bluuebunny/crossref_metadata_2025 huggingface dataset:
The influence of suction on the structure of turbulence in fully developed pipe flow
Authors: Schildknecht M. , Miller J. A. , Meier G. E. A.
Published: April 2006

The effect of uniform wall suction on the structure of turbulence in a fully established turbulent pipe flow has been measured, with special attention to the critical layers close to the wall. Uniform suction was introduced into a pipe flow with a Reynolds number of 17250 by means of a porous-walled section 2·2 diameters in length with very fine perforations. The effect of suction on the turbulent energy balance was then measured over the entire cross-section at four axial locations. The results indicate the following.

The amplitudes of the three principal velocity fluctuation components are reduced by suction, but to differing degrees. Moreover, the effects of suction on the amplitudes of these fluctuations develop at differing rates such that thex-wise components are first affected, then ther-wise and lastly the ϕ-wise components.

The suction-induced perturbation in the turbulent structure propagates from the wall to the pipe centre-line with a velocity approximately equal to the friction velocityUτ.

Even with very small rates of fluid extraction the maxima of the terms in the turbulent energy balance occurring close to the wall are drastically reduced. Nevertheless there is no tendency for the location of these maxima to move towards the wall.

The general reduction of the level of turbulent energy across the entire section is due to transport of this energy by the augmented mean radial velocity towards the wall, where it is dissipated since the boundary condition inhibits the passage of turbulent energy through the wall.
Vortex breakdown in a rotating cylindrical cavity
Authors: Owen J. M. , Pincombe J. R.
Published: April 2006

Flow visualization, laser-Doppler anemometry and pressure measurements have been used to identify and delineate the regimes of vortex breakdown in a rotating cavity with a central axial flow of air. For the particular cavity tested (where the ratio of the outer to the inner radius was ten and the ratio of the axial width to the inner radius was approximately five), spiral breakdown and axisymmetric breakdown occur in both laminar and turbulent flow. Rossby numbers ε characterizing the boundaries between the breakdown modes were established from visual observations of flow behaviour, from discontinuities in velocity components and in the pressure drop across the cavity, and from changes in the velocity spectra. In laminar flow, spiral breakdown occurs for 1·6 [lsim ] ε [lsim ] 3·2 and axisymmetric breakdown occurs for 0·8 [lsim ] ε [lsim ] 1·5. In turbulent flow, spiral breakdown occurs for 21 [lsim ] ε [lsim ] 100 and 1·5 [lsim ] ε [lsim ] 2·6, and axisymmetric breakdown occurs for 2·6 [lsim ] ε [lsim ] 21 and 0·8 [lsim ] ε [lsim ] 1·5. At the higher Rossby numbers, the flow under laminar conditions is significantly different to that under turbulent conditions; at the lower Rossby numbers, it was found to be impossible to distinguish between laminar and turbulent flow.
Small-scale structure of two-dimensional magnetohydrodynamic turbulence
Authors: Orszag Steven A. , Tang Cha-Mei
Published: April 2006

The formation of singularities in two-dimensional magnetohydrodynamic flow is investigated by direct numerical simulation. It is shown that two-dimensional magnetohydrodynamic turbulence is not as singular as three-dimensional hydrodynamic turbulence (in the sense that it has a less highly excited small-scale structure) but that it is more singular than two-dimensional hydrodynamic turbulence.
A note on the viscous diffusion of rolled vortex sheets
Authors: Guiraud J. P. , Zeytounian R. Kh.
Published: April 2006

It is well known that vortex sheets are diffused by viscosity. For a plane sheet this diffusion is described by a linear diffusion equation. Here we consider a rolled vortex sheet, and show that the viscous diffusion of the vorticity concentrated at the turns of the sheet, when they are very closely spaced, can also be described by a linear equation, in appropriately transformed variables.
Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 2. Separated flows
Authors: Zilker Daniel P. , Hanratty Thomas J.
Published: April 2006

A study has been carried out of turbulent flow over a sinusoidally shaped solid boundary of large enough amplitude that the flow separates from the downstream side of the wave. Measurements are presented of the conditions under which separated flows exist, the extent of the separated region and the variation of the pressure and shear stress along and the velocity profile above the wavy surface. The results are consistent with the model D turbulent solution of the linear momentum equations discussed in Zilker, Cook & Hanratty (1977, hereafter referred to as I) in that reversed flows are possible for wave height to wavelength ratios 2a/λ > 0·033 and in that the range of flow rates for which reversed flows exist increases with increasing 2a/λ. For non-separated flows and for flows with thin separated regions the amplitude of the pressure variation changes linearly with wave height; however, for very large amplitude waves with thick separated regions it is much less sensitive to variations in wave height since the external flow that controls the pressure variation sees a wave profile consisting of a composite of the solid wave and the separated region. The variation of the velocity field along the wave surface in the non-separated region is similar to that predicted by linear theory for small amplitude waves. The flow separates in a region of increasing pressure and reattaches in the region where the pressure on the wave surface is a maximum. A large increase in the wall shear stress is noted immediately downstream of reattachment.
Theory and experiments on the control of the stratification in almost-enclosed regions
Authors: Rahm Lars , Walin Gösta
Published: April 2006

