bluuebunny/crossref_metadata_2025 huggingface dataset:
Self-similar piston problems with radiative heat transfer
Authors: Helliwell J. B.
Published: March 2006

A differential approximation for the equations of radiative transfer in a grey gas is applied in a study of the effects of thermal radiation upon the classical problem of the compressive action of a plane, cylindrical or spherical piston. The ambient gas ahead of the precursor shock wave is supposed cool and the shock wave transparent, whilst the piston is taken to be neither an emittor nor reflector of radiative energy. It is shown that self-similar flow patterns may arise if the ambient density and piston speed are both non-uniform with variations linked to the absorption coefficient which is assumed to be density and temperature dependent. Detailed flow patterns are obtained in the case of general opacity and also in the transparent limit from which it is deduced that under certain conditions the approximation provided by the latter may be rather dubious.
Velocity and pressure distributions in the aortic valve
Authors: Bellhouse B. J.
Published: March 2006

The distribution of pressure in normal and stenosed aortic valves is investigated experimentally with a rigid-walled model placed in a pulsatile water-tunnel, and the experiments are complemented by a one-dimensional solution of the unsteady inviscid-flow equations. In the normal valve, convectively fed vortices are formed in the aortic sinuses; the vortices aid cusp positioning and the prevention of jet formation during valve closure. Aortic valve stenosis is shown to prevent the generation of vortices, causing the formation of a turbulent jet, with reduction of the pressure difference between the inlets (ostia) of the coronary arteries and the ventricle. This pressure difference is calculated for man resting and exercising, and for various degrees of stenosis.
Stokes flow around a circular cylindrical post confined between two parallel plates
Authors: Lee J. S. , Fung Y. C.
Published: March 2006

A slow viscous flow around a circular cylindrical post confined between two parallel flat plates is analyzed. The solution is given in the form of a series each term of which satisfies the equations of motion and continuity as well as the no-slip condition on the plates. A number of arbitrary constants left open in the series can then be determined according to the no-slip condition at the surface of the cylinder. Numerical results are presented. The series is found to be adequate when the ratio of the distance between the plates and the diameter of the post is not much larger than unity. The coefficient of resistance of the flow decreases rapidly as the sheet-thickness-to-post-diameter ratio increases. It is shown that the series converges rapidly when the thickness ratio is small, so that an approximate solution consisting of the two leading terms of the series, gives a reasonable representation of the velocity field and a good approximation to the flow resistance.
On the trapping of long-period waves round islands
Authors: Longuet-Higgins M. S.
Published: March 2006

The trapping of short-period gravity waves by islands and seamounts has been studied by Chambers (1965) and by Longuet-Higgins (1967). It was shown by the latter that in the absence of rotation, or when the wave frequency σ is large compared with the Coriolis parameter f, these waves cannot be perfectly trapped; some energy must always leak away to infinity. Very long-period oscillations in the presence of a sloping shelf surrounding an island, with σ [Lt ] f, have been studied by Mysak (1967) and Rhines (1967, 1969). Here perfect trapping is possible. However, as pointed out in Longuet-Higgins (1968), the rotation itself exerts a strong trapping effect not only when |σ| [Lt ] f, but also whenever a |σ| < f. It seems not to have been noticed that this effect is capable of trapping waves round an island in an ocean of uniform depth, in the absence of any shelf or sloping region offshore.

The existence of such waves is demonstrated for a circular island in § 1 of the present paper. It is shown that the waves exist only when the azimuthal wave-number n is at least 1. The waves always progress round the island in a clockwise sense in the northern hemisphere. At large distances r from the island, the wave amplitude decays exponentially, but this exponential trapping occurs only if the radius a of the island exceeds the critical value (n(n − 1)gh)½/f. When n = 1, this critical radius is zero, so that in theory the waves exist for any island of non-zero radius.

The application of these results to the ocean is discussed in § 2. Except possibly for baroclinic motions, it appears that only the waves corresponding to n = 1 could exist in fact, and that their frequency would be nearly equal to the inertial frequency f. It is unlikely that f could be regarded as constant over a sufficiently wide area for the model to apply without qualification. Nevertheless, the oscillations may be regarded as the local adjustment of the pressure field to inertial currents in the neighbourhood of the island. It is possible that the peak at about 0·73 c.p.d. in the spectrum of sea-level at Oahu, as found by Miyata & Groves (1968), can be interpreted in this way.
A computational method for the flow through non-uniform gauzes: the general two-dimensional case
Authors: Turner J. T.
Published: March 2006

A computational method is presented for the analysis of two-dimensional flow through a non-uniform gauze. The method, based upon the linearized theory due to Elder (1959), permits solutions for most practical cases to be obtained using relatively simple numerical techniques. Comparison with experimental data shows that the computed solutions are satisfactory provided the restrictions inherent in the linearized theory are observed.
Natural convection above unconfined horizontal surfaces
Authors: Rotem Zeev , Claassen Lutz
Published: March 2006

