bluuebunny/crossref_metadata_2025_split huggingface dataset:
Internal waves in a wedge-shaped region
Authors: Hurley D. G. 
Published: March 2006

The Green's functions are found for a line source of internal waves in a wedge of stratified fluid of constant Brunt–Väisälä frequency, and are used to discuss the diffraction of internal waves by a wedge in all cases when the vertex angle of the wedge of fluid exceeds the acute angle between a characteristic and the horizontal. Robinson's (1970) results are confirmed and extended.It is found that the diffracted waves are as important as the incident and reflected ones at all points that lie within a quarter-wavelength or so of either characteristic that passes through the apex. Also, in cases when all the reflected waves are inclined forwards, the diffracted waves lead to a positive backscatter of energy. When the vertex angle of the fluid wedge is less than the characteristic angle, the diffraction problem appears to be ill-posed, and, instead, the motion due to a vibrating body in the wedge of fluid is considered.A general conclusion is that the so-called ray theory for internal waves, in which the incident and reflected waves alone are considered, has similar limitations to the geometrical theory of optics. Both theories involve the assumption that the typical dimensions in the problem are large compared to the wavelength.
Experimental investigations of the stability of channel flows. Part 1. Flow of a single liquid in a rectangular channel
Authors: Kao Timothy W. , Park C. 
Published: March 2006

The stability of the laminar flow in a rectangular channel with aspect ratio 1:8 was investigated experimentally, with and without artificial excitation. The critical Reynolds number based on the hydraulic diameter and the average velocity was found to be 2600. Behaviour of damped and growing waves, using artificial excitation, was examined in detail. In particular the progress of growing disturbances was followed. Breaking was found to be the ultimate fate of a growing wave. Spectra of growing and damped waves were also obtained. Measurements were made for wavelengths, wave speeds and amplification or damping rates. The neutral stability boundary in the αr, R plane was determined. In the damped region, comparison of several aspects of the behaviour of the measured disturbances with the plane Poiseuille theory for spatial decay yielded good agreement.Three-dimensionality and non-linear subcritical instability were briefly examined. Neutral subcritical waves at low Reynolds numbers appeared possible when the exciter amplitude was quadrupled.The possible bearings of the present study on the stability of plane Poiseuille flow are suggested.
Rheometrical flow systems Part 3. Flow between rotating eccentric cylinders
Authors: Abbott T. N. G. , Walters K. 
Published: March 2006

We give further consideration to flow situations which are steady in the sense that ∂/∂t ≡ 0 but for which individual fluid elements are subjected to a small sinusoidal deformation. The particular situation studied involves the flow between eccentric circular cylinders which rotate about their axes with the same angular velocity Ω. The eccentricity is assumed to be small. It is shown that measurements of the force on the inner cylinder can be used to determine the complex dynamic viscosity of an elastico-viscous liquid.The theory provides the necessary mathematical background for the operation of a new commercial rheometer. Consideration is given to the possibility of ‘on-line’ use of such an instrument for control purposes.
Statistical properties of turbulent density fluctuations
Authors: Wilson L. N. , Damkevala R. J. 
Published: March 2006

The cross-correlation technique has been used to obtain statistical properties of scalar density fluctuations. Two schlieren instruments with their optical beams intersecting in the turbulent field each give a signal proportional to the density gradient in the flow direction but integrated along the beam path. Cross-correlation of the two signals gives an area integral of the density-gradient covariance. For locally isotropic conditions the area integration can exactly compensate for the two gradients giving a result proportional to the local mean-square density fluctuation at the beam intersection point.Experiments performed in the shear layer of a subsonic jet show results which tend to verify the principles of crossed-schlieren measurement. Intensity levels are close to those predicted assuming density fluctuations are related isentropically to local, incompressible pressure fluctuations.
The break-up of axisymmetric liquid sheets
Authors: Huang J. C. P. 
Published: March 2006