A comparison is made between the theoretically predicted and the observed stratification in a container which is traversed by a prescribed flux of fluid. Two different geometries were used illustrating respectively a useful procedure for the control of a stratified laboratory system and a mechanism which is believed to be geophysically significant, e.g. for the control of the stratification in certain estuaries. The behaviour of the fluid system was in all cases characterized by an almost stagnant interior with a boundary layer at the non-horizontal wall of buoyancy-layer type. Agreement between theory and experiment was satisfactory within experimental errors, say 10% of the overall temperature difference.
Wave-tank experiments on an immersed parallel-plate duct
Authors: Knott G. F. , Flower J. O.
Published: April 2006

A series of experiments is described in which a fully submerged parallel-plate enclosure is subjected to regular incident waves. The resulting wave-interaction effects are defined in terms of a reflexion coefficient derived from wave-height measurements and a pressure coefficient derived from measurements of pressure in the depths of the enclosure. The latter parameter describes the pressure induced in the enclosure by the passage of regular waves above it and is of particular interest, at present, in having a bearing on the operation and performance of a sub-sea wave-energy converter currently under development. The outcome of these experiments is the partial verification of some recent theoretical work, including the demonstration of a pressure intensification at certain wave frequencies.

These experiments form part of a wider study concerned generally with the performance of immersed, pressure-driven, wave-energy converters.
Turbulent velocity profiles from stability criteria
Authors: Malkus Willem V. R.
Published: April 2006

A velocity-defect law for channel flow is shown to result from the single requirement of Reynolds-stress spectral ‘smoothness’ for any mean profile maintained free of inflexions by transient instabilities. The deduced velocity is a logarithmic function of position near boundaries and parabolic in mid-regions of the flow, independent of the detailed mechanisms of momentum transport by the fluid. However, if the ‘smoothness’ of the spectral tail is decreased, a second logarithmic layer of steeper slope emerges inside the first layer. Profile data from drag-reduction experiments gathered by Virk (1975) exhibit the deduced inner log layer and its transition region to the usual outer flow.
Numerical solution of wave scattering problems in the parabolic approximation
Authors: Candel Sébastien M.
Published: April 2006

A numerical analysis of two-dimensional wave scattering problems is performed. The treatment relies on the parabolic approximation and provides the forward scattered wave field. Two problems are considered in particular: (i) the scattering of plane waves by a cylindrical inhomogeneity of uniform refraction index, (ii) the scattering of plane waves by a viscous core vortex. The structure of the scattered field is examined in detail and the numerical solutions of the two problems are compared to analytical results obtained in the Born approximation and interpreted according to the method of smooth perturbation.
On the scaling of stress-driven entrainment experiments
Authors: Price James F.
Published: April 2006

The entrainment experiments of Kato & Phillips (1969) and Kantha, Phillips & Azad (1977) (hereafter KP and KPA) are analysed to demonstrate a more general and effective scaling of the entrainment observations. The preferred scaling is
\[
V^{-1} dh/dt = E(R_v),
\]
where h is the mixed-layer depth, V is the mean velocity of the mixed layer, Rv = B/V2 and B is the total mixed-layer buoyancy. This scaling effectively collapses entrainment data taken at various h/L, where L is the tank width, and in cases in which the interior is density stratified (KP) or homogeneous (KPA). The entrainment law E(Rv) is computed from the KP and KPA observations using the conservation equations for mean momentum and buoyancy. A side-wall drag term is included in the momentum conservation equation. In the range 0·5 < Rv < 1·0, which includes nearly all of the KP, KPA data, E ≃ 5 × 10−4R−4v. This is very similar to the entrainment law followed by a surface half-jet (Ellison & Turner 1959) and by the wind-driven ocean surface mixed layer (Price, Mooers & Van Leer 1978).

The analysis shows that, when forcing is steady, Rv is quasi-steady and, provided that side-wall drag is not large, Rv ≃ 0·6 over a wide range of RT = B/U2*, where U* is the friction velocity of the imposed stress. In the absence of side-wall drag (vanishing h/L) the conservation of momentum then leads to U−1*dh/dt = n(0·6)½R−½T, where n = ½ or 1 if the interior is linearly stratified or homogeneous. The KP, KPA data show this dependence throughout the range 17 < RT < 160 where the effect of side-wall drag is negligible or can be removed by a linear extrapolation. This result, together with the form and magnitude of the observed side-wall effect, suggests that mean momentum conservation is a key constraint upon the entrainment rate in the KP, KPA experiments.
Sphere drag at Mach numbers from 0·3 to 2·0 at Reynolds numbers approaching 107
Authors: Miller Donald G. , Bailey Allan B.
Published: April 2006

