bluuebunny/crossref_metadata_2025 huggingface dataset:
Spatial dynamics of invasion in sinusoidally varying environments
Authors: Kinezaki Noriko , Kawasaki Kohkichi , Shigesada Nanako
Published: April 2006

Range expansions of invading species in homogeneous environments have been extensively studied since the pioneer works by Fisher (Ann Eugen 7:255–369,1937) and Skellam (Biometrika 38:196–218,1951). However, environments for living organisms are often fragmented by natural or artificial habitat destruction. Here we address how such environmental heterogeneity affects the range expansion of invading species. We consider a single‐species invasion in heterogeneous environments whose habitat parameters vary in a sinusoidal or quasi‐sinusoidal manner. Accordingly, Fisher's model is modified to make the intrinsic growth rate and diffusion coefficient spatially variable. By numerically solving the model, we examine the spatio‐temporal pattern of propagating waves, and predict the speed as a function of the amplitude and the wave length of the diffusion coefficient and the intrinsic growth rate. Firstly, the results demonstrate that in the sinusoidally varying environment, if the intrinsic growth rate solely oscillates, the speed increases with increases in the amplitude of oscillation. Conversely, if the diffusion coefficient solely oscillates, the speed decreases with increases in the amplitude of oscillation. When both the intrinsic growth rate and diffusion coefficient oscillate, the speed is synergistically accelerated if the oscillations are in anti‐phase, whereas it is decelerated if the oscillations are in same phase. Secondly, the increase in the wave length in either the intrinsic growth rate or the diffusion coefficient leads to decreases in the speed. Thirdly, in the irregularly varying environment, the irregularity in the amplitude of the intrinsic growth rate enhances the speed, while that of the diffusion coefficient attenuates the speed.
Positive career orientation as an inhibitor of adolescent problem behaviour
Authors: Skorikov Vladimir , Vondracek Fred W.
Published: April 2006

This study tested the hypothesis that positive career orientation can prevent adolescents from engaging in or escalating problem behaviour. A 1‐year, longitudinal study was conducted on a sample of 234 junior‐high and high‐school students, who were 14.8 years old on the average in the beginning of the study. Using structural equation modeling, a developmental, two‐wave, two‐factor empirical model corresponding to the predicted relationships between career orientation and problem behaviour was found to fit the data well. According to the fitted model, positive career orientation had a significant negative longitudinal effect on problem behaviour. In contrast, we found no evidence in support of the assumption that career orientation can be affected by problematic behavioural tendencies.
Fumagillin suppresses HIV‐1 infection of macrophages through the inhibition of Vpr activity
Authors: Watanabe Nobumoto , Nishihara Yoshifumi , Yamaguchi Tomoyuki , Koito Atsushi , Miyoshi Hiroyuki , Kakeya Hideaki , Osada Hiroyuki
Published: April 2006

HIV‐1 viral protein R (Vpr) is one of the human immunodeficiency virus type 1 encoded proteins that have important roles in viral pathogenesis. However, no clinical drug for AIDS therapy that targets Vpr has been developed. Here, we have established a screening system to isolate Vpr inhibitors using budding yeast cells. We purified a Vpr inhibitory compound from fungal metabolites and identified it as fumagillin, a chemical already known to be a potent inhibitor of angiogenesis. Fumagillin not only reversed the growth inhibitory activity of Vpr in yeast and human cells, but also inhibited Vpr‐dependent viral gene expression upon the infection of human macrophages.
On the growth of turbulent regions in laminar boundary layers
Authors: Gad-El-Hak Mohamed , Blackwelderf Ron F. , Riley James J.
Published: April 2006

Turbulent spots evolving in a laminar boundary layer on a nominally zero pressure gradient flat plate are investigated. The plate is towed through an 18 m water channel, using a carriage that rides on a continuously replenished oil film giving a vibrationless tow. Turbulent spots are initiated using a solenoid valve that ejects a small amount of fluid through a minute hole on the working surface. A novel visualization technique that utilizes fluorescent dye excited by a sheet of laser light is employed. Some new aspects of the growth and entrainment of turbulent spots, especially with regard to lateral growth, are inferred from the present experiments. To supplement the information on lateral spreading, a surbulent wedge created by placing a roughness element in the laminar boundary layer is also studied both visually and with probe measurements. The present results show that, in addition to entrainment, another mechanism is needed to explain the lateral growth characteristics of a turbulent region in a laminar boundary layer. This mechanism, termedgrowth by destabilization, appears to be a result of the turbulence destabilizing the unstable laminar boundary layer in its vicinity. To further understand the growth mechanisms, the turbulence in the spot is modulated using drag-reducing additives and salinity stratification.
Interaction between a vortex filament and an approaching rigid sphere
Authors: Dhanak M. R.
Published: April 2006