The paper discusses free convective flows above a horizontal plate, both theoretically and on the basis of experiments which yield quantitative data. The theory is applicable to the semi-infinite plate and is extended to cover the complete range of Prandtl number values including Pr → 0 and Pr → ∞. Experiments were carried out to demonstrate the existence of a laminar boundary layer above a horizontal plate at intermediate Grashof (respectively Rayleigh) numbers, and its extent along the plate. This layer breaks down into large-eddy instability some distance from the leading edge. The value of the critical Rayleigh number for this to occur, obtained experimentally using semi-focusing colour-Schlieren photography is in reasonable qualitative agreement with previously known data (Tritton 1963a,b).
The model of a single infinite disk oscillating about a state of steady rotation
Authors: Jones A. F.
Published: March 2006

The flow produced by a disk performing small oscillations in a rotating system is considered. Results are obtained for the first-order harmonic velocity and the second-order steady velocity. It is then shown that this mathematical model does not always represent an axially bounded fluid in the limit of infinite separation, and to be general one must allow a steady, azimuthal, perturbation velocity with an arbitrary value to exist at infinity.
The radiatively driven discrete acoustic wave
Authors: Cogley A. C.
Published: March 2006

A complete and detailed study of a radiatively driven plane acoustic wave in a non-grey radiating and absorbing gas is carried out on the assumption of local molecular equilibrium. Specifically, the response of the gas in a semi-infinite space to a step input of radiation from a stationary black wall is investigated. The problem is physically interesting because radiative heat addition is the only driving mechanism, and this mechanism is unique and fundamental to the field of radiative gas dynamics. The solution shows that the heat addition gives rise initially to a compression-expansion wave in the gas, with the wave front controlled by radiation. This wave-front disturbance, though caused initially by the direct effect of radiative transfer, eventually outruns the region of appreciable heating near the wall and becomes a modified-classical disturbance that propagates away from the wall at the isentropic speed of sound. The radiative heat addition continues directly to affect the gas near the wall and in this manner drives the modified-classical wave indirectly by causing the formation of an ‘effective gas piston’. The solution thus exhibits a linearized phenomenology corresponding to that observed in the non-linear leading wave associated with the nuclear fireball.
Steady free convection above a point heat source and a horizontal line heat source in a vertical magnetic field
Authors: Soward A. M.
Published: March 2006

An electrically conducting fluid is contained above a horizontal plane. A uniform vertical magnetic field is applied externally and the plane is maintained at a uniform temperature except for a point or a line heat source. Density variations are ignored except where they give rise to buoyancy forces.

(i) The point heat source. Non-linear effects are small sufficiently far from the source. The resulting buoyancy forces interact with the magnetic forces to maintain a radial inflow towards the heat source. This fluid then escapes vertically as a jet, its structure now depending on the additional influence of viscosity. The perturbations of the temperature distribution and the magnetic field due to the motion are obtained. Finally, the effects of these perturbations back on to the fluid velocity are considered. The most striking features of the perturbations are (a) the action of the jet as a line source of heat for the fluid in the outer regions, (b) the large (compared to other perturbations) eddy in the jet.

(ii) The line heat source. The temperature distribution and magnetic field are weakly perturbed only if the thermal and electrical conductivities are sufficiently small. Similar results are obtained, as in (i) above, provided ε (a dimensionless number characterising the strength of thermal convection: see (1.32), (3.24)) is less than ¼. However, even for small ε, the effects of thermal convection cannot be ignored. Hence, superimposed on the jet is an eddy (driven by buoyancy forces) whose flux of fluid increases indefinitely with its height above the plane. When ε > ¼, the results suggest that numerous eddies will be formed.
Stability and dynamics of rotating dielectrophoretic equilibria
Authors: Calvert R. T. , Melcher J. R.
Published: March 2006

In the design of dielectrophoretic liquid orientation and expulsion systems for zero-gravity environments, maximum electromechanical effect of an imposed electric field is obtained by concentrating the field gradients in the neighbourhood of liquid interfaces. In typical configurations, the electric field gradient plays the role of an electromechanical wall, with a stiffness and inertia represented dynamically by electrohydrodynamic surface waves. As an orientation system rotates, the liquid motions are characterized by these waves as they couple to inertial bulk oscillations and centrifugal surface waves resulting from the rotation. A study is made of configurations typified by an equilibrium in which a circular cylindrical column of inviscid liquid undergoes rigid body rotation. The equilibrium is made possible, even though the cylindrical interface is bounded from outside only by its vapour, because the interface is stressed by an essentially tangential axial electric field intensity, with a strong gradient in the radial direction. Dispersion equations are developed for the electrohydrodynamic centrifugal waves of small amplitude. Conditions for incipience of instability and the frequencies of normal modes of oscillation are given. Experimental observations, which demonstrate the destabilizing influence of the rotation and the effect of rotation and electric field intensity on the normal mode frequencies, are in satisfactory agreement with the theory.
A note on shear flow past a sphere
Authors: Cousins R. R.
Published: March 2006