Our analysis of 18th and 19th century cannon firings shows that knowledge of sphere drag can be substantially extended into the region of 0·3 ≤ M∞ ≤ 2·0 and Re∞d up to 107. Bashforth’s chronographic measurements (1868) are of a quality comparable to modern measurements. The data of Mayevski (chronograph, 1868), Hutton (ballistic pendulum, 1787-1791), and Didion (ballistic pendulum, 1839-1840) are of lesser accuracy but in agreement with Bashforth’s. These cannon data are combined with modern data to provide the most extensive curves available of CD vs. Re∞d in this region. Interesting features of these curves for M∞ ≤ 1·0 are briefly described.
The inner regions of annular jets
Authors: Ko N. W. M. , Chan W. T.
Published: April 2006

Further experiments on the detailed study of annular jets are described in which the mean and fluctuating properties in the inner region have been measured. The experiments in the conical jetf have shown, besides the jet† vortices in the outer mixing region, another train of vortices in the inner region. This train of vortices is due to the wake formed by the boundary layer on the surface of the conical bullet.

The experiments in the inner region of the basic annular jet have similar mean velocity profiles to those in the internal recirculating region. Good correlation is found for the location of the vortex centre, the location of reattachment, the minimum and maximum mean static pressure and their locations with the non-dimensional available pressure M°/AiPatm for entrainment behind the interface. A train of wake vortices is generated in the internal recirculating region and a train of jet vortices is found in the inner mixing region. Both types of vortices in the inner region seem to decay fairly rapidly within a distance of one outer diameter D° downstream.

The disturbances associated with the wake vortices in the inner region seem to excite the outer mixing region. This results in another wave or train of vortices observed in the outer shear layer in addition to the jet vortices which are already in existence.
The radiation of sound by the instability waves of a compressible plane turbulent shear layer
Authors: Tam Christopher K. W. , Morris Philip J.
Published: April 2006

The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near-and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.
Oscillatory flow in curved pipes. Part 2. The fully developed case
Authors: Mullin T. , Greated C. A.
Published: April 2006

A theoretical and experimental investigation of oscillatory flow in curved pipes is presented. The equations for fully developed laminar flow are found to depend on an amplitude parameterGand a frequency parameter α. Initially the Navier–Stokes equations are expanded in terms ofGand the resulting linearized equations are solved numerically using finite Hankel integral transforms. A further expansion is used for the case α → 0 and closed-form solutions are presented.

Laser-Doppler anemometry has been used to obtain velocity information in oscillatory air flow in small-diameter curved glass tubes. Using this technique, low-Reynolds-number experiments were carried out and comparison between theory and experiments is presented.

For α [les ] 1 the velocity distributions found are essentially those for steady flow, while for α [ges ] 11·0 the results are not at variance with earlier work. It is for the transition stage between these two regimes that unexpected behaviour is recorded, but a satisfactory explanation is found in terms of general trends within the flow.
Seasonal and spring-neap tidal dependence of axial dispersion coefficients in the Severn - a wide, vertically mixed estuary
Authors: Uncles R. J. , Radford P. J.
Published: April 2006

Results are presented of a simplified description of the seasonal and spring–neap tidal dependence of the axial dispersion coefficients in the Severn Estuary. The coefficients are derived from salt budget calculations, which are based on 29 sets of observations of the axial salinity distributions in the estuary during 1971–1976. Regression analyses of the salinity distributions determine simple linear and logarithmic relationships for the dispersion coefficients in terms of tidal range and the total rate of input of fresh water to the estuary, the appropriate averaging periods for the freshwater inputs being computed as part of the analyses.

The results show that the coefficients generally increase with increasing run-off, and, away from the mouth, depend upon the tidal range, showing a small decrease with increasing tidal range in the seaward part of the estuary, and a large increase with increasing tidal range towards the head. The yearly averaged coefficients lie in the order-of-magnitude range 102–103 m2s−1, with the larger values occurring near the head.

The computed dispersion coefficients are applied to calculations of the seasonal dependence of residence times, the results being expressed as functions of axial distance along the estuary. It is shown that the residence time of the whole estuary varies from roughly 100 days during winter conditions to 200 days during summer conditions, and that the residence time landward of a particular section decreases rapidly as the section taken approaches the head of the estuary.
Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigation
Authors: Paliwal R. C. , Chen C. F.
Published: April 2006

The stability boundary of a density-stratified fluid contained in an inclined slot subjected to a lateral temperature gradient was determined experimentally. The initial stratification due to salt was stable and linear in the vertical direction. Experiments were conducted in a 1·0 × 11.1 × 25·7 cm slot with the inclination angle θ from the vertical varying from −75° to + 75°. A positive angle denotes heating from the lower wall while a negative angle denotes heating from the upper wall. The temperature difference across the slot was increased slowly until the onset of instability was observed by means of a shadowgraph. The critical thermal Rayleigh number was found to be non-symmetrical with respect to θ = 0°, with heating of the upper wall less stable than heating of the lower wall. This is because there is a larger vertical solute gradient in the steady-state regime prior to the onset of instabilities when the lower wall is heated. The secondary flow consisting of horizontal convecting layers was very stable θ < 0° cases because of the stabilizing temperature effect. The motion of the layers when θ > 0° was quite vigorous. At θ = +75°, the secondary flow became unstable in a rather dramatic manner not observed heretofore.
The effect of centrifugal acceleration on axisymmetric convection in a shallow rotating cylinder or annulus
Authors: Daniels P. G.
Published: April 2006