The evolution of an infinitely long straight vortex filament in the presence of an approaching rigid sphere is considered. The fluid is regarded as being inviscid and incompressible. The shape of the vortex filament when the sphere is sufficiently far away from the vortex is determined approximately using linear theory. The subsequent evolution is followed numerically by integrating the nonlinear equation of motion.
Stratified flow over a bounded obstacle in a channel of finite height
Authors: Janowitz G. S.
Published: April 2006

The steady-state solution for the stratified flow over a bounded obstacle in a channel of finite height is obtained through the use of the inviscid unsteady Oseen equations; the body streamline encloses and is produced by a planar momentum sink. The calculations are compared with the experimental observations of Wei, Kao & Pao (1975) and Baines (1977). In a case where theoretical and experimental values match, good agreement was found. This suggests that the Oseen model with its columnar, wavelike and decaying solutions may provide a reasonable alternative to Long's model for subcritical flows.
Trajectories of particles at the surface of steep solitary waves
Authors: Longuet-Higgins M. S.
Published: April 2006

Theoretical calculations show that the horizontal displacement of particles in the surface of steep solitary waves exceeds that predicted by the Korteweg–de Vries equation by as much as 100%.

Experimental evidence is given in support of the higher values.
The focusing of weak shock waves at an axisymmetric arête
Authors: Cramer M. S.
Published: April 2006

The focusing of a weak and nearly plane shock wave at an axisymmetric arête is examined. The initial-value problem governing the flow in the focal region is derived. A similitude is introduced which shows that the details of the flow depend on the initial shape and strength of the shock only through a simple rescaling of the variables. The dependence of the pressure coefficient on the physical parameters is given. It is seen that the maximum pressure coefficient is proportional to a parameter measuring the rate of focusing of the shock and to the square root of a parameter measuring the initial strength of the shock.
Structure in turbulent mixing layers and wakes using a chemical reaction
Authors: Breidenthal R.
Published: April 2006

Plane turbulent mixing between two streams of water which contained dilute chemical reactants was studied in a new blow-down water tunnel. In a diffusion-limited reaction, a pH indicator, phenolphthalein, in one stream mixed and reacted with a base, sodium hydroxide, in the other stream to form a visible reaction product. The product was found to exist, as expected, in concentrated regions associated with the large, span-wise-coherent structures of the turbulence. A transition in the mixing was observed in which the aqueous mixing product increased by an order of magnitude. The transition is a consequence of the appearance and development of small-scale three-dimensional motions in the flow. Downstream of the transition, the amount of mixing product was independent of Reynolds number (for an order-of-magnitude increase in the latter) and at most only weakly dependent on Schmidt number.
A note on the singularity of an inner problem for head-sea diffraction by a slender body
Authors: Yue Dick K. P. , Mei Chiang C.
Published: April 2006

In studying head-sea diffraction by a slender body via matched asymptotics, Haren & Mei (1981) found numerically that the normalized inner problem is singular at a special frquency. In the present note, this singularity is confirmed by a different numerical method and by an analytical demonstration in the shallow-water limit.
Experimental study of high-Rayleigh-number convection in a horizontal cavity with different end temperatures
Authors: Bejan Adrian , Al-Homoud Adnan A. , Imberger Jorg
Published: April 2006

The paper summarizes results from an experimental study of buoyancy-induced motion and heat transfer in a horizontal rectangular cavity with the two vertical ends at different temperatures and the long horizontal walls adiabatic. The cavity height/length ratio isA= 0·0625. The high-Rayleigh-number range reported on in this paper, 2 × 108<Ra< 2 × 109, has not been studied before. It is shown that, contrary to lower-Rayleigh-number behaviour known previously, the core flow structure is non-parallel and is dominated by horizontal intrusions flowing along each of the two insulated horizontal walls of the enclosure. The fluid embraced by the two horizontal jets is practically stagnant and thermally stratified. Flow visualization experiments suggest that adjacent to the two horizontal jets two secondary flat cells are formed by the baroclinic pressure field in an analogous way to what is observed in intrusions in a stratified fluid. Nusselt-number-Rayleigh-number results for the overall end-to-end heat transfer in the horizontal direction are reported and compared with previous experimental and theoretical results available for lower Rayleigh numbers. It is shown also that the transition from a parallel core structure to one dominated by intrusion layers is governed by the parameterRa½A, withRa¼A< 1 as necessary condition for a parallel core flow.
On the stability and flow reversal of an asymmetrically heated open convection loop
Authors: Bau Haim H. , Torrance K. E.
Published: April 2006

Experimental results are reported for a U-shaped, free convection loop. The top of the loop is open to an isothermal reservoir. The horizontal leg and one vertical leg are heated at rates Q1 and Q2, respectively. The loop is filled either with water or a water-saturated porous medium. Symmetric heating and asymmetric heating favouring the ascending leg of the loop both yield stable flows. Asymmetric heating favouring the descending leg leads to stable flows when the ratio Q1/Q2 is above a critical value. Below this critical value, the flow is observed to oscillate with increasing amplitude until the direction of flow in the loop undergoes a reversal. A steady flow follows the reversal. Analytical results include a stability analysis and time-dependent, one-dimensional numerical calculations, both of which compare favourably with experiment.

