bluuebunny/crossref_metadata_2025_split huggingface dataset:
Linear stability of natural convection in spherical annuli
Authors: Gardner David R. , Douglass Rod W. , Trogdon Steven A. 
Published: April 2006

Natural convection in a Boussinesq fluid filling the narrow gap between two isothermal, concentric spheres at different temperatures depends strongly on radius ratio, Prandtl number, and Grashof number. When the inner sphere has a higher temperature than the outer sphere, and for fixed values of radius ratio and Prandtl number, experiments show the flow to be steady and axisymmetric for sufficiently small Grashof number and quasi-periodic and axisymmetric for Grashof numbers greater than a critical value. It is our hypothesis that the observed transition is a flow bifurcation. This hypothesis is examined by solving an appropriate eigenvalue problem. The critical Grashof number, critical eigenvalues, and corresponding eigenvectors are obtained as functions of the radius ratio, Prandtl number, and longitudinal wavenumber. Critical Grashof numbers range from 1.18 × 104 to 2.63 × 103 as Prandtl number Pr increases from zero to 0.7, for radius ratios of 0.900 and 0.950. A transitional Prandtl number Prt exists such that for Pr < Prt the bifurcation is time-periodic and axisymmetric. For Pr > Prt the bifurcation is steady and non-axisymmetric with wavenumber twoA first approximation to the bifurcated flow is obtained using the critical eigenvectors. For Pr < Prt the bifurcation sets in as a cluster of relatively strong cells with alternating directions of rotation. The cells remain fixed in location, but pulsate with time. The cluster moves toward the top of the annulus as Pr increases toward Prt. An important feature of the non-axisymmetric bifurcation for Pr > Prt is a set of four cells located at each pole of the annulus in which the radial velocity alternates direction in moving from any one cell to an adjacent one. For fixed radius ratio, the average Nusselt number at criticality varies only slightly with Prandtl number.
Flame balls stabilized by suspension in fluid with a steady linear ambient velocity distribution
Authors: Buckmaster J. , Joulin G. 
Published: April 2006

The ignition of lean H2/air mixtures under microgravity (μg) conditions can lead to the formation of spherical premixed flames (flame balls) with small Péclet number (Pe). A central question concerning these structures is the existence of appropriate stationary stable solutions of the combustion equations. In this paper we examine an individual flame ball that is suspended in a fluid whose velocity far from the flame is steady and varies linearly in space. Detailed results are obtained for simple shear flows and simple straining flows, both axisymmetric and plane.Convection enhances the flux of heat from the flame and the flux of mixture to the flame, but because the Lewis number (Le) is less than unity the relative impact on the former is greater than on the latter. Consequently, there is a net loss of energy from the flame to the far field, and if large enough this will quench the flame. For values of shear or strain less than the quenching value there are two possible stationary solutions, but one of these is unstable to spherically symmetric disturbances of the flame ball. The radius of the other solution is unbounded as Pe goes to zero. Examination of a class of three-dimensional disturbances reveals no additional instability when the energy losses are due only to convection, but sufficiently large flame balls are unstable when volumetric heat losses from radiation are accounted for. This last result is in agreement with previous results that have been obtained for zero Pe, albeit with inadequate accounting for the flow field generated by the perturbations.
Short-time Lyapunov exponent analysis and the transition to chaos in Taylor–Couette flow
Authors: Vastano John A. , Moser Robert D. 
Published: April 2006

Short-time Lyapunov exponent analysis is a new approach to the study of the stability properties of unsteady flows. At any instant in time the Lyapunov perturbations are the set of infinitesimal perturbations to a system state that will grow the fastest in the long term. Knowledge of these perturbations can allow one to determine the instability mechanisms producing chaos in the system. This new method should prove useful in a wide variety of chaotic flows. Here it is used to elucidate the physical mechanism driving weakly chaotic Taylor–Couette flow.Three-dimensional, direct numerical simulations of axially periodic Taylor–Couette flow are used to study the transition from quasi-periodicity to chaos. A partial Lyapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. The axial wavelength and the particular quasi-periodic state are chosen to correspond to the most complete experimental studies of this transition. The computational results are consistent with available experimental data, both for the flow characteristics in the quasi-periodic regime and for the Reynolds number at which transition to chaos is observed.The dimension of the chaotic attractor near onset is estimated from the Lyapunov exponent spectrum using the Kaplan–Yorke conjecture. This dimension estimate supports the experimental observation of low-dimensional chaos, but the dimension increases more rapidly away from the transition than is observed in experiments. Reasons for this disparity are given. Short-time Lyapunov exponent analysis is used to show that the chaotic state studied here is caused by a Kelvin–Helmholtz-type instability of the outflow boundary jet of the Taylor vortices.
Velocities and concentrations in oscillatory flow over beds of sediment
Authors: Dick J. E. , Sleath J. F. A. 
Published: April 2006