This paper considers the nature of stationary axisymmetric convection in a shallow rotating annulus or cylinder heated from below. The horizontal and vertical walls of the container are assumed to be perfect conductors and insulators respectively. The critical regime is considered in which the circulations due to the centrifugal force and the vertical gravitational instability are of equal significance. Among the effects of the centrifugal acceleration on the gravitational instability are a shift in the value of the Rayleigh number at which instability sets in, a modification in the distribution and amplitude of convection cells in the container and, most significantly, a smooth transition to finite amplitude convection as the Rayleigh number is increased.
Accurate fluxes across a salt-sugar finger interface deduced from direct density measurements
Authors: Griffiths R. W. , Ruddick B. R.
Published: April 2006

The buoyancy flux ratio, r = αFT/βFS, across a salt-sugar fingering interface is determined from accurate measurements of the density variations in a two-layer run-down experiment. Since r is close to 1, the net buoyancy flux, βFS − αFT, which is proportional to 1 − r, gives r with a resolution that is much improved over that of previous measurements. The value of r is found to decrease from r ≈ 0·94 ± 0·01 at Rρ = 1·02 to r = 0·88 ± 0·01 at Rρ = 2, where Rρ is the density anomaly ratio. The latter is smaller than the previous (constant) value of 0·92. The buoyancy flux due to sugar is found to decrease rapidly with increasing Rρ, varying approximately as R−6ρ.
Vortex shedding from bluff bodies in oscillatory flow: A report on Euromech 119
Authors: Bearman P. W. , Graham J. M. R.
Published: April 2006

European Mechanics Colloquium number 119 was held at Imperial College on 16–18 July 1979, when the subject of vortex shedding from bodies in unidirectional flow and oscillatory flow, was discussed. A wide range of experimental work was presented including low-Reynolds-number flows around circular cylinders, the influence of disturbances on bluff body flow, the measurement of fluctuating forces and the influence of oscillations of the stream. About a third of the 33 papers presented concentrated on theoretical aspects and the majority of these were concerned with the ‘method of discrete vortices’.
Boundary-layer velocities and mass transport in short-crested waves
Authors: Hsu J. R. C. , Silvester R. , Tsuchiya Y.
Published: April 2006

A comprehensive programme of research is being undertaken on short-crested waves produced by obliquely reflecting waves from a rigid vertical wall. This has included a new wave theory to third-order approximation. The second-order Eulerian water-particle velocities throughout the bottom boundary layer are now investigated. From this the resulting mass transport is considered to the first approximation. The vertical velocity component has a non-zero value within and just beyond the boundary layer. The limiting two-dimensional cases of progressive and standing waves are obtained and compared with published results. Comparison is also made with available experimental data. Graphs of some analytical solutions are presented.
A finite-rate theory of resonance in a closed tube: discontinuous solutions of a functional equation
Authors: Seymour Brian R. , Mortell Michael P.
Published: April 2006

The only solutions to date which describe nonlinear resonant acoustic oscillations are those for which the distortion of the travelling waves is negligible. Many experiments do not comply with this small-rate restriction. A finite-rate theory of resonance for an inviscid gas, in which the intrinsic nonlinearity of the waves is taken into account, necessitates the construction of periodic solutions of a nonlinear functional equation. This is achieved by introducing the notion of a critical point of the functional equation, which corresponds physically to a resonating wavelet. In a finite-rate theory a wave may break in a single cycle in the tube, and thus there may be more than one shock present even at fundamental resonance. Discontinuous solutions of the functional equation are constructed which satisfy the weak shock conditions.
Theory and observations of waves on hollow-core vortices
Authors: Keller Jakob J. , Escudier M. P.
Published: April 2006

A linear non-homogeneous analysis is presented for the standing waves produced on the hollow core of an irrotational vortex by an arbitrary obstacle on the wall of the tube containing the vortex. The group-velocity criterion based upon Kelvin's corresponding dispersion relation predicts whether a certain asymptotic wave pattern appears upstream or downstream of the obstacle. The analysis leads to amplitude singularities for the standing waves at certain critical radii of the core. The particularly interesting case of a counter-helix for which the wave energy is propagating upstream appears for a first-mode angular disturbance. For this situation it seems to be possible that the helix ends in a hydraulic jump and is continued by a counter-helix downstream, as the core size gradually diminishes due to the deceleration of the flow caused by viscous effects (not included in the analysis). The capillary-wave pattern produced by surface tension is also considered. A brief outline for the analogous wave problem is given for the case where the fluid rotates like a rigid body.

