors: Young James A. , Hirt C. W.
Published: March 2006

A finite-difference technique for the numerical calculation of two-dimensional stratified incompressible fluid flows is presented. Small density variations are not assumed, so that this method is generally applicable to a wide variety of problems. To illustrate this new technique a calculation has been made of the collapse of a uniformly mixed region in a linearly stratified fluid. In addition to giving excellent agreement with experimental data, the calculations also reveal the mechanism for an observed change in scaling behaviour.
Some properties of sink-flow turbulent boundary layers
Authors: Jones W. P. , Launder B. E.
Published: March 2006

An experimental study of asymptotic sink-flow turbulent boundary layers is reported. Three levels of acceleration corresponding to values of the acceleration parameter K of 1·5 × 10−6, 2·5 × 10×6 and 3·0 × 10×6 have been examined. In addition to mean velocity profiles, measurements have been obtained of the profiles of longitudinal turbulence intensity, and, for the lowest value of K, of the lateral and transverse components as well. Measurements at selected positions in the boundary layer of the power spectral density indicate that none of the boundary layers exhibit an inertial subrange; for the steepest acceleration, in particular, throughout the boundary layer the spectrum shapes are similar in form to those reported within the viscous sublayer of a high Reynolds number turbulent flow.
Finite amplitude doubly diffusive convection
Authors: Straus Joe M.
Published: March 2006

A layer of fluid containing gradients of both temperature and salinity is subject to several instabilities of geophysical interest. When the salinity and temperature increase upwards, the layer may become unstable even if the density profile indicates stability. This ‘doubly diffusive’ instability, first treated by Stern, is seen experimentally to consist of thin fingers of up- and downgoing fluid. Linear analysis cannot explain this small horizontal scale for a steady-state process, but a nonlinear treatment of the problem combined with a stability analysis indicates that only small-scale motions are stable when the salinity gradient is larger than that necessary for the onset of instability. In the limit of small salt diffusivity the flux of salt is calculated using the Galerkin technique and found to reach a maximum at a wavelength that decreases with increasing salinity and temperature gradients. The stability of the finite amplitude solutions is treated; only small-scale motions are found to be stable and the wavelength of the most stable mode is found to compare favourably with the wavelength that maximizes the salt flux.
The hydrodynamic interaction of two small freely-moving spheres in a linear flow field
Authors: Batchelor G. K. , Green J. T.
Published: March 2006

Two rigid spheres of radii a and b are immersed in infinite fluid whose velocity at infinity is a linear function of position. No external force or couple acts on the spheres, and the effect of inertia forces on the motion of the fluid and the spheres is neglected. The purpose of the paper is to provide a systematic and explicit description of those aspects of the interaction between the two spheres that are relevant in a calculation of the mean stress in a suspension of spherical particles subjected to bulk deformation. The most relevant aspects are the relative velocity of the two sphere centres (V) and the force dipole strengths of the two spheres (S′ij, S″ij), as functions of the vector r separating the two centres.

It is shown that V, S′ij and S″ij depend linearly on the rate of strain at infinity and can be represented in terms of several scalar parameters which are functions of r/a and b/a alone. These scalar functions provide a framework for the expression of the many results previously obtained for particular linear ambient flows or for particular values of r/a or of b/a. Some new results are established for the asymptotic forms of the functions both for r/(a + b) [Gt ] 1 and for values of r − (a + b) small compared with a and b. A reasonably complete numerical description of the interaction of two rigid spheres of equal size is assembled, the main deficiency being accurate values of the scalar functions describing the force dipole strength of a sphere in the intermediate range of sphere separations.