The disturbance amplification mechanism is explained in terms of thermal anomalies which move through the loop with the material motion of the fluid. Since the heating and buoyancy generation processes are in phase in the heated, descending leg, a thermal anomaly can amplify as it flows through that leg. As the anomaly moves through the ascending leg, it initiates a subsequent anomaly of opposite sign in the descending leg. The result is an oscillating flow which, under appropriate conditions, can amplify.
The excitation of Tollmien-Schlichting waves in low subsonic boundary layers by free-stream sound waves
Authors: Tam Christopher K. W.
Published: April 2006

The excitation of Tollmien-Schlichting waves in low subsonic flat-plate boundary layers by sound is investigated theoretically. The problem is formulated mathematically as an inhomogeneous boundary-value problem which is then solved by a Green's-function technique. It is found that the amplitude of the excited Tollmien-Schlichting wave satisfies an inhomogeneous first-order differential equation. The calculated wave amplitude according to this equation exhibits spatial oscillations in the region ahead of the lower branch neutral stable point of the boundary layer. This characteristic feature resembles that observed experimentally by Shapiro (1977). The theoretical value of the coupling constant between incident sound wave and excited Tollmien-Schlichting wave agrees favourably with measured data. Other predictions of the theory also seem to compare well with available experimental measurements.
Axisymmetric bubble or drop in a uniform flow
Authors: Miksis Michael , Vanden-Broeck Jean-Marc , Keller Joseph B.
Published: April 2006

The deformation of an axisymmetric bubble or drop in a uniform flow of constant velocity U is computed numerically. The flow is assumed to be inviscid and incompressible. The problem is formulated as a nonlinear integrodifferential system of equations for the bubble surface and for the potential function on the surface. These equations are discretized and the resulting algebraic system is solved by Newton's method. For U = 0 the bubble is a sphere. The results show that as U increases the bubble becomes oblate, spreading out in the direction normal to the flow and contracting in the direction of the flow. Then the poles get pushed in and ultimately they touch each other. The results also show that there is a maximum value of the Weber number above which there is no steady axially symmetric bubble. This value is somewhat smaller than the approximate value obtained by Moore (1965) but close to that found by El Sawi (1974). We also compute the added mass, the drag on the bubble, and its terminal velocity in a gravitational field, for large Reynolds numbers.
The stability of spatially periodic flows
Authors: Beaumont D. N.
Published: April 2006

The stability characteristics for spatially periodic parallel flows of an incompressible fluid (both inviscid and viscous) are studied. A general formula for the determination of the stability characteristics of periodic flows to long waves is obtained, and applied to approximate numerically the stability curves for the sinusoidal velocity profile. The neutral curve for the sinusoidal velocity profile is obtained analytically. The stability of two broken-line velocity profiles in an inviscid fluid is studied and the results are used to describe the overall pattern for the sinusoidal velocity profile in the case of long waves. In an inviscid fluid it is found that all periodic flows (other than the trivial flow in which the basic velocity is constant) are unstable to long waves with a value of the phase speed determined by simple integrals of the basic flow. In a viscous fluid it is found that the sinusoidal velocity profile is very unstable with the inviscid solution being a good approximation to the solution of the viscous problem when the value of the Reynolds number is greater than about 20.
Array measurements of atmospheric pressure fluctuations above surface gravity waves
Authors: Snyder R. L. , Dobson F. W. , Elliott J. A. , Long R. B.
Published: April 2006

A joint experiment to study microscale fluctuations of atmospheric pressure above surface gravity waves was conducted in the Bight of Abaco, Bahamas, during November and December 1974. Field hardware included a three-dimensional array of six wave sensors and seven air-pressure sensors, one of which was mounted on a wave follower. The primary objectives of the study were to resolve differences in previous field measurements by Dobson (1971), Elliott (1972b) and Snyder (1974), and to estimate the vertical profile of wave-induced pressure and the corresponding input of energy and momentum to the wave field.

Analysis of a pre-experiment intercalibration of instruments and of 30 h of field data partially removes the discrepancy between the previous measurements of the wave-induced component of the pressure and gives a consistent picture of the profile of this pressure over a limited range of dimensionless height and wind speed. Over this range the pressure decays approximately exponentially without change of phase; the decay is slightly less steep than predicted by potential theory. The corresponding momentum transfer is positive for wind speeds exceeding the phase speed. Extrapolation of present results to higher frequencies suggests that the total transfer is a significant fraction of the wind stress (0·1 to 1·0, depending on dimensionless fetch).