Photographic observations of hollow-core vortices in water flow are presented which confirm the qualitative predictions of the analysis, both for the response to an axisymmetric area contraction and also to a 90° bend at the downstream end of the vortex tube.
The motion of the front of a gravity current travelling down an incline
Authors: Britter R. E. , Linden P. F.
Published: April 2006

The motion of the head of a gravity current travelling down a slope of angle θ to the horizontal is investigated in the laboratory. The head is produced by suddenly initiating a buoyancy flux from a line source at the top of the slope. It is found that for very small slopes (θ [les ] 0.5°) the head decelerates with distance from the source, but at greater slopes the buoyancy force is large enough to overcome frictional effects and a steady head velocity results. Over a wide range of slope angles the front velocity Uf, non-dimensionalized by the cube root of the buoyancy flux (g′0Q)1/3, is almost independent of the slope angle and Uf/(g’0Q)1/3 = 1.5 ± 0.2 for 5° [les ] θ [les ] 90°. This result is shown to follow from some simple analysis which relates the velocity of the front to the following flow. For a Boussinesq plume the front velocity is found to be approximately 60% of the mean velocity of the following flow. This means that the head increases in size as it travels down the slope, both by direct entrainment into the head itself and by addition of fluid from the following flow. We find that direct entrainment increases with increasing slope and accounts for one-tenth of the growth of the head at 10° and about two-thirds at 90°.
The formation of ripples and dunes on an erodible bed
Authors: Richards Kelvin J.
Published: April 2006

A two-dimensional stability analysis is presented of flow of low Froude number over an erodible bed. Particular regard is given to the modelling of the turbulent flow close to the bed. In contrast to previous theories that use a constant eddy-viscosity approach the present theory predicts the occurrence of two separate modes of instability, with wavelengths related to the roughness of the bed and the depth of the flow. It is postulated that these two modes correspond to the formation of ripples and dunes respectively. The results are strongly dependent on the two parametersz0, the roughness length of the bed, and β, the effect of the local bed slope on the bed-load transport. Using physically plausible estimates for these parameters the results of the analysis are in good agreement with observations for both ripples and dunes.
A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 1. Perpendicular motion
Authors: Ganatos Peter , Weinbaum Sheldon , Pfeffer Robert
Published: April 2006

This paper presents the first ‘exact’ solutions to the creeping-flow equations for the transverse motion of a sphere of arbitrary size and position between two plane parallel walls. Previous solutions to this classical Stokes flow problem (Ho & Leal 1974) were limited to a sphere whose diameter is small compared with the distance of the closest approach to either boundary. The accuracy and convergence of the present method of solution are tested by detailed comparison with the exact bipolar co-ordinate solutions of Brenner (1961) for the drag on a sphere translating perpendicular to a single plane wall. The converged series collocation solutions obtained in the presence of two walls show that for the best case where the sphere is equidistant from each boundary the drag on the sphere predicted by Ho & Leal (1974), using a first-order reflexion theory, is 40 per cent below the true value when the walls are spaced two sphere diameters apart and is one order-of-magnitude lower at a spacing of 1.1 diameters.
Onsager's pancake approximation for the fluid dynamics of a gas centrifuge
Authors: Wood Houston G. , Morton J. B.
Published: April 2006

A previously unpublished theory for describing the internal flow in a gas centrifuge is presented. The theory is based on boundary-layer-type arguments on the side walls of the centrifuge with the additional approximation of neglecting radial diffusion of radial momentum. The effects of the top and bottom end caps are incorporated through Ekman-layer solutions. The results are presented in a form amenable to numerical calculations.

Some sample calculations are presented for the special case of a centrifuge with a linear temperature profile on the wall and the top and bottom of the centrifuge at the same temperature as the corresponding end of the side wall.
An asymptotic theory of incompressible turbulent boundarylayer flow over a small hump
Authors: Sykes R. I.
Published: April 2006

A rational asymptotic theory describing the perturbed flow in a turbulent boundary layer encountering a small two-dimensional hump is presented. The theory is valid in the limit of very high Reynolds number in the case of an aerodynamically smooth surface, or in the limit of small drag coefficient in the case of a rough surface. The method of matched asymptotic expansions is used to obtain a multiple-structured flow, along the general lines of earlier laminar studies. The leading-order velocity perturbations are shown to be precisely the inviscid, irrotational, potential flow solutions over most of the domain. The Reynolds stresses are found to vary across a thin layer adjacent to the surface, and display a singular behaviour near the surface which needs to be resolved by an even thinner wall layer. The Reynolds stress perturbations are calculated by means of a second-order closure model, which is shown to be the minimum level of sophistication capable of describing these variations. The perturbation force on the hump is also calculated, and its order of magnitude is shown to depend on the level of turbulence closure; a cruder turbulence model gives rise to spuriously large forces.
The mixing layer of Loch Ness
Authors: Thorpe S. A. , Hall A. J.
Published: April 2006