The break-up mechanism of axisymmetric liquid sheets formed by the impingement of two co-axial jets has been examined. Three break-up regimes in the Weber number range from 100 to 3 × 104 are reported. In the first break-up regime, droplets are formed through successive mergings of liquid beads along the nearly circular periphery of the sheet. The formation of beads is caused by Rayleigh instability. In the transition regime, Taylor's cardioid wave pattern prevails in the first half of this regime, while the sheet begins to flap in the second half.In the second break-up regime, antisymmetric waves on the sheet grow radially. A semi-empirical equation has been deduced to predict the break-up radius of the sheet. The motion of an axisymmetric vibrating membrane with radially decreasing thickness has been studied to include Helmholtz instability as an analogue of the wave motion of the expanding circular sheet. A distorted progressive wave equation has been solved by the WKBJ method to indicate the effect of cylindrical geometry. The calculated wave speed agrees fairly well with experimental data at low Weber numbers.
Channel flow induced by a travelling thermal wave
Authors: Chow Chuen-Yen 
Published: March 2006

Experiments conducted elsewhere show that a mean fluid motion can be induced in a channel by a travelling thermal wave. An analysis is carried out, linearized under the assumption that the induced motion is slower than the speed of the heat source. The expression for the mean motion is obtained for any Prandtl number and circular frequency of the thermal wave, to complete the results presented by Davey (1967) for low and high frequency ranges.In the problem of the flow between two parallel plates, it is found that with a temperature profile symmetric about the centre of the channel, the induced flow does not exert a net shear force on either plate, while with a non-symmetric one, the plates are subjected to equal and opposite forces.For the problem that the upper surface of the fluid is free and thermally insulated, an approximated result can be deduced from that of the previous problem by a simple transformation. It should agree with the result of Davey, obtained through a more elaborate procedure, except in the low frequency range when the surface deformation becomes important.In agreement with the experiments, our analysis indicates that the induced mean motion is always in a direction opposite to that of the thermal wave, and its magnitude increases rapidly with decreasing Prandtl number. According to the theory, some of the previous experiments were not conducted under the optimum situations, and improved experimental conditions are suggested.
Contrails and aircraft downwash
Authors: Scorer R. S. , Davenport L. J. 
Published: March 2006

Aircraft downwash consists initially of a vortex pair descending with its accompanying fluid through the atmosphere. Condensation trails are formed in exhaust emitted into the accompanying fluid and the shapes of them and their evolution depend on the positions of the engines in relation to the wing tip vortices.The atmosphere is stably stratified and so the descending accompanying fluid acquires upward buoyancy. Consequently vorticity is generated at the outside of the accompanying fluid and the flow pattern in the vortex pair is altered so as to produce detrainment of its exterior part. So long as any air which is a mixture of accompanying fluid and exterior air is detrained, the vortices remain stable, but the width of the pair decreases and its downward velocity increases with time as a result of the buoyancy. Eventually the upper stagnation point in the motion relative to the vortices begins to move upwards relative to the vortices so that some mixed fluid is entrained into the circulation and the vortices immediately become unstable, mixing occurs, the pressure in the core rises, and any vortex core trails that may exist appear to burst.The motion produces downward-thrust blobs in trails from centrally placed engines, which correspond to the holes sometimes seen in cloud when distrails are formed.
Large amplitude waves in stratified media: acoustic pulses
Authors: Varley E. , Cumberbatch E. 
Published: March 2006

A general theory is presented which describes disturbances generated by large amplitude, high frequency pulses in stratified media. The theory is used to discuss large amplitude, but shockless, acoustic pulses propagating under the influence of a constant gravity force into an atmosphere which need not be in thermal equilibrium before their arrival.The modulating influences of pressure and temperature stratification on the amplitudes of such pulses as they move towards or away from earth are described in detail.The paper generalizes techniques already established by Whitham (1956) so that they are applicable to disturbances of any amplitude.
Sound generation by hydrodynamic sources near a cavitated line vortex
Authors: Williams J. E. Ffowcs , O'shea S. 
Published: March 2006