In the case of steady simple shearing motion at infinity, some of the trajectories of one sphere centre relative to another are closed, a fact which has consequences for the rheological problem. These closed forms are described analytically, and also numerically in the case b/a = 1.
Super-Alfvénic supersonic flow over a cone in aligned fields
Authors: Bertram Lee A. , Lynn Y. M.
Published: March 2006

Super-Alfvénic supersonic aligned magnetogasdynamic flow over a cone of finite semi-apex angle, with an attached fast shock wave, is solved numerically. We obtain ‘almond curves’ in the plane of magnetic induction vector variation, analogous to Busemann's ‘apple curves’ for supersonic cone flows, to describe the flow field near the cone. Total surface pressure coefficients, current and vorticity distributions are presented. A closed-form solution of the flow is obtained when a switch-on shock occurs.
Second-order Cowley-Imai analogy in magnetogasdynamics
Authors: Bertram Lee A. , Lynn Y. M.
Published: March 2006

The extended Cowley–Imai analogy is derived and employed to obtain explicit equations which allow transcription of gasdynamic perturbation solutions into magnetogasdynamic solutions. The transcription is written down to second order for axisymmetric super-Alfvénic flows of a perfect gas at arbitrary Mach numbers. Speed and field perturbations are shown to vanish in the Alfvénic limit for such solutions, although this is not a property of the exact solution. Van Dyke's supersonic-cone-flow solution is then transcribed and compared with the exact numerical solution over the range 1 < A∞, ≥ 20, 1 < M∞, ≥ 20 for a cone of 5° semi-apex angle, showing excellent agreement which improves with increasing field strength. The large-cone-angle behaviour of the solution is also quite good for the upstream state A∞ = M∞ = 2·0.
On a class of magneto-convective boundary-layer flows
Authors: Rotem ZeëV
Published: March 2006

A class of laminar rotating free-convective flows over a horizontal boundary in the presence of a strong magnetic field is investigated. The range of applicability of boundary-layer approximations is obtained, as well as a class of similarity solutions valid within a domain of multi-parameter space.
An experimental and analytical study of natural convection with appreciable thermal radiation effects
Authors: Audunson T. , Gebhart B.
Published: March 2006

An experimental and theoretical investigation has been carried out to determine the effect of thermal radiation on a natural convection boundary layer formed adjacent to a vertical flat surface with uniform heat flux input. In the experiment, the gases air, argon and ammonia were used as the fluid medium, thus permitting the observation of radiation effects in non-abosrbing and absorbing media. Experimental results were obtained for three different wall emittances at ambient pressures ranging from 2 to 8 atmospheres in air and argon and from 2 to 7 atmospheres in ammonia. An interferometer was used to measure the temperature distributions in the boundary layer and to evaluate the conductive (convective) heat flux from the surface into the fluid medium. The experimental temperature distributions and heat-transfer results obtained in ammonia gas are compared to the predictions of a perturbation analysis developed by the present writers. General agreement between theory and experiment is found. The presence of a radiating gas is seen to increase the convective heat transfer by as much as 40 % for the conditions of the present experiments. The results further indicate that the temperature distributions and wall-temperature gradients are strongly affected by both variations in the surface emittance and variations in gaseous emission and absorption. For non-absorbing gases, the experimental results are found to be in general agreement with existing theory. It is also shown that the experimental temperature distributions agree very well with theoretical predictions obtained by treating the convection and radiation processes as independent and superimposed.
The oscillatory instability of convection rolls in a low Prandtl number fluid
Authors: Busse F. H.
Published: March 2006

The instability of convection rolls in a fluid layer heated from below is investigated for stress-free boundaries in the limit of small Prandtl number. It is shown that the two-dimensional rolls become unstable to oscillatory three-dimensional disturbances when the amplitude of the convective motion exceeds a finite critical value. The instability corresponds to the generation of vertical vorticity, a mechanism which is likely to operate in the case of a variety of roll-like motions. In all aspects in which the theory can be related to experiments, reasonable agreement with the observations is found.
An experimental study of the velocity distribution and transition to turbulence in the aorta
Authors: Nerem R. M. , Seed W. A. , Wood N. B.
Published: March 2006