Measurements of the thermal and velocity structure of the near-surface mixing layer of a freshwater lake in moderate wind conditions from fixed or mobile arrays of sensors reveal large-scale coherent structures consisting of narrow fronts across which both the temperature and the horizontal component of the current increase. These fronts are generally transverse to the wind direction and are inclined to the vertical, and appear to be similar to fronts, reported as temperature ‘ramps’, in the near-surface atmospheric boundary layer. The time derivatives of the temperature are skewed in a sense consistent with observations in laboratory and atmospheric boundary layers, and of a magnitude consistent with measurements in the latter. Evidence is presented to show that bubbles generated by breaking waves are carried down in the large-scale pattern of flow associated with the fronts in the mixing layer. The presence of a Langmuir circulation associated with wind rows has not been established in these experiments. The relevance of the observations to the ocean mixing layer is discussed.
Thermophoresis of particles in a heated boundary layer
Authors: Talbot L. , Cheng R. K. , Schefer R. W. , Willis D. R.
Published: April 2006

A laser-Doppler velocimeter (LDV) study of velocity profiles in the laminar boundary layer adjacent to a heated flat plate revealed that the seed particles used for the LDV measurements were driven away from the plate surface by thermophoretic forces, causing a particle-free region within the boundary layer of approximately one half the boundary-layer thickness. Measurements of the thickness of this region were compared with particle trajectories calculated according to several theories for the thermophoretic force. It was found that the theory of Brock, with an improved value for the thermal slip coefficient, gave the best agreement with experiment for low Knudsen numbers, λ/R = O(10−1), where λ is the mean free path and R the particle radius.

Data obtained by other experimenters over a wider range of Knudsen numbers are compared, and a fitting formula for the thermophoretic force useful over the entire range 0 [les ] λ/R [les ] ∞ is proposed which agrees within 20% or less with the majority of the available data.
The nonlinear capillary instability of a liquid jet. Part 1. Theory
Authors: Chaudhary K. C. , Redekopp L. G.
Published: April 2006

Nonlinear capillary instability of an axisymmetric infinite liquid column is investigated with an initial velocity disturbance consisting of a fundamental and one harmonic component. A third-order solution is developed using the method of strained co-ordinates. For the fundamental disturbance alone, the solution shows that a cut-off zone of wavenumbers (k) exists such that the surface waves grow exponentially below the cut-off zone, linearly in the middle of the zone (near k = 1), and an oscillatory solution exists for wavenumbers above the boundary of the zone. For an input including both the fundamental and a harmonic, all wave components grow exponentially when the fundamental is below the cut-off zone. Using a Galilean transformation, the solution is applied to a progressive jet issuing from a nozzle. The jet breaks into drops interspersed with smaller (satellite) drops for k < 0·65; no satellites exist for k > 0·65. It is shown theoretically that the formation of satellites can be controlled by forcing the jet with a suitable harmonic added to the fundamental.
Streamline patterns and eddies in low-Reynolds-number flow
Authors: Jeffrey D. J. , Sherwood J. D.
Published: April 2006

The streamline patterns of some simple two-dimensional Stokes flows are studied and the results used both to understand and to predict the streamlines of flows in more complicated geometries, in particular the streamlines of flows that contain eddies or regions of closed streamlines. Initially, streamline patterns are studied locally, either around some special point, such as a stagnation point or a point where a streamline meets a wall, or in a special region, such as a corner. The use of these local analyses is illustrated by finding the streamlines for shear flow around a rotating cylinder; the illustration also shows how fluid in Stokes flow can be turned back on itself (‘blocked’). The local analyses of flow in a corner are used to understand the eddy patterns that have been discovered in a variety of flows. The eddies occur in corner-like regions and in these regions the flow can be regarded as the superposition of two components. One component, the eddy flow, is the result of flow outside the corner stirring the fluid in the corner, while the other is the direct result of local conditions in the corner. The competition between these two components determines whether eddies actually appear in a given flow. Finally, the approach developed here is applied to a new flow situation, namely a shear flow which is bounded by a moving wall and which contains a stationary cylinder touching the wall. The streamlines deduced for different ratios of the shear strength to the wall velocity show both new eddy patterns and unexpected regions of blocked flow.
Onset of convection in a layered porous medium heated from below
Authors: Mckibbin R. , O'Sullivan M. J.
Published: April 2006

The formalism required to determine the criterion for the onset of convection in a multi-layered porous medium heated from below is developed using a straightforward linear stability analysis. Detailed results for two- and three-layer configurations are presented. These results show that large permeability differences between the layers are required to force the system into an onset mode different from a homogeneous system.
Some effects of surface tension on steep water waves. Part 2
Authors: Hogan S. J.
Published: April 2006

This paper continues an investigation of the effects of surface tension on steep water waves in deep water begun in Hogan (1979a). A Stokes-type expansion method is given which can be applied to most wavelengths. For capillary waves (2 cm or less) it is found that the surface of the highest wave encloses a bubble of air, as was found for pure capillary waves by Crapper (1957). For intermediate waves (20 cm) the wave profiles are similar to those of pure gravity waves and the wave properties increase monotonically. For gravity waves (200 cm) the wave properties all exhibit a maximum just short of the maximum wave height obtained by the method. The integral properties for all the waves are drawn and given in numerical form in the appendix.
On diffusive instabilities of a rapidly rotating electrically conducting layer of compressible fluid of varying depth
Authors: Gibbons M. P.
Published: April 2006