Measurements are reported of the velocity and concentration distributions both within and above two beds of sediment in oscillatory flow. The experiments were carried out in an oscillatory flow water tunnel, the velocities were measured with a laser-Doppler anemometer and the concentrations of sediment with resistance probes operating through the sidewall of the tunnel. The sediments studied consisted of nylon granules of median diameter 4.0 mm and Perspex of median diameter 0.7 mm. Most of the beds were plane for the tests with the 0.7 mm sediment and rippled for those with the 4 mm sediment.The measured velocity profile could be divided into three regions: a central region in which the amplitude and phase of the velocity increased almost linearly with height and two outer regions in which the variation in velocity with height was much less rapid. It is suggested that at very high sediment transport rates the central region covers almost the entire depth of the moving bed but that at lower transport rates the outer regions are more significant.The effect of sediment movement on the velocity distribution above the bed is very marked. Bed roughness length is increased and the velocity amplitude falls off more slowly with height than for fixed beds under similar conditions.Within the bed the shear stress increases almost linearly with depth. Apparent viscosity also increases steadily with depth below the surface of the bed.The measurements of concentrations are in good agreement with the results of other investigators in the region above the moving bed. Within the bed the time-mean concentration rises steadily, with distance below the initial bed surface, towards the limiting value for a stationary bed. The concentration record also shows a fluctuation during the course of the cycle at twice the frequency of the fundamental oscillation. The amplitude of this fluctuation in concentration decreases with depth below the initial bed level. The phase variation with height is close to that of zero velocity gradient, within the moving bed.
The axisymmetric thermocapillary motion of a fluid particle in a tube
Authors: Chen Jinnan , Dagan Zeev , Maldarelli Charles 
Published: April 2006

The thermocapillary migration of a fluid particle in a tube, owing to an imposed axial temperature gradient, is studied theoretically for the case of steady, axisymmetric, creeping, translation in the absence of thermal convection and fluid particle distortion from sphericity, and for an insulated tube. Formulated with these assumptions, the migration is a linear Stokes flow which is separable into two fixed-fluid particle flow idealizations. One is the fluid motion in a quiescent continuous phase, owing only to the thermocapillary surface stress. This stress causes fluid streaming which exerts a lift force on the fluid particle in the direction of the warmer fluid described by a lift coefficient. The second idealization is uniform flow in the absence of thermocapillary forces. The force on the fluid particle owing to this flow represents the hydrodynamic resistance to the forward motion of the fluid particle in the presence of the tube wall, and is described in terms of a drag coefficient. Numerical solutions for the lift and drag coefficients are obtained by a boundary collocation technique.The migration velocity in the tube relative to that under identical conditions in an infinite medium is computed from the ratio of the lift and drag coefficients. The calculations show that for a fixed ratio of the sphere to the tube diameter, as the conductivity of the fluid particle phase decreases relative to that of the continuous phase, a greater proportion of energy is conducted through the gap between the insulated tube wall and the fluid particle. This conduction pattern creates a larger surface temperature gradient, and causes the relative migration velocity to increase. The enhancement in migration for decreasing fluid particle conductivity at a fixed ratio of the sphere to the tube diameter becomes more pronounced as the later ratio increases and the surface gradient intensifies. However, as the gap distance between the sphere and the tube decreases, hydrodynamic retarding forces develop, and these forces are overriding in the sense that the relative migration velocity in the tube decreases monotonically from the value of one as the gap thickness decreases, and therefore the migration velocity in the tube never exceeds the value in an infinite medium.
Elliptic jets. Part 2. Dynamics of coherent structures: pairing
Authors: Husain Hyder S. , Hussain Fazle 
Published: April 2006