Flow of an incompressible inviscid fluid past a sphere is considered, where the flow upstream consists of a slight shear flow superimposed on a uniform stream. Secondary vorticity, produced by deformation of vortex elements as they are carried past the sphere, is determined by a method due to Lighthill (1956b). Components of vorticity are calculated from a drift function for which expressions were previously available only in part of the flow field. For the region in which no expansion is valid an exact integral expression is obtained to replace the rough numerical approximation used by Lighthill (1956b). The velocity distribution over the upstream part of the sphere is determined numerically using a Biot–-Savart law. These results are required for the calibration of certain forms of Pitot tubes.
A transient flow problem in magnetohydrodynamics
Authors: Soward A. M.
Published: March 2006

A flat plate x = 0, |y| < L is initially at rest in an electrically conducting, inviscid, incompressible fluid permeated by a uniform magnetic field (B0, 0, 0). The plate is impulsively accelerated to a small velocity (— U, 0, 0) which is then kept constant. It is assumed that LV/λ 1 and U/V [Lt ] 1, where V is the Alfven velocity, and λ is the magnetic diffusivity.

Four stages in the development of the flow are distinguished, the last three being:

(ii) L [Lt ] Vt [Lt ] (λ)½. During this stage the initial potential flow is being disturbed by propagation of electric current and vorticity from the plate. The initial discontinuity on the plate has only propagated a small distance away compared to L, but a large distance compared to the length scale of diffusion (λt)½. Exact solutions to the flow are found in the neighbourhood of y = — L and y = 0 (x = 0).

(iii) Vt [Lt ] L [Lt ] (λt)½. The asymptotic behaviour of the electric current and vorticity on the plate are determined showing that a column of fluid of length Vt moves with the plate, aligned to the magnetic field. The transverse diffusion of the current sheets bounding the column accelerates the fluid in layers of thickness O(λt)½.

(iv) (λt)½ [Lt ] L. Unlike stages (ii) and (iii), where the motion is dominated by the propagation of vorticity and electric current as Alfven waves from the plate, diffusive mechanisms completely dominate the motion. ‘Slug’ flow is maintained. The nature of the flow, including the structure of the layers bounding the column are determined for |x| [Lt ] (λt)½.
Correction to Smyrl's results for thin yawed wedges
Authors: Arora N. L.
Published: March 2006

It is the purpose of this note to correct Smyrl's (1963) results for the perturbation pressure in the interaction field produced behind a plane shock which is being diffracted by a supersonically moving thin yawed wedge.
A non-linear equation incorporating damping and dispersion
Authors: Johnson R. S.
Published: March 2006

The steady-state solution of the non-linear equation
\[
h_t + hh_x + h_{xxx} = \delta h_{xx}
\]
with both damping and dispersion is examined in the phase plane. For small damping an averaging technique is used to obtain an oscillatory asymptotic solution. This solution becomes invalid as the period of the oscillation approaches infinity, and is matched to a straightforward expansion solution. The results obtained are compared with a numerical integration of the equation.
On Wilton's ripples: a special case of resonant interactions
Authors: McGoldrick L. F.
Published: March 2006

The phenomenon of second harmonic resonance for capillary-gravity waves is reconsidered here by the asymptotic method of multiple time and space scales. The periodic finite amplitude waves of permanent form found by Wilton in 1915 which correspond to this configuration are shown to be no more than a special case of the more general resonant interaction theory, and owe their existence to a critical choice of initial conditions. It is further suggested that the influence of viscous dissipation will render this solution virtually undetectable in a real liquid.
A note on forward wakes in rotating fluids
Authors: Stewartson K.
Published: March 2006

The two studies by Professor Miles (1970a, b) on the motion of a rotating fluid past a body raise the important question of the determinancy of such flows, by theoretical arguments, which it seems worth while making more precise. Suppose we have a fluid which when undisturbed has a uniform velocityUin the directionOxand a uniform angular velocity Ω aboutOx. It is slightly disturbed, the resulting motion having velocity components (u+U,v, Ωr+w) relative to cylindrical polar axes (x,r, θ), centreOand in whichrmeasures distance fromOx, while θ is the azimuthal angle. Assuming thatu, v, ware sufficiently small for their squares and products to be neglected, and are independent of θ, the equations governing their behaviour reduce to
The effects of a corner on a propagating internal gravity wave
Authors: Robinson R. M.
Published: March 2006