Compressibility is added to Busse's (1976) study of convection in a rotating, electrically conducting layer of fluid, of varying depth, which is permeated by an azimuthal magnetic field that is orthogonal to both the rotation vector Ω and the gravitational acceleration g. On the basis of a linear theory, we investigate the kinds of infinitesimal wave motion which the fluid can support when the dominant balance of forces is between pressure gradient and Coriolis force, so that the Proudman–Taylor theorem holds. Unlike Busse, however, we assume that the fluid is statically stable in the sense that the temperature gradient is sub-adiabatic.

In the absence of diffusion, these waves are dynamically neutral and take the form of Rossby waves modified by compressibility and magnetic field. The waves are examined in two limits, the adiabatic and the isothermal, and we define two distinct frequencies at which a pure Rossby wave can oscillate. When diffusion is restored, the disparity between these frequencies makes the fluid susceptible to overstability. We prove that all such amplifying waves must propagate eastward, i.e. in the direction of g ∧ Ω, irrespective of the sign of the depth gradient or the magnitudes of the diffusivities. The theorem does not apply if the fluid is incompressible or convectively unstable at the outset, and therefore does not contradict Busse's result that the direction of azimuthal propagation can be altered by the diffusivities. Nevertheless, we suggest reasons why Busse's method of regarding the imaginary part of the marginal stability equation as a dispersion relation is not in general a reliable one.

We examine the instabilities by subjecting the neutral waves to a weakly diffusive perturbation. We discover, in particular, a new kind of magnetic instability which is crucially dependent upon both compressibility and the depth gradient. In agreement with the general result described above, the instability takes the form of a slow, eastward propagating, amplifying wave.

The principal source for all instabilities is elastic energy, which cannot be tapped in a Boussinesq fluid, since the work done by compression is neglected under that approximation.
Non-parallel flow effects on the stability of film flow down a right circular cone
Authors: Zollars Richard L. , Krantz William B.
Published: April 2006

A global asymptotic solution for the linear stability of this flow with respect to axisymmetric disturbances is developed without invoking the usual quasi-parallel flow assumption. This solution predicts the occurrence of quasi-periodic spatially amplified disturbances relatively near the apex, which ultimately are stabilized further down the cone by the relative increase in viscous forces associated with the progressive thinning of the film. The wave speed and wavelength of these disturbances are found to decrease with increasing distance from the apex.
Modeling topographic and climatic control of east‐west asymmetry in Sierra Nevada glacier length during the Last Glacial Maximum
Authors: Kessler Mark A. , Anderson Robert S. , Stock Greg M.
Published: April 2006

Glaciers draining westward from the Sierra Nevada divide, California, during the Last Glacial Maximum (LGM) were ∼7 times longer than east‐draining glaciers. We address the degree to which this difference may be attributed to the topographic asymmetry of the west‐tilted Sierran block and the climate asymmetry resulting from orographic modification of Pacific Ocean storms. We simulate kilometer‐scale glaciers within the 50 × 50 km Kings Canyon region of the southern Sierra by employing a two‐dimensional numerical model that is driven by simple, spatially variable climates and treats ice transport by deformation, sliding, and avalanching. In numerical experiments, we match simulated termini to LGM moraine positions to constrain the parameters of different climate scenarios. The 38‐km‐long LGM glacier in Kings Canyon was reproduced by a climate specified by an equilibrium line altitude (ELA) of 3170 m, a mass balance gradient of 0.01 m/yr/m, and a maximum positive balance of 2 m/yr. This climate generates much shorter (average ∼6 km long) east‐draining glaciers that, however, overshoot the LGM moraines by ∼1 km. Roughly 97% of the E‐W difference in glacier lengths can therefore be attributed to topographic asymmetry alone. A second experiment suggesting a 120‐m‐higher ELA of 3290 m east of the divide can explain the shorter east‐draining glaciers. An experiment in which orographic precipitation is explicitly simulated and melt is prescribed using a positive degree‐day algorithm matches both Kings Canyon and the average east‐draining glacier length with an LGM climate that was 5.6°C cooler and ∼2 times wetter than the modern Sierra Nevada.
Role of dynamic grain boundary wetting in fluid circulation beneath volcanic arcs
Authors: Hier‐Majumder Saswata , Kohlstedt David L.
Published: April 2006