Analysis of the turbulent component of the atmospheric pressure shows that the ‘intrinsic’ downwind coherence scale is typically an order-of-magnitude greater than the crosswind scale, consistent with a ‘frozen’ turbulence hypothesis. These and earlier data of Priestley (1965) and Elliott (1972c) suggest a horizontally isotropic ‘intrinsic’ turbulent pressure spectrum which decays ask−νwherekis the (horizontal) wave-number and ν is typically −2 to −3; estimates of this spectrum are computed for the present data. The implications of these findings for Phillips’ (1957) theory of wave growth are examined.
Low-Prandtl-number convection in a layer heated from below
Authors: Clever R. M. , Busse F. H.
Published: April 2006

Steady solutions in the form of two-dimensional rolls are obtained numerically for convection in a horizontal layer of a low-Prandtl-number fluid heated from below. Prandtl numbers in the range 0·001 [les ] P [les ] 0·71 are investigated for Rayleigh numbers between the critical value, R = 1708, and R = 20,000 in the case of rigid boundaries. The calculations reveal that the convective heat transport is relatively independent of the Prandtl number at Rayleigh numbers greater than a finite critical value R2 of the order of 5 × 103. At R = 10,000 the convective heat transport varies by only about 30% for Prandtl numbers in the range investigated. As the Rayleigh number is increased above the critical value R2, the streamlines of the convection flow become circular, independent of the horizontal wavelength as long as the latter is larger than or about equal to twice the height of the layer.
The instability of the ocean to Langmuir circulations
Authors: Leibovich S. , Paolucci S.
Published: April 2006

It has been proposed that Langmuir circulations arise as an instability of the equations describing the Eulerian-mean flow in bodies of water supporting surface waves and subject to an applied wind stress. In infinitely deep density-stratified water, the solution of an appropriate initial-value problem is a unidirectional, time-dependent current. The stability of this current to two-dimensional (roll) disturbances is investigated by an energy analysis and by linear theory. It is found that the energy stability estimates and linear stability limits are very close, showing that subcritical instability, if it occurs, is limited to a very narrow region in parameter space. According to the present results, conditions typically occurring in the ocean are highly unstable to the Langmuir circulation instability.
The nonlinear dynamics of baroclinic wave ensembles
Authors: Pedlosky Joseph
Published: April 2006

A theory is developed to describe the weakly nonlinear dynamics which applies in the simultaneous presence of several, long, baroclinic waves. The geometry is flat (i.e. β = 0) and dissipation is modelled by Ekman friction in the context of the quasi-geostrophic two-layer model. Three main problems are discussed.

For free, unstable waves it is shown that the wave which is realized in finite amplitude is not the linearly most unstable wave. Rather a longer wave, capable of achieving the single largest steady amplitude, is favoured in the competition for the potential energy of the basic state. This result is shown necessary if the end state is steady and numerous numerical calculations indicate the pre-eminence of the same wave if the final state is vacillatory. The notion of conjugate waves, capable of identical final amplitude, is also discussed.

If the free waves are subject to time-varying supercriticality so that intervals of stability ensue, the response is asymmetric over the period of the forcing. Sufficiently rapid ‘seasonal’ forcing leads to long-term aperiodic response.

If each wave in the spectrum is directly forced a wave hysteresis phenomenon occurs. Sudden jumps in the wave amplitude at critical values of the forcing are intrinsic to the wave response. Again, sufficiently rapid wave forcing produces an aperiodic response.

The forced wave problem exhibits multiple equilibria. Each solution branch corresponds to a different dominant wave. The determination of the realized branch depends on the relative stability criteria developed for the free waves.
Some Hele Shaw flows with time-dependent free boundaries
Authors: Richardson S.
Published: April 2006

We consider a blob of Newtonian fluid sandwiched in the narrow gap between two plane parallel surfaces. At some initial instant, its plan-view occupies a given, simply connected domain, and its growth as further fluid is injected at a number of injection points in its interior is to be determined. It is shown that certain functionals of the domain of a purely geometric character, infinite in number, evolve in a predictable manner, and that these may be exploited in some cases of interest to yield a complete description of the motion.

By invoking images, these results may be used to solve certain problems involving the growth of a blob in a gap containing barriers. Injection at a point in a half-plane bounded by a straight line, with an initially empty gap, is shown to lead to a blob whose outline is part of an elliptic lemniscate of Booth for which there is a simple geometrical construction. Injection into a quarter-plane is also considered in some detail when conditions are such that the image domain involved is simply connected.
On a generalization of Kaden's problem
Authors: Pullin D. I. , Phillips W. R. C.
Published: April 2006

Kaden's problem of the roll-up of an initially planar semi-infinite vortex sheet with a parabolic distribution of circulation is extended to include vortex sheets exhibiting a general power law circulation distribution, resulting in the presence of a power law, and in one case a logarithmic-like, velocity-field singularity. Both semi-infinite and infinite initially plane sheets with this property are considered and the form of their roll-up in the similarity plane, into single and double-branched spirals respectively, is obtained numerically. Estimates of the Betz constant obtained from the solutions are found to be significantly different from values predicted by the Betz approximation.
On the coherent structure of the axisymmetric mixing layer: a flow-visualization study
Authors: Hussain A. K. M. F. , Clark A. R.
Published: April 2006