The paper examines the scattering properties of a cavitated line vortex when excited by line and point sources of sound. It is found that the vortex resonances discovered by Kelvin for incompressible flow are essentially unmodified by fluid compressibility, and that many of the resonant modes radiate energy to infinity. Those resonant modes dominate the vortex response, their amplitude growing algebraically with time in a driven instability of the model flow.The off resonance response is dependent on the value of a normalized frequency parameter (ω/Ω)2|ln ka|. Ω denotes the angular velocity of the steady vortex flow, k the acoustic wave-number, and a the cavity radius. Even off resonance the cavity is an extremely efficient wave scatterer, the scattering efficiency increasing with source order. For example, the scattered energy of a point quadrupole is shown to exceed that of the direct field by a factor of 108 for the typical underwater flow Mach number of 10−2.
Cholesteric energies
Authors: Jenkins James T. 
Published: March 2006

Repeated observations of a uniformly twisted director field in cholesteric liquid crystals are used to motivate an expression for a free energy which is obtained as an expansion about this state. Terms quadratic in the director perturbation and the gradients of this perturbation are retained. Utilizing invariance arguments, it is possible to obtain significant simplification of the coefficients which appear in the expansion. A properly invariant form of the free energy is produced which agrees with the expansion for small excursions about a twisted state, and which assigns arbitrary values to the non-vanishing coefficients.The consequences of requiring that a free energy achieve a minimum at a twisted state are explored. A commonly used form of the free energy for cholesteric liquid crystals is seen to be rather severely restricted by this requirement. An alternative to this form is proposed which is a special case of the free energy previously produced. The particular form suggested attains a unique absolute minimum at a characteristic uniform twist.
Boundary-layer separation on a sphere in a rotating flow
Authors: Miles John W. 
Published: March 2006

The velocity just outside the boundary layer and upstream of the separation ring on a sphere moving along the axis of a slightly viscous, rotating fluid is calculated through a least-squares approximation on the hypothesis of no upstream influence. A reverse flow is found in the neighbourhood of the forward stagnation point fork≡ 2Ωa/U>k= 2·20 (Ω = angular velocity of fluid,U= translational velocity of sphere,a= radius of sphere) and is accompanied by a forwardseparation bubble, such as that observed by Maxworthy (1970) fork[gsim ] 1. Rotation also induces a downstream shift of the peak velocity; the estimated shift of the separation ring in the absence of forward separation increases withkto a maximum of 24°, in qualitative agreement with Maxworthy's observations.The least-squares formulation is compared with that given by Stewartson (1958) for unseparated flow (Stewartson did not consider separation). Both formulations require truncation of an infinite set of simultaneous equations, but Stewartson's formulation yields a non-positive-definite matrix that may exhibit spurious singularities. The least-squares formulation yields a positive-definite matrix, albeit at the expense of slower convergence for fixedk, and is especially well suited for automatic computation.Anad hocincorporation of a cylindrical wave of strength [Uscr ], such that the maximum upstream axial velocity is [Uscr ]U, is considered in an appendix. It is found thatkdecreases monotonically from 2·2 to 0 as [Uscr ] increases from 0 to 1.
Wind-generated waves in thin liquid films with soluble contaminant
Authors: Smith F. I. P. , Craik Alex D. D. 
Published: March 2006

Craik (1968) has previously examined the stability of horizontal liquid films when an air stream flows over the liquid surface and when the surface is contaminated by an insoluble surface-active agent. The present theoretical work extends this investigation to examine the role of soluble surface-active agents for cases where the liquid Reynolds number is small. This role is found to be a rather complex one which, under suitable conditions, may be either stabilizing or destabilizing.Related experimental work is described which yields results in qualitative agreement with the theoretical analysis.
On stationary and travelling vortex breakdowns
Authors: Sarpkaya Turgut 
Published: March 2006