The development and evaluation of a hot-film probe, suitable for use within arteries and operated with a commercial constant-temperature anemometer and linearizcr, is described. The performance of the system in the recording of arterial velocity wave forms is described, and instantaneous and time-averaged velocity profiles constructed from measurements in the thoracic aorta of dogs are presented. The profiles were blunt, with boundary layers estimated to be less than 2 mm thick throughout the cycle, and significant skews were observed, the explanation for which appears to lie in the influence of local geometry on the flow. A preliminary study of flow disturbances in the aorta based on visual observation of instantaneous velocity wave forms and frequency spectrum analysis is reported. The occurrence of flow disturbances and turbulence is shown to be related to peak Reynolds number and the frequency parameter α. The possible roles of free-stream disturbances and boundary-layer transition in generating these disturbances are discussed.
Propagation of internal gravity waves in perfectly conducting fluids with shear flow, rotation and transverse magnetic field
Authors: Rudraiah N. , Venkatachalappa M.
Published: March 2006

The propagation of internal Alfvén-inertio-gravitational waves in a Boussinesq inviscid adiabatic perfectly conducting shear flow with rotation is investigated in the presence of a transverse magnetic field. It is shown that the effect of the rotational nature of electromagnetic force and Coriolis force is that linear momentum is not conserved anywhere in the fluid even at critical levels, whereas the angular momentum flux is conserved everywhere in the fluid except at the critical levels at which the Doppler-shifted frequency Ωd = 0, + ΩA or ± Ω ± (Ω2 + Ω2A)½, where ΩA is the Alfvén frequency and Ω is the Coriolis frequency, and the angular momentum is transferred to the mean flow there by Alfvén-inertio-gravitational waves. Asymptotic solutions to the wave equation are obtained near the critical levels and it is shown that the effect of the Lorentz force on the waves at the critical levels is to increase the process of critical layer absorption. The condition for neglection of rotation for higher frequency waves is also obtained and is found to be the same in both hydrodynamic and hydro-magnetic flows.
Taylor vortices and the evaluation of material constants: a critical assessment
Authors: Jones W. M. , Davies D. M. , Thomas M. C.
Published: March 2006

fldsjfldsjfdsjfdsfjds
Pressure drop due to the motion of a sphere near the wall bounding a Poiseuille flow
Authors: Bungay Peter M. , Brenner Howard
Published: March 2006

An expression is derived for the (low Reynolds number) additional pressure drop created by a relatively small sphere moving near the wall of a circular tube through which there is a Poiseuille flow. Two specific applications are examined: (i) the sedimentation of a homogeneous non-neutrally buoyant sphere in a quiescent fluid; and (ii) the motion of a neutrally buoyant sphere. In the latter case a pronounced increase in the additional pressure drop is predicted when the separation between the sphere and the tube wall is reduced to zero.

This analysis, which includes the behaviour for a sphere in contact with the tube wall, supplements previous ‘method of reflexions’ treatments valid only when the distance from the sphere centre to the wall is large compared with the sphere radius.
On the integral properties of separated laminar boundary layers
Authors: Sfeir A. A.
Published: March 2006

Detailed measurements of the flow over a compression corner were taken using hot-wire probes. The experiments were performed in supersonic flow (M = 2·64) under adiabatic wall conditions. The incompressible analogues of the boundary-layer profiles were obtained and their integral characteristics and shape factors correlated. Comparison with the self-similar profiles used by Lees & Reeves (1964) to describe interaction problems showed some similarities between the shape factors, but the measured negative shears in the separated bubble proved to be much less.
Flow past an impulsively started circular cylinder
Authors: Collins W. M. , Dennis S. C. R.
Published: March 2006

An accurate method is described for integrating the Navier-Stokes equations numerically for the time-dependent flow past an impulsively started circular cylinder. Results of integrations over the range of Reynolds numbers, based on the diameter of the cylinder, from 5 to ∞ are presented and compared with previous numerical, theoretical and experimental results. In particular, the growth of the length of the separated wake behind the cylinder has been calculated forR= 40, 100 and 200 and is found to be in very good agreement with the results of recent experimental measurements. The calculated pressure distribution over the surface of the cylinder forR= 500 is also found to be in reasonable agreement with experimental measurements for the caseR= 560.