A solution satisfying the usual radiation conditions is found to the problem of an internal wave propagating towards a corner. It is found that, far from the corner, and the characteristic emanating from the corner, the solution is asymptotically equivalent to the solution found by plane wave reflexions from an infinite wall. The present solution shows that, by imposing the radiation condition, a singularity predicted by the ray theory along the corner characteristic is absent. A further singularity in the present solution along the same characteristic is shown to be due to an inability of the usual linear internal wave equations to fully describe the motion. The solution is for restricted corner angles.
The laminar flow of dilute polymer solutions around circular cylinders
Authors: James David F. , Acosta Allan J.
Published: March 2006

This paper describes the measurements of heat transfer and drag for the flow of dilute polymer solutions around very small cylinders. The thermal experiments were carried out at Reynolds numbers less than 50, and the results establish the dependence of the heat transfer on fluid velocity, cylinder diameter, solution concentration, and polymer molecular weight. The drag measurements were conducted with the same type of solutions and in the same Reynolds-number range. To complement the heat-transfer and drag measurements, the flows around a cylinder and through an orifice were examined visually. These flow-visualization studies showed that the streamline pattern with dilute polymer solutions can be significantly different from that with Newtonian fluids because of viscoelastic effects.

An analysis of Rouse's theory of macromolecules shows that for low accelerations a dilute polymer solution behaves mechanically like a Maxwell model. The analysis thereby produces a relaxation time, a single parameter representing the elasticity of the fluid, which can be related to the properties of the solute and solvent. This relaxation time is contained in a new dimensionless group which governs dynamic similarity when induced elastic stresses dominate viscous stresses in the flow around a circular cylinder. The dimensionless group is shown to correlate the thermal data when the heat transfer does not depend on the free stream velocity.
On edge effects in rheometry
Authors: Griffiths D. F. , Walters K.
Published: March 2006

Consideration is given to the influence of edge effects on rheological measurements. To facilitate this, we discuss theoretically the flow generated by the slow steady rotation of a solid of revolution in an elastico-viscous liquid confined by convenient bath surfaces. The relevant linear partial differential equations are solved numerically. The simple problem of a rotating sphere and a concentric spherical container, for which an exact analytic solution is available, is first discussed to justify the method employed, and to indicate the necessary conditions to obtain a given accuracy. The numerical method is then applied to the case of a cone of finite dimensions rotating in a bath of elastico-viscous liquid. The predicted flow is shown to be in good agreement with experimental observations.

Application of the theory to rheogoniometric situations indicates that edge effects are not likely to be as significant as has been conjectured in the past.
The bed configuration of straight sand-bed channels when flow is nearly critical
Authors: Chang H. Y. , Simons D. B.
Published: March 2006

The diagonal pattern of bed form which appears in sand-bed channels when the channel width to depth ratio is great and the flow is nearly critical is discussed from the theoretical viewpoint by using the method of characteristics. Some photographs illustrate the phenomenon.
The development of horizontal boundary layers in stratified flow. Part 2. Diffusive flow
Authors: Redekopp L. G.
Published: March 2006

The boundary layer on the upper surface of a horizontal plane in a diffusive, stratified flow is examined. The analysis shows that density diffusion increases the role of the buoyancy forces and causes a significant change in the properties of the boundary layer when compared to the non-diffusive case. A uniformly valid first approximation for moderate Russell numbers is derived, and the effects of buoyancy and diffusion are evaluated by solving the resulting equations numerically.
Characteristics of turbulent boundary layers at low Reynolds numbers with and without transpiration
Authors: Simpson Roger L.
Published: March 2006

An extension to Coles's (1956) ‘law of the wall–law of the wake’ formulation for incompressible unblown boundary layers with momentum thickness Reynolds numberReθ> 6000. is made forReθ< 6000. It is found that κ = 0·40, the von Kármán constant forReθ> 6000, is replaced by Ω = 0·40 (Reθ/6000)⅛forReθ< 6000. Based upon the data of Simpson (1967) this formulation is extended to injection and undersucked (dθ/dx> 0) flows in ‘law of the wall’ and ‘velocity-defect’ representations. This law of the wall for the logarithmic turbulent region and Reichardt's sublayer variation of εM/ν are used to obtain a continuous expression for εM/ν as a function ofU+,V+w, andReθfor the wall region. This expression is in reasonable agreement with the generated εM/ν blowing results and in less agreement with the unblown and suction results. Eddy viscosity and mixing length results confirm that εM/δ*U∞∝ Ω2andl/δ ∝ Ω for the outer region and that εM/δ*U∞andl/δ are substantially independent of blowing and moderate suction, as also reflected by the velocity defect representation for injection and suction.
The constitutive equation for a dilute emulsion
Authors: Frankel N. A. , Acrivos Andreas
Published: March 2006

A constitutive equation for dilute emulsions is developed by considering the deformations, assumed infinitesimal, of a small droplet freely suspended in a time-dependent shearing flow. This equation is non-linear in the kinematic variables and gives rise to ‘fluid memory’ effects attributable to the droplet surface dynamics. Furthermore, it has the same form as the corresponding expression for a dilute suspension of Hookean elastic spheres (Goddard & Miller 1967), and reduces to a relation previously proposed by Schowalter, Chaffey & Brenner (1968) when time-dependent effects become small.