The dynamics of coherent structure interactions, in particular the jet column mode of vortex pairing, in the near field of an elliptic jet have been investigated using hotwire measurements and flow visualization. A 2:1 aspect-ratio jet with an initially laminar boundary layer and aconstantmomentum thickness all around the nozzle exit perimeter is used for this study. While detailed hot-wire measurements were made in air at a Reynolds numberReDe(≡UeDe/ν) = 3.2 × 104, flow visualization was performed in water at a lowerReDe= 1.7 × 104; hereUeis the exit speed andDeis the equivalent diameter of the nozzle exit cross-section. Excitation at the stable pairing mode induced successive pairings to occur periodically at the same location, allowing phase-locked measurements using a local trigger sensor. Coherent structures were educed at different phases of pairing in the planes of both the major and minor axes. These are compared with corresponding data in a circular jet, educed similarly.Pairing interactions are found to be quite different from those in a circular jet. Owing to non-planar and non-uniform self-induction of elliptical vortical structures and the consequent effect on mutual induction, pairing of elliptic vortices in the jet column does not occur uniformly around the entire perimeter, unlike in a circular jet. Merger occurs only in the initial major-axis plane through an entanglement process, while in the initial minor-axis plane, the trailing vortex rushes through the leading vortex without pairing and then breaks down violently. These motions produce considerably greater entrainment and mixing than in circular or plane jets. From distributions of dynamical properties over the extent of coherent structures, the production mechanism is explained in terms of the longitudinal vortices (orribs) connecting the elliptic structures. Time-average measures and their modification by controlled excitation are also discussed in terms of coherent structure dynamics. A significant space in this paper is devoted to documenting phase-dependent and time-average flow measures; these new results should serve as target data for numerical simulations. Further details are given in Husain (1984).
On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation
Authors: Dussan V. E. B. , Ramé Enrique , Garoff Stephen 
Published: April 2006

Over the past decade and a half, analyses of the dynamics of fluids containing moving contact lines have specified hydrodynamic models of the fluids in a rather small region surrounding the contact lines (referred to as the inner region) which necessarily differ from the usual model. If this were not done, a singularity would have arisen, making it impossible to satisfy the contact-angle boundary condition, a condition that can be important for determining the shape of the fluid interface of the entire body of fluid (the outer region). Unfortunately, the nature of the fluids within the inner region under dynamic conditions has not received appreciable experimental attention. Consequently, the validity of these novel models has yet to be tested.The objective of this experimental investigation is to determine the validity of the expression appearing in the literature for the slope of the fluid interface in the region of overlap between the inner and outer regions, for small capillary number. This in part involves the experimental determination of a constant traditionally evaluated by matching the solutions in the inner and outer regions. Establishing the correctness of this expression would justify its use as a boundary condition for the shape of the fluid interface in the outer region, thus eliminating the need to analyse the dynamics of the fluid in the inner region.Our experiments consisted of immersing a glass tube, tilted at an angle to the horizontal, at a constant speed, into a bath of silicone oil. The slope of the air–silicone oil interface was measured at distances from the contact line ranging between O.O13a. and O.17a, where a denotes the capillary length, the lengthscale of the outer region (1511 μm). Experiments were performed at speeds corresponding to capillary numbers ranging between 2.8 × 10-4 and 8.3 × 10-3. Good agreement is achieved between theory and experiment, with a systematic deviation appearing only at the highest speed. The latter may be a consequence of the inadequacy of the theory at that value of the capillary number.
Electrophoresis of a colloidal sphere along the axis of a circular orifice or a circular disk
Authors: Keh Huan J. , Lien Liang C. 
Published: April 2006

The axisymmetric electrophoretic motion of a dielectric sphere along the axis of an orifice in a large conducting plane or of a conducting disk is considered. The radius of the orifice or the disk may be either larger or smaller than that of the sphere. The assumption of thin electrical double layers at the solid surfaces is employed. To solve the electrostatic and hydrodynamic governing equations both the electric and the flow fields are partitioned at the plane of the orifice or the disk. For each field, separate solutions are developed on both sides of the plane that satisfy the boundary conditions in each region and the unknown functions for the field at the fluid interface. The continuities of the electric current flux and the fluid stress tensor at the matching interface lead to sets of dual integral equations which are solved analytically to determine the unknown functions for the fields at the matching interface. Then, a boundary–collocation technique is used to satisfy the boundary conditions on the surface of the sphere.The numerical solutions for the electrophoretic velocity of the colloidal sphere are presented for various values ofa/banda/d, whereais the particle radius,bis the radius of the orifice or the disk, anddis the distance of the particle centre from the plane of the wall. For the limiting case of electrophoresis of a sphere perpendicular to an infinite plane wall, our results for the boundary effects agree very well with the exact calculations using spherical bipolar coordinates. Interestingly, the electrophoretic velocity of a sphere approaching an orifice of a larger radius increases when the sphere is close to the orifice, and this velocity can be even larger than that for an identical sphere undergoing electrophoresis in an unbounded fluid. If the sphere has a radius larger than that of the orifice, or if the sphere has a smaller radius and is located sufficiently far from the orifice, its electrophoretic mobility will decrease with the increase of the spacing parametera/d. For the electrophoretic motion of a sphere along the axis of and close to a disk of finite radius, the resistance to the particle movement can be stronger than that for an equal sphere undergoing electrophoresis normal to an infinite plane wall at the same value ofa/d. As the particle approaches the disk wall, its mobility decreases steadily and vanishes at the limita/d→ 1. The boundary effects on the particle mobility and the fluid flow pattern in electrophoresis differ significantly from those of the corresponding sedimentation problem with which a comparison is made.
Numerical simulations of the nonlinear kink modes in linearly stable supersonic slip surfaces
Authors: Pedelty Jeffrey A. , Woodward Paul R. 
Published: April 2006