This paper describes some experiments in swirling flows in a diverging cylindrical tube in which various types of vortex breakdowns were observed.In one set of experiments, the position of the breakdown, axial component of the velocity of the vortex core, swirl angle distribution ahead of the breakdown, and the pressure distribution along the tube were determined for various flow rates and for various values of circulation imparted to the fluid (water). Basically, three types of vortex breakdown were observed, viz. mild (double helix) breakdown, spiral breakdown (followed by turbulent mixing), and axisymmetric breakdown (followed by a thicker vortex core, then a spiral breakdown, and finally by turbulent mixing). The type and the location of the stationary breakdowns were found to be dependent, for the particular vortex tube used, upon the Reynolds and circulation numbers of the flow. In a spiral breakdown, the vortex core filament maintained the same sense of rotation as the upstream fluid elements. In an axisymmetric breakdown, the bubble included an inclined vortex-ring whose axis gyrated about the axis of the tube.In a second set of experiments, the response of the abrupt structural change along the axis of flow to gradual and abrupt changes in the upstream and downstream flow conditions was examined. The axisymmetric breakdown responded in a manner analogous to the hydraulic jump in open-channel flow before if reached a new stationary position along the axis of the tube.The observations reported and the evidence presented herein revealed that the axisymmetric breakdown is a finite transition between two sequent states of flow as proposed by Benjamin (1962, 1965, 1967) on theoretical grounds.
Laminar momentum jets in a stratified fluid
Authors: List E. J. 
Published: March 2006

Solutions are presented for creeping flows induced by two-and three-dimensional horizontal and vertical momentum jets in a linearly stratified unbounded diffusive viscous fluid. These linear problems are solved by replacing the momentum jet by a body force singularity represented by delta functions and solving the partial differential equations of motion by use of multi-dimensional Fourier transforms. The integral representations for the physical variables are evaluated by a combination of residue theory and numerical integration.The solutions for vertical jets show the jet to be trapped within a layer of finite thickness and systems of rotors to be induced. The horizontal two-dimensional jet solution shows return flows above and below the jet and a pair of rotors. The three-dimensional horizontal jet has no return flow at finite distance and the diffusive contribution is found to be almost negligible in most situations, the primary character of the horizontal flows being given by the non-diffusive solution. Stokes's paradox is found to be non-existent in a density-stratified fluid.
The effect of a depth discontinuity on Kelvin wave diffraction
Authors: Pinsent H. G. 
Published: March 2006

The linearized problem of Kelvin wave diffraction at the sharp edge of a thin semi-infinite barrier on a rotating earth is considered in the case when a discontinuity in depth stems from the edge in a direction parallel to the barrier. The solution in closed form is obtained using the Wiener-Hopf technique.It is shown that the direct effect of the depth discontinuity is always to divert additional energy away from the barrier, in the form of outgoing cylindrical waves if the period is small, and provided conditions are suitable as double Kelvin waves if the period is sufficiently long. Results suggest that Kelvin waves which are the most persistent in following an irregular coastline bounding a sea of abruptly varying depth are of intermediate period.
Boundary-value problems in the kinetic theory of gases. Part 2. Thermal creep
Authors: Williams M. M. R. 
Published: March 2006

The effect of a temperature gradient in a gas inclined at an angle to a boundary wall has been investigated. For an infinite half-space of gas it is found that, in addition to the conventional temperature slip problem, the component of the temperature gradient parallel to the wall induces a net mass flow known as thermal creep. We show that the temperature slip and thermal creep effects can be decoupled and treated quite separately.Expressions are obtained for the creep velocity and heat flux, both far from and at the boundary; it is noted that thermal creep tends to reduce the effective thermal conductivity of the medium.
A numerical study of the Bénard cell
Authors: Cabelli André , de Vahl Davis G. 
Published: March 2006