We report the influence of shear deformation on the microstructure of water‐saturated olivine and clinopyroxene aggregates. Prior to deformation, the aqueous fluid was isolated in pockets along grain corners in the olivine‐water aggregates, while it was interconnected by a network of grain‐edge tubules in the clinopyroxene‐water aggregate. During deformation of both types of aggregates, the aqueous fluid phase segregates into grain boundaries at an angle of ∼16° to the shear direction, inclined in a sense antithetic to the applied shear. Fluid‐rich planes formed by such dynamic wetting of grain boundaries lead to the formation of high permeability paths in the matrix. In a deforming mantle, such high permeability paths will enhance the efficiency of aqueous fluid extraction from subducting slabs.
Structure and formation mechanism of V defects in multiple InGaN∕GaN quantum well layers
Authors: Shiojiri M. , Chuo C. C. , Hsu J. T. , Yang J. R. , Saijo H.
Published: April 2006

A variety of different transmission electron microscopy techniques, and particularly high-angle annular dark-field scanning transmission electron microscopy, has been used to reveal that V defects or inverted hexagonal pyramid defects in multiple InGaN∕GaN quantum well (QW) layers nucleate on threading dislocations that cross the InGaN QW. The defects have thin walls lying parallel to {101¯1} with the InGaN∕GaN QW structure. A formation mechanism for the V defects is proposed taking into account the growth kinetics of GaN and the segregation of In atoms in the strain field around the cores of the threading dislocations.
Ion-beam induced transformations in nanoscale multilayers: Evolution of clusters with preferred length scales
Authors: Bera S. , Satpati B. , Goswami D. K. , Bhattacharjee K. , Satyam P. V. , Dev B. N.
Published: April 2006

Ion-irradiation-induced modifications of a periodic Pt∕C multilayer system containing a small amount of Fe have been analyzed by transmission electron microscopy and grazing incidence x-ray diffraction (GIXRD) studies. The multilayer stack with 16 Pt∕C layer pairs (period of 4.23nm) was fabricated on a glass substrate. A 2MeV Au2+ ion beam was rastered on the sample to obtain uniformly irradiated strips with fluences from 1×1014to1×1015ions∕cm2. Ion irradiation has been found to cause preferential migration of Fe towards Pt layers [Bera et al., Nucl. Instrum. Methods Phys. Res. B 212, 530 (2003)]. Cross-sectional transmission electron microscopy (XTEM) shows considerable atomic redistribution for irradiation at the highest ion fluence (1×1015ions∕cm2). This structure is composed of small clusters. Phase separation and cluster formation processes are discussed. Periodic multilayers have periodicity only in the direction normal to the multilayer surface. However, Fourier transform (FT) of the XTEM images of the sample irradiated at the highest fluence shows extra off-normal Fourier components of superlattice periodicities arising due to ion irradiation. These extra spots in the FT are due to preferential length scales in intercluster separation in three dimensions. With a proper understanding of this phenomenon it may be possible to fabricate useful three-dimensional self-assembled structures of nanoclusters. Our high resolution transmission electron microscopy and GIXRD results reveal the formation of an FePt alloy. As FePt is a magnetic alloy, our observation raises the possibility of fabrication of ion-beam induced magnetic nanocluster lattices.
Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows
Authors: Guo Zhaoli , Zhao T. S. , Shi Yong
Published: April 2006

In this paper, we study systematically the physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation (LBE) for microgas flows in both the slip and transition regimes. We show that the physical symmetry and the spatial accuracy of the existing LBE models are inadequate for simulating microgas flows in the transition regime. Our analysis further indicates that for a microgas flow, the channel wall confinement exerts a nonlinear effect on the relaxation time, which should be considered in the LBE for modeling microgas flows.
Ion association in aqueous LiCl solutions at high concentration: Predicted results via molecular simulation
Authors: Chialvo Ariel A. , Simonson J. Michael
Published: April 2006

We perform molecular dynamics simulations to study the ionic solvation and association behavior in concentrated aqueous LiCl solutions at ambient conditions, including consideration of expected signatures of ion pairing that might be found in neutron diffraction experiments with isotopic substitution. The ten possible pair radial distribution functions that define the microstructure of the systems are determined and used to assess the first-order difference of the neutron-weighted correlation functions for these solutions in heavy and null water. Then, both sets of correlation functions are applied to the interpretation of the ion’s local environment in terms of the location of the relevant peaks and the penetration of ions into the counterion solvation shells as a signature of ion-pair formation. Finally, we illustrate how first-order difference experiments involving null and heavy water might be used to assess the magnitude of the Mv+−Xv− ion-pair formation for a salt Mv+Xnv− in an aqueous solution, provided the significant experimental challenges in these studies could be overcome.
Electromagnetic wave propagation in dense carbon nanotube arrays
Authors: Dragoman D. , Dragoman M.
Published: April 2006

At signal frequencies close to the mechanical resonant frequency of an array of metallic cantilevered carbon nanotubes, the array sandwiched between two coplanar waveguide lines shows a notch in the transmission coefficient of the microwave signal. This resonant phenomenon is explained by a Drude-Lorentz theory applied to the charges at the carbon nanotube tips that are excited by the electric field of the microwave signal. The theory demonstrated a metal-lossy dielectric transition of the carbon nanotube array at the mechanical resonant frequency of the cantilever.