Numerical solutions are also presented for the case of a small bubble in a steady extensional flow for the purpose of estimating the range of validity of the small deformation analysis. It is shown that, unlike the drag of a bubble which, in creeping motion, is known to be relatively insensitive to its exact shape, the macroscopic stress field in an emulsion is not well described by the present analysis unless the shapes of the deformed bubbles agree closely with those given by the first-order theory. Thus, the present rheological equation should prove of value in a qualitative rather than a quantitative sense.
Vortex growth in jets
Authors: Beavers Gordon S. , Wilson Theodore A.
Published: March 2006

Observations are reported on the growth of vortices in the vortex sheets bounding the jet emerging from a sharp-edged two-dimensional slit and from a sharp-edged circular orifice. A regular periodic flow is observed near the orifice for both configurations when the Reynolds number of the jet lies between about 500 and 3000. The two-dimensional jet produces a symmetric pattern of vortex pairs with a Strouhal number of 0·43. Vortex rings are formed in the circular jet with a Strouhal number of 0·63. Computer experiments show that a growing pair of vortices in two parallel vortex sheets produces a symmetric pattern of vortices upstream from the original disturbance.
Axial and transverse Stokes flow past slender axisymmetric bodies
Authors: Tillett J. P. K.
Published: March 2006

This paper deals with Stokes flow due to a stationary axially symmetric slender body in a uniform stream, which may be either parallel or perpendicular to the axis of the body. The effect of the body is represented by distributions of singularities along a segment of its axis of symmetry. Systems of linear integral equations for these distributions are obtained, and the first few terms of uniformly valid (in the Stokes region) asymptotic expansions in the slenderness ratio are discussed. The leading terms yield the expected result that the drag on the body in a transverse stream is double that in an axial stream. The second approximation to the ratio of these two drags is also independent of the body shape.
The non-linear refraction of shock waves by upstream disturbances in steady supersonic flow
Authors: Weinbaum Sheldon , Goldburg Arnold
Published: March 2006

The general problem studied is the propagation of an oblique shock wave through a two-dimensional, steady, non-uniform oncoming flow. A higher-order theory is developed to treat the refraction of the incident oblique shock wave by irrotational or rotational disturbances of arbitrary amplitude provided the flow is supersonic behind the shock. A unique feature of the analysis is the formulation of the flow equations on the downstream side of the shock wave. It is shown that the cumulative effect of the downstream wave interactions on the propagation of the shock wave can be accounted for exactly by a single parameter Φ, the local ratio of the pressure gradients along the Mach wave characteristic directions at the rear of the shock front. The general shock refraction problem is then reduced to a single non-linear differential equation for the local shock turning angle θ as a function of upstream conditions and an unknown wave interaction parameter Φ. To lowest order in the expansion variable θΦ, this equation is equivalent to Whitham's (1958) approximate characteristic rule for the propagation of shock waves in non-uniform flow. While some further insight into the accuracy of Whitham's rule does emerge, the theory is not a selfcontained rational approach, since some knowledge of the wave interaction parameter Φ must be assumed. Analytical and numerical solutions to the basic shock refraction relation are presented for a broad range of flows in which the principal interaction occurs with disturbances generated upstream of the shock. These solutions include the passage of a weak oblique shock wave through: a supersonic shear layer, a converging or diverging flow, a pure pressure disturbance, Prandtl–-Meyer expansions of the same and opposite family, an isentropic non-simple wave region, and a constant pressure rotational flow. The comparison between analytic and numerical results is very satisfactory.
Shock propagation into inhomogeneous media
Authors: Strachan J. D. , Huni J. P. , Ahlborn B.
Published: March 2006

An analytic relation is derived for the shock front velocity as a function of the initial parameters (pressure, density, and particle velocity) in a continuous, in-homogeneous medium. This relation was verified experimentally by using it to predict the propagation of a shock wave through a known rarefaction wave.
Hypersonic viscous interaction on curved surfaces
Authors: Stollery J. L.
Published: March 2006

Cheng's analysis of strong viscous interaction between a laminar boundary layer growing over a flat plate and the external hypersonic flow field is extended to cover curved surfaces. It is demonstrated that the solutions for some concave surfaces are oscillatory and quantitatively unrealistic. The reason for this behaviour is that the Busemann term in the Newton–Busemann pressure law used in Cheng's analysis over-corrects for centrifugal effects. The removal of the Busemann term or the substitution of the tangent-wedge pressure law results in an alternative analysis which can cover both strong and weak viscous interaction over a wide variety of two-dimensional shapes. A number of examples are included together with comparative experimental data.
Global stability of spiral flow
Authors: Joseph D. D. , Munson B. R.
Published: March 2006