In an effort to resolve some controversies regarding the turbulent mixing-layer structure, the near field of a large (18 cm diameter) air jet has been investigated for the jet exit speed of 30 m s−1. The smoke-laden axisymmetric mixing layer has been illuminated by a thin sheet of laser light in an azimuthal plane passing through the jet axis. High-speed visualization films of the mixing layer in the region of its self-preservation (of which a few picture sequences depicting space-time evolutions of the structure of the layer are presented) reveal that most of the time the mixing layer is in a state of disorganization, consisting of relatively smaller scale, random and diffuse turbulent motions; only occasionally are organized distinct large-scale coherent structures formed. The survival distances of the large-scale structures are found to be comparable to their average sizes. The survival time of these structures is about one ‘turnover’ time, each being roughly about five times the local characteristic time scale of the mixing layer. It is seen that tearing is as dominant a mode of large-scale interaction as pairing is; large-scale structures are continually sheared and typically fragmented due to a segment on the high-speed side being torn and swept away from the slower-moving outer portion. Evolution of the large structures occur not primarily through complete pairing as widely believed but quite frequently through ‘fractional pairing’ between segments which have been torn from different upstream large-scale coherent structures or through ‘partial pairing’ when one structure captures only a part of another. The movies show that along with entrainment of non-vortical ambient fluid, radially outward ejection of vortical fluid into the ambient is an important aspect of jet mixing. From aligned displays of ciné film frame sequences, space-time trajectories of identifiable vortical fluid elements have been traced. The convection velocity variation across the shear layer and even the overall structure convection velocity measured from these trajectories agree with those determined from the wave-number-celerity spectra, obtained from double-Fourier transformation of longitudinal velocity space-time correlation measurements with hot-wires.

The visualization films do not bear out the two-street vortex ring model recently propounded by Lau. Based on our observations, we propose that tearing, ‘slippage’ and fractional and partial pairings are responsible for the observed radial variation of structure passage frequency, and the causes of the different coherent structures educed by Bruun on the high- and low-speed sides of the mixing layer and for Yule's failure in educing a coherent structure on the low-speed side of the layer.
The interaction between waves and a turbulent current: waves propagating with the current
Authors: Kemp P. H. , Simons R. R.
Published: April 2006

This paper describes an experimental programme carried out in a laboratory channel with rough and smooth beds, to investigate the interaction between gravity waves and a turbulent current. In particular, changes induced in the mean-velocity profiles, turbulent fluctuations, bed shear stresses and wave attenuation rates are considered for a range of wave heights, keeping the wave period constant. The smooth-boundary tests were carried out as a necessary preliminary to the more-realistic rough-boundary condition.

A directionally sensitive laser anemometer was used to measure horizontal, vertical, and 45° velocity components in the oscillating fluid, and an on-line minicomputer was programmed to produce ensemble averages of velocities, Reynolds stresses and wave-elevation data. The cycle was sampled at 200 separate phase positions, with 180 observations at each position. Measurements were made at up to 30 points in the vertical.

Preliminary tests were carried out on the unidirectional current and on the waves alone. These show that mean-velocity profiles and turbulence parameters of the current agree satisfactorily with previous experiments, and that the waves are approximated closely by Stokes’ second-order theory.

For combined wave and current tests, mean-velocity profiles are generally found to differ from those suggested by a linear superposition of wave and current velocities, a change in boundary-layer thickness being indicated. However, shear stresses at the smooth boundary are found to be described by such a linear addition.
Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity
Authors: Clavin P. , Williams F. A.
Published: April 2006

To study effects of flow inhomogeneities on the dynamics of laminar flamelets in turbulent flames, with account taken of influences of the gas expansion produced by heat release, a previously developed theory of premixed flames in turbulent flows, that was based on a diffusive-thermal model in which thermal expansion was neglected, and that applied to turbulence having scales large compared with the laminar flame-thickness, is extended by eliminating the hypothesis of negligible expansion and by adding the postulate of weak-intensity turbulence. The consideration of thermal expansion motivates the formal introduction of multiple-scale methods, which should be useful in subsequent investigations. Although the hydrodynamic-instability mechanism of Landau is not considered, no restriction is imposed on the density change across the flame front, and the additional transverse convection correspondingly induced by the tilted front is described. By allowing the heat-to-reactant diffusivity ratio to differ slightly from unity, clarification is achieved of effects of phenomena such as flame stretch and the flame-relaxation mechanism traceable to transverse diffusive processes associated with flame-front curvature. By carrying the analysis to second order in the ratio of the laminar flame thickness to the turbulence scale, an equation for evolution of the flame front is derived, containing influences of transverse convection, flame relaxation and stretch. This equation explains anomalies recently observed at low frequencies in experimental data on power spectra of velocity fluctuations in turbulent flames. It also shows that, concerning the diffusive-stability properties of the laminar flame, the density change across the flame thickness produces a shift of the stability limits from those obtained in the purely diffusive-thermal model. At this second order, the turbulent correction to the flame speed involves only the mean area increase produced by wrinkling. The analysis is carried to the fourth order to demonstrate the mean-stretch and mean-curvature effects on the flame speed that occur if the diffusivity ratio differs from unity.
Elastic jumps on fluid-filled elastic tubes
Authors: Cowley S. J.
Published: April 2006

This paper is concerned with fluid flows through membranous elastic tubes. The tubes are assumed to be either untethered (except at the ends), or to be tethered by axial forces that prevent all axial motion of the tube.