When a layer of liquid is heated from below at a rate which exceeds a certain critical value, a two- or three-dimensional motion is generated. This motion arises from the action of buoyancy and surface tension forces, the latter being due to variations in the temperature of the liquid surface.The two-dimensional form of the flow has been studied by a numerical method. It consists of a series of rolls, rotating alternately clockwise and anticlockwise, which are shown to be symmetrical about the dividing streamlines. As well as a detailed description of the motion and temperature of the liquid, and of the effects on these characteristics of variations in the Rayleigh, Marangoni, Prandtl and Biot numbers, a study has been made of the conditions under which the motion first starts, the wavelength of the rolls and the rate of heat transfer across the liquid layer.
An experimental investigation of pulsating turbulent water flow in a tube
Authors: Gerrard J. H. 
Published: March 2006

Experiments were made on a pulsating water flow at a mean flow Reynolds number of 3770 in a cylindrical tube of diameter 3·81 cm. Pulsations were produced by a piston oscillating in simple harmonic motion with a period of 12 s. Turbulence was made visible by means of a sheet of dye produced by electrolysis from a fine wire stretched across a diameter. The sheet of dye is contorted by the turbulent eddies, and ciné-photography was used to find the velocity of convection which was shown to be the flow speed except in certain circumstances which are discussed. By subtracting the mean flow velocity profile the profile of the component of the motion oscillating at the imposed frequency was determined.The Reynolds number of these experiments lies in the turbulent transition range, so that large effects of laminarization are observed. In the turbulent phase, the velocity profile was found to possess a central plateau as does the laminar oscillating profile. The level and radial extent of this were little different from the laminar ones. Near to the wall, the turbulent oscillating profile is well represented by the mean velocity power law relationship, u/U ∝ (y/a)1/n. In the laminarized phase, the turbulent intensity is considerably reduced at this Reynolds number. The velocity profile for the whole flow (mean plus oscillating) relaxes towards the laminar profile. Laminarization contributes appreciably to the oscillating component.Extrapolation of the results to higher Reynolds numbers and different frequencies of oscillation is suggested.
Flow and pressure drop in systems of repeatedly branching tubes
Authors: Pedley T. J. , Schroter R. C. , Sudlow M. F. 
Published: March 2006

The airways of the lung form a rapidly diverging system of branched tubes, and any discussion of their mechanics requires an understanding of the effects of the bifurcations on the flow downstream of them. Experiments have been carried out in models containing up to two generations of symmetrical junctions with fixed branching angle and diameter ratio, typical of the human lung. Flow visualization studies and velocity measurements in the daughter tubes of the first junction verified that secondary motions are set up, with peak axial velocities just outside the boundary layer on the inner wall of the junction, and that they decay slowly downstream. Axial velocity profiles were measured downstream of all junctions at a range of Reynolds numbers for which the flow was laminar.In each case these velocity profiles were used to estimate the viscous dissipation in the daughter tubes, so that the mean pressure drop associated with each junction and its daughter tubes could be inferred. The dependence of the dissipation on the dimensional variables is expected to be the same as in the early part of a simple entrance region, because most of the dissipation will occur in the boundary layers. This is supported by the experimental results, and the ratio Z of the dissipation in a tube downstream of a bifurcation to the dissipation which would exist in the same tube if Poiseuille flow were present is given by
\[
Z = (C/4\surd{2})(Re\,d/L)^{\frac{1}{2}},
\]
where L and d are the length and diameter of the tube, Re is the Reynolds number in it, and the constant C (equal to one for simple entry flow) is equal to 1·85 (the average value from our experiments). In general, C is expected to depend on the branching angles and diameter ratios of the junctions used. No experiments were performed in which the flow was turbulent, but it is argued that turbulence will not greatly affect the above results at Reynolds numbers less than and of the order of 10000. Many more experiments are required to consolidate this approach, but predictions based upon it agree well with the limited number of physiological experiments available.