Energy and linear limits are calculated for the Poiseuille–Couette spiral motion between concentric cylinders which rotate rigidly and rotate and slide relative to one another. The addition of solid rotation can bring the linear limit down to the energy limit with coincidence achieved in the limit of infinitely fast rotation. If the differential rotation is also added, the solid rotation rate need be only finite to achieve near coincidence. Sufficient conditions for non-existence of sub-linear instability are derived. The basic spiral character of the instability is analysed and the results compared with the experiments of Ludwieg (1964).
On fluid motions induced by an electric current source
Authors: Sozou C.
Published: March 2006

In this paper we consider the flow field induced in an incompressible viscous conducting fluid, occupying the interior of a right circular cone, by an electriccurrent source situated at the vertex of the cone. We assume that the velocity field is small and its effect on the electromagnetic field is negligible. A similarity solution is obtained for the non-linear problem. This solution is an adaptation of Slezkin's solution for the momentum transfer through a viscous jet and, apart from the numerical solution of a Riccati type of equation, is exact. In particular, we investigate the case when the half angle of the cone is ½π and the fluid occupies the whole space on one side of an infinite plane. We also consider the corresponding inviscid flow problem that was recently investigated by another author and suggest that the solution obtained is not physically realistic.
A note on turbulent shear-layer reattachment downstream of a backward-facing step in confined supersonic two-dimensional flow
Authors: Mukerjee T. , Farshi A. , Martin B. W.
Published: March 2006

The reattachment of a supersonic jet with a turbulent separating boundary layer abruptly expanding into a two-dimensional parallel diffuser has been experimentally investigated using a surface-flow technique. The reattachment criterion proposed by Mukerjee & Martin (1969) for axisymmetric confined and unconfined flows is found to correlate equally well similar two-dimensional flow measurements in terms of the free-stream Mach number after separation.
Potential flow of segmental jet deflectors
Authors: Chang H. Y. , Conly J. F.
Published: March 2006

A solution is developed for the deflexion of an inviscid, incompressible, twodimensional jet by a series of segments of arbitrary number, lengths, and angles. The Schwarz–Christoffel transformation and free-streamline theory are used. Results are calculated for a number of configurations, using an IBM 360 computer. Excellent comparison is found with several previous calculations for special cases.
The diffraction of tides by a narrow channel
Authors: Buchwald V. T.
Published: March 2006

A Green's function for a semi-infinite rotating ocean of uniform depth is obtained, and the resulting near and far fields are estimated asymptotically.

Given a tide of uniform height at the mouth of a narrow channel on a semiinfinite ocean, the Green's function is used to calculate the diffracted Kelvin and Poincaré waves propagating up the channel and into the ocean.
Entry flow in a channel. Part 2
Authors: Wilson S. D. R.
Published: March 2006

This paper complements an earlier paper by Van Dyke which has appeared under the same title. The problem of channel entry flow is re-examined and the early work is found to be formally incorrect. The techniques of modern boundary-layer theory are used to examine the region near the entrance. Various inlet conditions are considered and it is found that the usual condition of uniform entry velocity causes the intrusion of fractional powers of the Reynolds number into the expansions. The most satisfactory model is that of uniform flow into an infinite cascade of parallel plates.

The non-uniformity of the expansions at large downstream distances was studied in Van Dyke's paper and is not dealt with here, except to show that it may be treated separately.
Turbulent air flow over the dominant component of wind-generated water waves
Authors: Chang P. C. , Plate E. J. , Hidy G. M.
Published: March 2006

This paper presents a laboratory study of the dynamic properties of air flow over small wind-generated water waves. On the basis of measurements of mean velocity profiles, turbulent intensity profiles and energy spectra, the detailed structure of turbulent wind immediately above and between the crests of progressive water waves has been examined.

The velocity sensor (a hot-wire anemometer) was fastened to a self-adjusting positioner to measure instantaneous air velocities at a fixed distance from a moving water surface. The waves had a dominant frequency, 2·4 Hz, and a ratio of wave celerity and air friction velocity close to one. With the aid of a digital computer, the desired parameters of air flow were obtained by a statistical technique which was developed to sample and average simultaneous recordings of water surface displacements and instantaneous air velocities.

The results of the wind field measurements over representative waves indicate that, on the average, the air flow separates from the wavy water surface just behind crests, and reattaches somewhere on the windward face of the next wave. The measured turbulent quantities consistently show the characteristics of separated air flow. The separation phenomenon suggests that, without some modification, the Benjamin-Miles shearing flow mechanism is inapplicable to the growth of fully-developed small water waves, at least when the ratio of the phase speed to air friction velocity is of order unity. The observed flow configuration tends to support the separation mechanism of energy transfer originally outlined by Jeffreys and later explored further by Stewart and Deardorff.