We have performed high-resolution numerical simulations of supersonic slip surfaces to confirm and illuminate earlier analytic nonlinear stability calculations of such structures. This analytic work was in turn inspired by earlier computer simulations reported in Woodward (1985) and Woodward et al. (1987). In particular Artola & Majda (1987) examined the response of a supersonic slip surface to an incident train of small-amplitude nonlinear sound waves. They found analytic solutions which indicate that nonlinear resonance occurs at three angles of incidence which depend upon the Mach number of the relative motion. The two-dimensional simulations described here numerically solve this problem for a Mach-4 flow using the piecewise-parabolic method (Colella & Woodward 1984; Woodward & Colella 1984). The simulations show that sound waves incident at a predicted resonance angle excite nonlinear behaviour in the slip surface. At these angles the amplitude of the reflected waves is much greater than the incident wave amplitude (i.e. a shock forms). The observed resonance is fairly broad, but the resonance narrows as the strength of the incident waves is reduced.The nature of the nonlinear kink modes observed in the simulations is similar to that discussed by Artola & Majda. Most of the modes move in either direction with speeds near the predicted value. Speeds of other than this value are observed, but the disagreement is not serious in view of the strongly nonlinear behaviour seen in the simulations but not treated in the analytic work. The stationary modes seen in the analytic results are perhaps observed as transient structures. They may eventually dominate the flow at late times (Woodward et al. 1987).The role of the kink modes in the stability of slab jets is discussed, and it is argued that the stationary modes are more disruptive than the propagating modes.
Vorticity dynamics in an oscillatory flow over a rippled bed
Authors: Blondeaux P. , Vittori G. 
Published: April 2006

In the present paper we determine the oscillatory flow generated by surface gravity waves near a sea bottom covered with large-amplitude ripples. The vorticity equation and Poisson equation for the stream function are solved by means of a numerical approach based on spectral methods and finite-difference approximations. In order to test the numerical algorithm and in particular the numerical scheme used to generate vorticity along the ripple profile, we also perform an asymptotic analysis, which holds as the timettends to zero. The main features of the time development of vorticity are analysed and particular attention is paid to the dynamics of the large vortices generated by flow separation at the ripple crests and along the ripple profile. Some of the results obtained by Longuet-Higgins (1981) are recovered; in particular, the present results show a vortex pair shed from the ripple crest every half-cycle. The determination of flow separation along the ripple profile induced by the pressure gradient and the inclusion of viscous effects allows us to obtain accurate quantitative results and detect some important phenomena never observed before.In particular it is shown that: (i) Whenever a vortex structure moves towards the bottom, a secondary vortex is generated near the ripple profile, which interacts with the primary vortex and causes it to move away from the bottom, (ii) Depending on the values of the parameters, the time development of the free shear layer shed from the ripple crest may produce two or even more vortex structures, (iii) Occasionally vortices generated previously may coalesce with the free shear layer shed from the ripple crest, generating a unique vortex structure.
The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models
Authors: Waugh D. W. , Dritschel D. G. 
Published: April 2006

The linear stability of filaments or strips of ‘potential’ vorticity in a background shear flow is investigated for a class of two-dimensional, inviscid, non-divergent models having a linear inversion relation between stream function and potential vorticity. In general, the potential vorticity is not simply the Laplacian of the stream function – the case which has received the greatest attention historically. More general inversion relationships between stream function and potential vorticity are geophysically motivated and give an impression of how certain classic results, such as the stability of strips of vorticity, hold under more general circumstances.In all models, a strip of potential vorticity is unstable in the absence of a background shear flow. Imposing a shear flow that reverses the total shear across the strip, however, brings about stability, independent of the Green-function inversion operator that links the stream function to the potential vorticity. But, if the Green-function inversion operator has a sufficiently short interaction range, the strip can also be stabilized by shear having the same sense as the shear of the strip. Such stabilization by ‘co-operative’ shear does not occur when the inversion operator is the inverse Laplacian. Nonlinear calculations presented show that there is only slight disruption to the strip for substantially less adverse shear than necessary for linear stability, while for co-operative shear, there is major disruption to the strip. It is significant that the potential vorticity of the imposed flow necessary to create shear of a given value increases dramatically as the interaction range of the inversion operator decreases, making shear stabilization increasingly less likely. This implies an increased propensity for filaments to ‘roll-up’ into small vortices as the interaction range decreases, a finding consistent with many numerical calculations performed using the quasi-geostrophic model.