For Reynolds numbers up to 100 the equations were integrated until most of the features of the flow showed a close approximation to steady-state conditions. The results obtained are in good agreement with previous calculations of the steady flow past a circular cylinder. ForR> 100 the integrations were continued until the implicit method of integration broke down by reason of its failure to converge. A secondary vortex appeared on the surface of the cylinder in the caseR= 500, but for higher Reynolds numbers, including the caseR= ∞, the procedure broke down before the appearance of a secondary vortex. In all cases the flow was assumed to remain symmetrical.
Global stability of time-dependent flows: impulsively heated or cooled fluid layers
Authors: Homsy G. M.
Published: March 2006

The method of energy is used to discuss the stability of time-dependent diffusive temperature profiles in fluid layers subject to impulsive changes in surface temperature.

Bounds for the ratio of disturbance energy production to dissipation are found to be parametric functions of time because the basic temperature develops through diffusion. This time dependence leads to the demarcation of regions of stability in a Rayleigh number-time plane and the interpretation of these regions is given. Numerical results are presented for the cases of impulsive heating and cooling of initialty isothermal fluid layers. New global stability results which give the Rayleigh number below which the diffusive solution to the Boussinesq equations is unique are reported for these cases.
Negative shock waves
Authors: Thompson P. A. , Lambrakis K. C.
Published: March 2006

Negative or rarefaction shock waves may exist in single-phase fluids under certain conditions. It is necessary that a particular fluid thermodynamic quantity Γ ≡ −½δ In (δP/δν)s/δ In ν be negative: this condition appears to be met for sufficiently large specific heat, corresponding to a sufficient level of molecular complexity. The dynamic formation and evolution of a negative shock is treated, as well as its properties. Such shocks satisfy stability conditions and have a positive, though small, entropy jump. The viscous shock structure is found from an approximate continuum model. Possible experimental difficulties in the laboratory production of negative shocks are briefly discussed.
Analytic solutions for potential flow over a class of semi-infinite two-dimensional bodies having circular-arc noses
Authors: Hess John L.
Published: March 2006

A new class of analytic solutions to the problem of two-dimensional potential fnow is presented here. The method of solution has features of both direct and indirect solutions. The bodies about which flow is computed are semi-infinite and have forward regions that either are flat or consist of a circular arc, which may be convex or concave to the flow. Closed-form solutions are obtained for the surface velocity. Afterbody shapes are defined by implicit equations containing a quadrature. Certain analytic properties of the solutions are investigated. An interesting feature of the bodies is the presence of a ‘pseudo corner’ where the slope angle is continuous but the curvature is infinite. The surface velocity becomes logarithmically infinite at these points in contrast to the power-law behaviour at a true corner. One case of the convex circular arc has finite velocity everywhere, and in some sense represents flow over a circular cylinder with a ‘natural’ separation point. This point occurs at 77·45° from the front stagnation point, which is close to the separation point for incompressible laminar boundarylayer flow.
On strong blowing into an incompressible airstream
Authors: Smith F. T.
Published: March 2006

An experimental study of distributed air-injection from a porous section of a flat plate into a uniform incompressible airflow is described. The relative mass flow rates of the injection varied between 0·008 and 0·053 (strong injection) and the blowing was fairly uniformly distributed. In the resulting flow field, which was predominantly laminar except near the dividing streamline, where unsteadiness prevailed, velocity profile and pressure measurements were taken and the position of the dividing streamline thereby estimated. Overall the results agree fairly well with the steady laminar theory for strong normal blowing, outlined in §2, although for the strongest blow some signs of separation some way upstream of the blow are apparent.
Heat transfer from a hypersonic turbulent boundary layer on a flat plate
Authors: Coleman G. T. , Osborne C. , Stollery J. L.
Published: March 2006

A hypersonic gun tunnel has been used to measure the heat transfer to a sharpedged flat plate inclined at various incidences to generate local Mach numbers from 3 to 9. The measurements have been compared with a number of theoretical estimates by plotting the Stanton number against the energy-thickness Reynolds number. The prediction giving the most reasonable agreement throughout the above Mach number range is that due to Fernholz (1971).

The values of the skin-friction coefficient derived from velocity profiles and Preston tube data are also given.
Some further studies on the transition to turbulent convection
Authors: Krishnamurti Ruby
Published: March 2006

In a horizontal convecting layer of fluid, several distinct transitions occur at certain distinct Rayleigh numbersR, for a given Prandtl numberPr.The regime diagram has been extended to include the Prandtl-number range

2·5 × 10−2[les ]Pr[les ] 0·85 × 104.