Mean properties of the turbulent air flow referred to the mean water level were obtained by continuous sampling of the air flow over many waves with a sensing probe, either at a fixed distance from the mean water level (fixed probe measurement) or at a constant distance from the moving water surface (moving probe measurement). It was found that for continuously averaged measurements, the fixed probe yielded results which deviate less from the local mean than the moving probe results. This holds for the mean velocity distributions and especially for the turbulent quantities.
Instability of a thermal boundary layer in a constant electric field
Authors: Turnbull Robert J.
Published: March 2006

The thermal boundary layer near a heated vertical plate in a poorly conducting liquid is subject to a horizontal d.c. electric field. If the electric field is strong enough, the boundary layer becomes unstable. In this paper a theory is developed to predict the onset of this instability. Experiments measuring the threshold voltage for instability are compared with the theoretical predictions. Other experiments are reported which determine the effect of this instability on the heat transferred from the heated plate.
The breakdown of electrical insulation in a plane layer of insulating fluid by electrocapillary instability
Authors: Michael D. H. , O'Neill M. E. , Zuercher J. C.
Published: March 2006

A theoretical and experimental study is made of the failure of electrical insulation in a layer of dielectric fluid filling a circular hole in a horizontal solid dielectric sheet. A potential difference is applied between conducting fluids which bound the fluid and solid dielectric layer above and below. It is observed that a critical potential difference is reached at which the fluid dielectric becomes statically unstable under the action of surface tension and normal electrical stresses at its interfaces. When this potential is reached the dielectric fluid insulation fails.

The critical potential difference is calculated by both an approximate and an exact theory. The approximate theory ignores the changes in the electrostatic field within the solid dielectric by allowing a charge distribution at the curved surface of the hole. Comparison with the results of an exact theory shows that such an approximation introduces only small errors in the calculated points of transition to instability.

It is shown that failure may take the form of a symmetric (sausage) mode of displacement, or an antisymmetric (kink) mode, depending on whether the radius of the hole is greater or less than approximately the depth of the layer respectively. The two forms of failure were indicated in the experiments, and the observed critical voltages are in good agreement with those predicted by the theory.
Low Reynolds number oscillatory flow through a hole in a wall
Authors: de Mestre N. J. , Guiney D. C.
Published: March 2006

For a viscous incompressible fluid the low Reynolds number description of the flow generated by a three-dimensional point source of oscillating strength situated on a wall is approximately quasi-steady in the neighbourhood of the singularity. This quasi-steady solution contains a number of unacceptable features, the principal one being that it is not a uniformly valid approximation within a small region surrounding the source point. In addition to this the vorticity in this region is predicted to be zero everywhere on the wall except at the singular point where it is infinite, which does not seem to be a physically reasonable distribution. When account is taken of the finite radius of the hole through which the fluid is driven and the finite width of the wall, the above difficulties are resolved yielding results that are quite realistic and informative.
The determination of the rate of dissipation in turbulent pipe flow
Authors: Lawn C. J.
Published: March 2006

Measurements of turbulence energy diffusion and the spectral distributions of stress components in the core of turbulent pipe flow are presented. The results tend to confirm the proposal of Bradshaw (1967a, b) that an inertial subrange in the spectra can exist at quite modest laboratory Reynolds numbers. They also illuminate the inconsistencies in Laufer's (1954) measurements of dissipation and suggest that the fitting of a −5/3 power law to the spectra may well provide the most accurate method of determining dissipation forRe[gsim ] 105.
Upstream boundary-layer separation in stratified flow
Authors: Miles John W.
Published: March 2006

Stratified, inviscid channel flow over a thin barrier or into an abrupt contraction is considered on the hypotheses that the upstream dynamic pressure and density gradient are constant (Long's model) for those parametric régimes in which the hypotheses are tenable for finite-amplitude disturbances, namelyk< 2 for the barrier andk< 1 for the contraction, wherek=NH/πUis an inverse Froude number based on the Vaisälä frequencyN, the channel heightH, and the upstream velocityU. Reverse flow in the neighbourhood of the forward stagnation point, which implies the formation of an upstream separation bubble, is found for certain critical ranges ofk. The maximum barrier height for which the dominant lee-wave mode can exist without reversed flow either upstream or downstream of the barrier is 0·34H. The limiting case of a half space is considered briefly, and forward separation is found for κ =Nh/U> κs, where κs= 2·05 for a thin barrier and 1·8 for a semi-circular barrier. The corresponding values for reverse flow in the lee-wave field are κc= 1·73 and 1·3, respectively.
On an invariant property of water waves
Authors: Benjamin T. Brooke , Mahony J. J.
Published: March 2006

The discussion concerns free wave motions generated from rest in a finite region of an ocean of heavy liquid lying on a horizontal plane. It is shown that the horizontal fist moment of the free-surface displacement varies linearly with time. Hence, if the total volume displaced is not zero and therefore the centroid of the displacement is definable, the centroid travels with a constant horizontal velocity as the wave motion evolves. This conclusion holds exactly for waves of any amplitude and even remains applicable subsequent to the breaking of waves.
On the initial-value problem in the kinetic theory of gases
Authors: Baum Howard R.
Published: March 2006

The relaxation of an initially non-uniform gas to equilibrium is studied within the framework of the kinetic theory of gases. The macroscopic gas properties are taken to depend on one spatial dimension as well as the time. The amplitude of the non-uniformity is assumed to be small with a length scale large compared with the mean free path, and the Krook model of the Boltzmann collision integral is employed.