First we verify, for axisymmetric deformations that vary slowly in the axial direction, that the elastic balance of the tube can be expressed in terms of a ‘tube law’. In the case of the tethered tubes, the tube law takes the widely used form of a pressure/area relation for both steady and unsteady deformations. However, for untethered tubes, the tube law will generally be time-dependent if the deformations are unsteady. Conditions are then derived between the up- and downstream flows of a turbulent elastic jump. Although it is necessary for the elastic balance to be described by a tube law far up- and far downstream of the jump, we do not assume that the tube law is valid inside the jump. The conditions we derive are believed to hold for both collapsed and expanded tubes.

The theory has applications in describing fluid flows within, for example, the airways, blood vessels and the urethra.
Direct numerical simulation of laminar and turbulent Bénard convection
Authors: Grötzbach Günther
Published: April 2006

The TURBIT-3 computer code has been used for the direct numerical simulation of Bénard convection in an infinite plane channel filled with air. The method is based on the three-dimensional non-steady-state equations for the conservation of mass, momentum and enthalpy. Subgrid-scale models of turbulence are not required, as calculations with different grids show that the spatial resolution of grids with about 322 × 16 nodes provides sufficient accuracy for Rayleigh numbers up to Ra = 3·8 × 105. Hence this simulation model contains no tuning parameters.

The simulations start from nearly random initial conditions. This has been found to be essential for calculating flow patterns and statistical data insensitive to grid parameters and agreeing with experimental experience. The numerical results show the theoretically predicted ‘skewed varicose’ instability at Ra = 4000. Warm and cold ‘blobs’ are identified as causing temperature-gradient reversals for all the high Rayleigh numbers under consideration. The calculated wavelengths and the corresponding flow regimes observed in the transition range confirm the stability maps determined theoretically. In the turbulent range the wavelengths agree qualitatively with low-aspect-ratio experiments. Accordingly, the Nusselt numbers lie at the upper end of the scatter band of experimental data, as these also depend on the aspect ratio. Appropriately normalized, the velocity and temperature fluctuation peaks are independent of the Rayleigh number. The vertical profiles agree largely with experimental data and, especially in case of temperature statistics, exhibit comparable or less scatter.
Mass transfer between a plane surface and an impinging turbulent jet: the influence of surface-pressure fluctuations
Authors: Kataoka K. , Kamiyama Y. , Hashimoto S. , Komai T.
Published: April 2006

Local measurement of the mass-transfer rate and velocity gradient when an axisymmetric jet impinges on a flat plate was carried out using an electrochemical technique. Local measurement of the surface pressure on the flat plate was carried out separately using piezoelectric pressure transducers. The stagnation-point mass-transfer coefficient reaches a maximum when the flat plate is placed at 6 nozzle diameters from a convergent nozzle. It has been confirmed that the mass transfer to the flat plate for a high Schmidt number is greatly enhanced owing to the velocity-gradient disturbances in the wall region of the boundary layer, while the momentum transfer is insensitive to such disturbances. The relative intensity of the velocity-gradient fluctuations on the wall has an extremely large value at and near to the stagnation point, and decreases downstream, approaching a large constant value.

These velocity-gradient disturbances are not due to the usual interaction of Reynolds stress with the shear stress of the mean flow, but are due to the interaction with the surface-pressure fluctuations converted from the velocity fluctuations of the oncoming jet.

The three co-ordinate dimensions of large-scale eddies are calculated from the auto- and spatial correlations of the surface-pressure fluctuations. It is considered that such large-scale eddies play an important role in the production of a velocity-gradient disturbance in the wall region of the boundary layer from the velocity turbulence of the approaching jet.
Capillary displacement and percolation in porous media
Authors: Chandler Richard , Koplik Joel , Lerman Kenneth , Willemsen Jorge F.
Published: April 2006

We consider capillary displacement of immiscible fluids in porous media in the limit of vanishing flow rate. The motion is represented as a stepwise Monte Carlo process on a finite two-dimensional random lattice, where at each step the fluid interface moves through the lattice link where the displacing force is largest. The displacement process exhibits considerable fingering and trapping of displaced phase at all length scales, leading to high residual retention of the displaced phase. Many features of our results are well described by percolation-theory concepts. In particular, we find a residual volume fraction of displaced phase which depends strongly on the sample size, but weakly or not at all on the co-ordination number and microscopic-size distribution of the lattice elements.
An experimental study of pressure fluctuations on fixed and oscillating square-section cylinders
Authors: Bearman P. W. , Obasaju E. D.
Published: April 2006