In particular it is found that distinct changes in the slope of the heat-flux curve occur even forPr= 2·5 × 10−2. The flow is steady up toR=Rt= 2·4 × 103. ForR>Rt, the period of oscillation is compared with the theoretical values of Busse. ForPr= 0·71 decreases as well as increases in the slope of the heat-flux curve are observed.

ForRjust greater thanRc, the preferred orientation of rolls in various side-wall geometries is investigated. For high Prandtl number, the effect of curvature of the roll axis, forced by curved side walls, upon the second transition atRIIis investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering ofRII. These results, along with the observed hysteresis, support the view that there are metastable states attainable by finite amplitude instability. Finally the nature of the time-dependent flow at largeRand high Prandtl number is investigated in a Hele-Shaw cell. It is shown unequivocally that the observed periodicity at a fixed point is due to hot or cold plumes moving past the point.
Oscillatory motion in Bénard cell due to the Soret effect
Authors: Platten J. K. , Chavepeyer G.
Published: March 2006

The period of oscillations for the Bénard problem in a two-component system taking into account thermal diffusion is given. Schmidt-Milverton plots are presented for water-methanol and water-isopropanol systems. Anomalous heating curves are observed. Thermocouple responses are given for some heating powers and show oscillations in the temperature field. A qualitative agreement exists with the predicted values of the period given by the theory.
The laser-Doppler velocimeter and its application to the measurement of turbulence
Authors: George William K. , Lumley John L.
Published: March 2006

In 1964, Yeh & Cummins demonstrated that coherent light sources could be used for the measurement of steady fluid velocities by observing the Doppler shift in the frequency of light scattered from small particles moving with the fluid. Since 1964 many investigators have attempted to extend this technique to the measurement of turbulent velocity fluctuations.

A fundamental limitation on this type of velocimeter is the Doppler ambiguity introduced by the finite transit time of particles through the scattering volume, turbulent velocity fluctuations across the scattering volume, mean velocity gradients and electronic noise. A unified account of the effect of the Doppler ambiguity on the measurement of the instantaneous velocities is presented and results are interpreted using the power spectrum. The influence of the ambiguity on the measurement of other statistical quantities is also examined.

Limitations on the spatial and temporal resolution imposed by the finite sampling volume are examined using the power spectrum and criteria for optimization of the response are proposed.

An operational laser-Doppler velocimeter is described and measurements of spectra in both laminar and turbulent flow are presented. The experimental results are seen to be in excellent agreement with theoretical predictions.
Unsteady transonic flows with shock waves in two-dimensional channels
Authors: Adamson T. C. , Richey G. K.
Published: March 2006

A two-dimensional unsteady transonic flow of a perfect gas with constant specific heats is considered, solutions being found in the form of perturbations from a uniform, sonic, isentropic flow. Longitudinal viscous stress terms are retained so that shock waves can be included. The case where the characteristic time of a temporal flow disturbance is large compared with the time taken by a sonic disturbance to traverse the transonic regime is studied. A similarity solution involving an arbitrary function of time is employed, such that the channel walls are in general not stationary. Solutions are presented for thick (shock fills transonic region) and thin (shock tends to a discontinuity) shock waves for both decelerating and accelerating channel flows. For the thin-shock case, both numerical and asymptotic solutions are given. Flow pictures illustrating variations in shock position and structure as well as velocity distributions are shown for exponentially decreasing and for harmonic temporal flow disturbances.
Evolution of inertial frequency oscillations
Authors: Smith Ronald
Published: March 2006

Approximate equations are derived for the slow variation in amplitude of free oscillations at the inertial frequency in a slightly stratified ocean. In an ocean of constant depth with horizontally uniform stratification the evolution equation for waves of small vertical mode number can be reduced to a Schrödinger equation, with the increment in Coriolis parameter playing the role of the potential. An exact solution of the Schrödinger equation is presented which demonstrates the transience of inertial oscillations.