By applying multi-time scale perturbation methods to this reduced problem, uniformly valid analytical solutions for the macroscopic velocity, density and temperature are obtained. The macroscopic equations appropriate to each stage of the relaxation process are obtained in a straightforward and unambiguous manner. The distribution function obtained is shown to be a re-expansion of the Chapman–Enskog solution of the Krook equation, with additional terms accounting for the relaxation of the initial conditions to a near equilibrium form. The results indicate that the uniformly valid frst approximation to the macroscopic velocity, density and temperature can be obtained from the Navier–Stokes equations, but that no purely macroscopic set of equations will suffice for the determination of higher approximations.
Effects of plane progressive irrotational waves on thermal boundary layers
Authors: Witting James
Published: March 2006

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.

The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.

Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.
On hydromagnetic oscillations in a rotating cavity
Authors: Gans Roger F.
Published: March 2006

Time-dependent hydromagnetic phenomena in a rotating spherical cavity are investigated in the framework of an interior boundary-layer expansion. The interior problem is shown to contain waves whose frequencies are of order ω, Aω and A2ω, where ω is the rotation rate of the cavity and A2 = B2/4πρωA2 [Lt ] 1 is the Alfvén number. B is an imposed magnetic field, ρ the fluid density and R the radius of the cavity. The first type of wave is a modification of the hydro-dynamic inertial wave, the second is a pseudo-geostrophic wave and is involved in spin-up, and the third is related to the MAC waves of Braginskiy (1967).

It is shown that the MAC waves must satisfy more than the usual normal boundary conditions and that reference must be made to the boundary-layer solution to resolve the ambiguity regarding which conditions are to be taken. For normal liquid metals of small magnetic Prandtl number the MAC waves must satisfy full magnetic boundary conditions; only the no-slip conditions may be deferred to the boundary layers.

The boundary-layer structure is investigated in detail to display the interactions between applied field, viscosity, electrical conductivity, frequency and latitude. The decay of the pseudo-geostrophic modes, essentially the spin-up problem, is discussed for a non-axisymmetric constraining field and non-zero container conductivity. Three regimes exist, depending on container conductivity.
Rotating flow over a step
Authors: Boyer Don L.
Published: March 2006

The flow of a rotating homogeneous incompressible fluid over a step is investigated. In the physical system considered the rotation axis is vertical and the step, which is assumed to be infinitely long, is located on a horizontal plane surface. Upstream of the step the fluid is in a uniform free stream motion at an angle α to a line perpendicular to the step axis. The analysis is restricted by the following: E [Lt ] 1, Ro ∼ E½, h/D ∼ E½, H/D ∼ E0, and cos α ∼ E0 where Ro and E are the Rossby and Ekman numbers and h/D and H/D are the step height to step width and water depth to step width ratios respectively. The flow field is shown to consist of interior geostrophic regions, Ekman layers on the horizontal surfaces and vertical shear layers located in the vicinity of vertical planes defined by the edges of the step. In the vertical layers there is a balance between the inertial, Coriolis, and pressure terms in the momentum equations while the effects of viscosity are found to be negligible. Downstream of the step the streamlines are shifted to the right (positive or Northern Hemisphere rotation) of their upstream locations by a distance of S = 2½(h/D) E−½ cos α. Experiments are presented which are in good agreement with the theory advanced.
Viscous rotational stagnation-point flow
Authors: Hersh Alan S.
Published: March 2006

The investigation by Hayes (1964a) of the behaviour of a constant-density inviscid rotational flow in the neighbourhood of a stagnation point on a plane wall has been extended to include the effects of viscosity. The principal effect is the manner in which the singularity in vorticity discovered by Hayes is removed. A solution of only the boundary-layer equatiosn indicates the vorticity decays algebraically from the wall. Application of the method of matched asymptotic expansions, however, shows that the difference between boundary layer and outer vorticity, when carried out to second order in the outer flow, does not contribute to an algebraic decay. These results suggest that an infinite number of higher-order outer terms are generated which match the algebraic terms thereby yielding the conventional exponential decay. Numerical results are presented which also support this conclusion. The main contribution of the wall shear stress in the immediate neighbourhood of the stagnation point is shown to come from the external lateral vorticity.