Measurements are presented of the pressure fluctuations acting on a stationary squaresection cylinder, with the front face normal to the flow, and one forced to oscillate, transverse to a flow, at amplitudes up to 25% of the length of a side. The range of reduced velocities investigated, 4–13, includes the vortex lock-in regime. At lock-in the amplification of the coefficient of fluctuating lift is found to be much less than that found for a circular cylinder. The variation of the phase angle, between lift and displacement, is also different from that measured on a circular cylinder, and vortex-induced oscillations are possible only at the high-reduced-velocity end of the lock-in range. At reduced velocities sufficiently far below lock-in the natural vortex-shedding mode is suppressed and vortices are found to form over the side faces at the body frequency. Intermittent reattachment occurs over the side faces and, for an amplitude of oscillation equal to 10% of the length of a side face, the time-mean drag coefficient can be reduced to 60% of its fixed-cylinder value.
Bifurcation in steady laminar flow through curved tubes
Authors: Nandakumar K. , Masliyah Jacob H.
Published: April 2006

The occurrence of dual solutions in curved ducts is investigated through a numerical solution of the Navier-Stokes equations in a bipolar-toroidal co-ordinate system. With the shape of duct being the region formed by the natural co-ordinate surfaces, it was possible to alter the duct geometry gradually and preserve the prevailing form of the velocity field, in a manner suggested by Benjamin (1978).

In addition to the Dean number Dn = Re/Rc½, a geometrical parameter that defines the shape of the duct was also varied systematically to study the bifurcation of a two-vortex solution into a two- and four-vortex solution. Dual solutions have been found for all geometrical shapes investigated here. Of particular interest are the shapes of a full circle and a semicircle with a curved outer wall.
Fluid dynamical aspects of the levitation-melting process
Authors: Sneyd A. D. , Moffatt H. K.
Published: April 2006

When a piece of metal is placed above a coil carrying a high frequency current, the induced surface currents in the metal can provide a Lorentz force which can support it against gravity; at the same time the heat produced by Joule dissipation can melt the metal. This is the process of ‘levitation melting’, which is a well-established technique in fundamental work in physical and chemical metallurgy. Most theoretical studies of magnetic levitation have dealt only with solid conductors and so have a voided the interesting questions of interaction between the free surface, the magnetic field and the internal flow. These fluid dynamical aspects of the process are studied in this paper.

A particular configuration that is studied in detail is a cylinder levitated by two equal parallel currents in phase; this is conceived as part of a toroidal configuration which avoids a difficulty of conventional configurations, viz the leakage of fluid through the ‘magnetic hole’ at a point on the metal surface where the surface tangential magnetic field vanishes. The equilibrium and stability of the solid circular cylinder is first considered; then the dynamics of the surface film when melting begins; then the equilibrium shape of the fully melted body (analysed by means of a general variational principle proved in § 5); and finally the dynamics of the interior flow, which, as argued in § 2, is likely to be turbulent when the levitated mass is of the order of a few grams or greater.
Phase-distribution mechanisms in turbulent low-quality two-phase flow in a circular pipe
Authors: Drew D. A. , Lahey R. T.
Published: April 2006

The radial distribution of the volumetric vapour (or void) fraction in steady, fully developed turbulent two-phase flow is described for vertical low-quality bubbly flows in a circular pipe. The analysis is based on the phasic equations of conservation of momentum in the axial and radial directions. Mixing-length theory is used to model the turbulent stresses in the continuous phase. The predicted flow structure shows three distinct regions. The ‘outer’ region, that is, the region away from the wall and the centre-line, has a uniform void distribution. For upflow, a bubble layer is predicted near the wall, while for downflow, vapour coring is predicted, with a peak in void fraction at the centre-line. These predictions are in agreement with observed void profiles.
General theory for the creeping motion of a finite sphere along the axis of a circular orifice
Authors: Dagan Z. , Weinbaum S. , Pfeffer R.
Published: April 2006

This paper presents the first infinite-series solutions to the creeping-flow equations for the axisymmetric motion of a sphere of arbitrary size towards an orifice whose diameter is either larger or smaller than the sphere. To obtain the solution the flow field is partitioned in the plane of the opening, and for the flow to the left and right of the fluid interface separate solutions are developed that satisfy the viscous-flow boundary conditions in each region and unknown functions for the axial and radial velocity components in the plane of the opening. The continuity of the fluid stress tensor at the matching interface leads to a set of dual integral equations which are solved analytically to determine the unknown functions for the velocity components in the matching plane. A boundary collocation technique is used to satisfy the no-slip boundary conditions on the surface of the sphere.

The accuracy and convergence of the present solution is tested by detailed numerical comparison with the exact bipolar co-ordinate solutions of Brenner (1961) for the drag on a sphere translating perpendicular to an infinite plane wall up to a distance of 0·1 sphere radii and is found to be in agreement to five significant digits. The converged-series collocation solutions are presented for the sphere in motion in quiescent fluid or for flow past a rigidly held sphere positioned axisymmetrically near a fixed orifice. Solutions are also presented for the zero-drag velocity of a neutrally buoyant sphere in a flow through an orifice, and the pressure–volume flow relation for a ball-valve geometry.
The lateral wave at a depth discontinuity in the ocean and its relevance to tsunami propagation
Authors: King D. R. , LeBlond P. H.
Published: April 2006

The theory of lateral waves is reviewed in the context of long surface gravity waves and is used to interpret the results of experiments performed in a wave tank to simulate tsunami propagation following a disturbance on a continental shelf. It is suggested that since the lateral wave precedes the direct wave at coastal stations its detection might prove useful in tsunami warning systems.
Internal-wave interactions in the induced-diffusion approximation
Authors: Meiss James D. , Watson Kenneth M.
Published: April 2006

Dynamical equations for the interaction of high-wavenumber, high-frequency internal waves with a prescribed, linear, large-scale internal-wave field are obtained from the Boussinesq–Euler equations. The relationship of these ‘induced-diffusion’ interactions to the Taylor–Goldstein equation is discussed. Exact equations are derived in the induced-diffusion limit of McComas & Bretherton (1977) for the evolution of the first and second moments of the small-scale flow when the large-scale flow is assumed random. Estimates of corrections to the induced-diffusion approximation for the Garrett–Munk internal-wave model indicate the domain of applicability of these equations. Computations of the autocorrelation function and action transport in wavenumber and physical space are presented. Severe limitations are found on the applicability of two-time perturbation theory and the resonant-interaction approximation. The high transfer rates found by McComas & Bretherton in the induceddiffusion regime are reduced significantly in the present calculations.
Ageostrophic instability of ocean currents
Authors: Griffiths R. W. , Killworth Peter D. , Stern Melvin E.
Published: April 2006

We investigate the stability of gravity currents, in a rotating system, that are infinitely long and uniform in the direction of flow and for which the current depth vanishes on both sides of the flow. Thus, owing to the role of the Earth's rotation in restraining horizontal motions, the currents are bounded on both sides by free streamlines, or sharp density fronts. A model is used in which only one layer of fluid is dynamically important, with a second layer being infinitely deep and passive. The analysis includes the influence of vanishing layer depth and large inertial effects near the edges of the current, and shows that such currents are always unstable to linearized perturbations (except possibly in very special cases), even when there is no extremum (or gradient) in the potential vorticity profile. Hence the established Rayleigh condition for instability in quasi-geostrophic models, where inertial effects are assumed to be vanishingly small relative to Coriolis effects, does not apply. The instability does not depend upon the vorticity profile but instead relies upon a coupling of the two free streamlines. The waves permit the release of both kinetic and potential energy from the mean flow. They can have rapid growth rates, the e-folding time for waves on a current with zero potential vorticity, for example, being close to one-half of a rotation period. Though they are not discussed here, there are other unstable solutions to this same model when the potential vorticity varies monotonically across the stream, verifying that flows involving a sharp density front are much more likely to be unstable than flows with a small ratio of inertial to Coriolis forces.

Experiments with a current of buoyant fluid at the free surface of a lower layer are described, and the observations are compared with the computed mode of maximum growth rate for a flow with a uniform potential vorticity. The current is observed to be always unstable, but, contrary to the predicted behaviour of the one-layer coupled mode, the dominant length scale of growing disturbances is independent of current width. On the other hand, the structure of the observed disturbances does vary: when the current is sufficiently narrow compared with the Rossby deformation radius (and the lower layer is deep) disturbances have the structure predicted by our one-layer model. The flow then breaks up into a chain of anticyclonic eddies. When the current is wide, unstable waves appear to grow independently on each edge of the current and, at large amplitude, form both anticyclonic and cyclonic eddies in the two-layer fluid. This behaviour is attributed to another unstable mode.
Mathematical models for coating processes
Authors: Savage M. D.
Published: April 2006

The flow is considered of a Newtonian fluid, of viscosity η and surface tension T, in the narrow gap between a pair of rollers of radii R1 and R2, whose peripheral speeds are constant and equal to U1 and U2 respectively. The objective is to determine the coating thickness h1∞ on the upper roller as a function of the non-dimensional parameters H0/R, ηU/T and U1/U2, where H0 is the minimum gap thickness, U = ½(U1 + U2), and 2R−1 = R1−1 + R2−1.

Using lubrication theory to provide an adequate description of the fluid flow, two mathematical models are derived whose essential difference lies in the specification of the boundary conditions. In the separation model it is assumed that the pressure distribution will terminate at a position which is both a stagnation point and a point of separation, whereas the Reynolds model incorporates the classical Reynolds conditions. In each case, theoretical predictions for the non-dimensional coating thickness, h1∞/H0 as a function of U1/U2 are found to compare well with experiment. However, theory does suggest that the two models are applicable to different and complementary regions of parameter space, and hence together they may form a basis for further investigations into the various features of coating processes.